rfc.vac.dev/assets/js/f464b151.44493889.js

"use strict";(self.webpackChunklogos_docs_template=self.webpackChunklogos_docs_template||[]).push([[6778],{27588:(a,e,t)=>{t.r(e),t.d(e,{assets:()=>i,contentTitle:()=>p,default:()=>o,frontMatter:()=>m,metadata:()=>r,toc:()=>l});var s=t(87462),n=(t(67294),t(3905));const m={title:"LIBP2P-MIX",name:"Libp2p Mix Protocol",status:"raw",category:"Standards Track",editor:"Prem Prathi &lt;prem@status.im&gt;",contributors:"Akshaya Mani &lt;akshaya@status.im&gt;, Daniel Kaiser &lt;danielkaiser@status.im&gt;, Hanno Cornelius &lt;hanno@status.im&gt;"},p=void 0,r={unversionedId:"raw/mix",id:"raw/mix",title:"LIBP2P-MIX",description:"- Status: raw",source:"@site/vac/raw/mix.md",sourceDirName:"raw",slug:"/raw/mix",permalink:"/vac/raw/mix",draft:!1,tags:[],version:"current",frontMatter:{title:"LIBP2P-MIX",name:"Libp2p Mix Protocol",status:"raw",category:"Standards Track",editor:"Prem Prathi &lt;prem@status.im&gt;",contributors:"Akshaya Mani &lt;akshaya@status.im&gt;, Daniel Kaiser &lt;danielkaiser@status.im&gt;, Hanno Cornelius &lt;hanno@status.im&gt;"},sidebar:"defaultSidebar",previous:{title:"LOGOS-CAPABILITY-DISCOVERY",permalink:"/vac/raw/logos-capability-discovery"},next:{title:"NOISE-X3DH-DOUBLE-RATCHET",permalink:"/vac/raw/noise-x3dh-double-ratchet"}},i={},l=[{value:"Abstract",id:"abstract",level:2},{value:"1. Introduction",id:"1-introduction",level:2},{value:"2. Terminology",id:"2-terminology",level:2},{value:"3. Motivation and Background",id:"3-motivation-and-background",level:2},{value:"3.1 Comparison with Tor",id:"31-comparison-with-tor",level:3},{value:"4. Mixing Strategy and Packet Format",id:"4-mixing-strategy-and-packet-format",level:2},{value:"4.1 Mixing Strategy",id:"41-mixing-strategy",level:3},{value:"4.2 Mix Packet Format",id:"42-mix-packet-format",level:3},{value:"5. Protocol Overview",id:"5-protocol-overview",level:2},{value:"5.1 Integration with Origin Protocols",id:"51-integration-with-origin-protocols",level:3},{value:"5.2 Mixify Option",id:"52-mixify-option",level:3},{value:"5.3 Why a Protocol, Not a Transport",id:"53-why-a-protocol-not-a-transport",level:3},{value:"5.4 Protocol Interaction Flow",id:"54-protocol-interaction-flow",level:3},{value:"5.5 Stream Management and Multiplexing",id:"55-stream-management-and-multiplexing",level:3},{value:"6. Pluggable Components",id:"6-pluggable-components",level:2},{value:"6.1 Discovery",id:"61-discovery",level:3},{value:"6.2 Delay Strategy",id:"62-delay-strategy",level:3},{value:"6.3 Spam Protection",id:"63-spam-protection",level:3},{value:"6.4 Cover Traffic",id:"64-cover-traffic",level:3},{value:"6.5 Incentivization",id:"65-incentivization",level:3},{value:"7. Core Mix Protocol Responsibilities",id:"7-core-mix-protocol-responsibilities",level:2},{value:"7.1 Protocol Identifier",id:"71-protocol-identifier",level:3},{value:"7.2 Initiation",id:"72-initiation",level:3},{value:"7.3 Sphinx Packet Receiving and Processing",id:"73-sphinx-packet-receiving-and-processing",level:3},{value:"7.3.1 Intermediary Processing",id:"731-intermediary-processing",level:4},{value:"7.3.2 Exit Processing",id:"732-exit-processing",level:4},{value:"8. Sphinx Packet Format",id:"8-sphinx-packet-format",level:2},{value:"8.1 Packet Structure Overview",id:"81-packet-structure-overview",level:3},{value:"8.2 Cryptographic Primitives",id:"82-cryptographic-primitives",level:3},{value:"8.3 Packet Component Sizes",id:"83-packet-component-sizes",level:3},{value:"8.3.1 Header Field Sizes",id:"831-header-field-sizes",level:4},{value:"8.3.2 Payload Size",id:"832-payload-size",level:4},{value:"8.3.3 Padding and Fragmentation",id:"833-padding-and-fragmentation",level:4},{value:"8.3.4 Anonymity Set Considerations",id:"834-anonymity-set-considerations",level:4},{value:"8.4 Address and Delay Encoding",id:"84-address-and-delay-encoding",level:3},{value:"8.5 Packet Construction",id:"85-packet-construction",level:3},{value:"8.5.1 Inputs",id:"851-inputs",level:4},{value:"8.5.2 Construction Steps",id:"852-construction-steps",level:4},{value:"8.6 Sphinx Packet Handling",id:"86-sphinx-packet-handling",level:3},{value:"8.6.1 Shared Preprocessing",id:"861-shared-preprocessing",level:4},{value:"8.6.2 Node Role Determination",id:"862-node-role-determination",level:4},{value:"8.6.3 Intermediary Processing",id:"863-intermediary-processing",level:4},{value:"8.6.4 Exit Processing",id:"864-exit-processing",level:4},{value:"9. Spam Protection Architecture",id:"9-spam-protection-architecture",level:2},{value:"9.1 Spam Protection Mechanism Requirements",id:"91-spam-protection-mechanism-requirements",level:3},{value:"9.2 Integration Architecture",id:"92-integration-architecture",level:3},{value:"9.2.1 Sender-Generated Proofs",id:"921-sender-generated-proofs",level:4},{value:"9.2.1.1 How It Works",id:"9211-how-it-works",level:5},{value:"9.2.1.2 Advantages",id:"9212-advantages",level:5},{value:"9.2.1.3 Disadvantages",id:"9213-disadvantages",level:5},{value:"9.2.1.4 Impact on Header Size",id:"9214-impact-on-header-size",level:5},{value:"9.2.2 Per-Hop Generated Proofs",id:"922-per-hop-generated-proofs",level:4},{value:"9.2.2.1 How It Works",id:"9221-how-it-works",level:5},{value:"9.2.2.2 Advantages",id:"9222-advantages",level:5},{value:"9.2.2.3 Disadvantages",id:"9223-disadvantages",level:5},{value:"9.2.2.4 Impact on Header Size",id:"9224-impact-on-header-size",level:5},{value:"9.2.3 Comparison",id:"923-comparison",level:4},{value:"9.3 Node Responsibilities",id:"93-node-responsibilities",level:3},{value:"9.3.1 For Sender-Generated Proofs",id:"931-for-sender-generated-proofs",level:4},{value:"9.3.2 For Per-Hop Generated Proofs",id:"932-for-per-hop-generated-proofs",level:4},{value:"9.4 Anonymity and Security Considerations",id:"94-anonymity-and-security-considerations",level:3},{value:"9.5 Recommended Methods",id:"95-recommended-methods",level:3},{value:"9.6 Spam Protection Interface",id:"96-spam-protection-interface",level:3},{value:"9.6.1 Deployment Configuration",id:"961-deployment-configuration",level:4},{value:"9.6.2 Interface Procedures",id:"962-interface-procedures",level:4},{value:"9.6.2.1 Proof Generation",id:"9621-proof-generation",level:5},{value:"9.6.2.2 Proof Verification",id:"9622-proof-verification",level:5},{value:"9.6.3 Integration Points in Sphinx Processing",id:"963-integration-points-in-sphinx-processing",level:4},{value:"9.6.3.1 For Sender-Generated Proofs",id:"9631-for-sender-generated-proofs",level:5},{value:"9.6.3.2 For Per-Hop Generated Proofs",id:"9632-for-per-hop-generated-proofs",level:5},{value:"10. Security Considerations",id:"10-security-considerations",level:2},{value:"10.1 Security Guarantees of the Core Mix Protocol",id:"101-security-guarantees-of-the-core-mix-protocol",level:3},{value:"10.2 Exit Node Trust Model",id:"102-exit-node-trust-model",level:3},{value:"10.2.1 Message Delivery and Origin Trust",id:"1021-message-delivery-and-origin-trust",level:4},{value:"10.2.2 Origin Protocol Trust and Client Role Abuse",id:"1022-origin-protocol-trust-and-client-role-abuse",level:4},{value:"10.3 Destination as Final Hop",id:"103-destination-as-final-hop",level:3},{value:"10.4 Known Protocol Limitations",id:"104-known-protocol-limitations",level:3},{value:"10.4.1 Undetectable Node Misbehavior",id:"1041-undetectable-node-misbehavior",level:4},{value:"10.4.2 No Built-in Retry or Acknowledgment",id:"1042-no-built-in-retry-or-acknowledgment",level:4},{value:"10.4.3 No Sybil Resistance",id:"1043-no-sybil-resistance",level:4},{value:"10.4.4 Vulnerability to Denial-of-Service Attacks",id:"1044-vulnerability-to-denial-of-service-attacks",level:4}],N={toc:l};function o(a){let{components:e,...t}=a;return(0,n.kt)("wrapper",(0,s.Z)({},N,t,{components:e,mdxType:"MDXLayout"}),(0,n.kt)("ul",null,(0,n.kt)("li",{parentName:"ul"},"Status: raw"),(0,n.kt)("li",{parentName:"ul"},"Category: Standards Track"),(0,n.kt)("li",{parentName:"ul"},"Editor: Prem Prathi ","<",(0,n.kt)("a",{parentName:"li",href:"mailto:prem@status.im"},"prem@status.im"),">")),(0,n.kt)("h2",{id:"abstract"},"Abstract"),(0,n.kt)("p",null,"The Mix Protocol defines a decentralized anonymous message routing layer for libp2p networks.\nIt enables sender anonymity by routing each message through a decentralized mix overlay network composed of participating libp2p nodes, known as mix nodes.\nEach message is routed independently in a stateless manner, allowing other libp2p protocols to selectively anonymize messages without modifying their core protocol behavior."),(0,n.kt)("h2",{id:"1-introduction"},"1. Introduction"),(0,n.kt)("p",null,"The Mix Protocol is a custom libp2p protocol that defines a message-layer routing abstraction designed to provide sender anonymity in peer-to-peer systems built on the libp2p stack.\nIt addresses the absence of native anonymity primitives in libp2p by offering a modular, content-agnostic protocol that other libp2p protocols can invoke when anonymity is required."),(0,n.kt)("p",null,"This document describes the design, behavior, and integration of the Mix Protocol within the libp2p architecture.\nRather than replacing or modifying existing libp2p protocols, the Mix Protocol complements them by operating independently of connection state and protocol negotiation.\nIt is intended to be used as an optional anonymity layer that can be selectively applied on a per-message basis."),(0,n.kt)("p",null,"Integration with other libp2p protocols is handled through external interface components","\u2014","the Mix Entry and Exit layers","\u2014","which mediate between these protocols and the Mix Protocol instances.\nThese components allow applications to defer anonymity concerns to the Mix layer without altering their native semantics or transport assumptions."),(0,n.kt)("p",null,"The rest of this document describes the motivation for the protocol, defines relevant terminology, presents the protocol architecture, and explains how the Mix Protocol interoperates with the broader libp2p protocol ecosystem."),(0,n.kt)("h2",{id:"2-terminology"},"2. Terminology"),(0,n.kt)("p",null,'The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT", "SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this document are to be interpreted as described in ',(0,n.kt)("a",{parentName:"p",href:"https://datatracker.ietf.org/doc/html/rfc2119"},"RFC 2119"),"."),(0,n.kt)("p",null,"The following terms are used throughout this specification:"),(0,n.kt)("ul",null,(0,n.kt)("li",{parentName:"ul"},(0,n.kt)("p",{parentName:"li"},(0,n.kt)("strong",{parentName:"p"},"Origin Protocol"),"\nA libp2p protocol (",(0,n.kt)("em",{parentName:"p"},"e.g.,")," Ping, GossipSub) that generates and receives the actual message payload.\nThe origin protocol MUST decide on a per-message basis whether to route the message through the Mix Protocol or not.")),(0,n.kt)("li",{parentName:"ul"},(0,n.kt)("p",{parentName:"li"},(0,n.kt)("strong",{parentName:"p"},"Mix Node"),"\nA libp2p node that supports the Mix Protocol and participates in the mix network.\nA mix node initiates anonymous routing when invoked with a message.\nIt also receives and processes Sphinx packets when selected as a hop in a mix path.")),(0,n.kt)("li",{parentName:"ul"},(0,n.kt)("p",{parentName:"li"},(0,n.kt)("strong",{parentName:"p"},"Mix Path"),"\nA non-repeating sequence of mix nodes through which a Sphinx packet is routed across the mix network.")),(0,n.kt)("li",{parentName:"ul"},(0,n.kt)("p",{parentName:"li"},(0,n.kt)("strong",{parentName:"p"},"Mixify"),"\nA per-message flag set by the origin protocol to indicate that a message should be routed using the Mix Protocol or not.\nOnly messages with mixify set are forwarded to the Mix Entry Layer. Other messages SHOULD be routed using the origin protocol's default behavior.\nThe phrases 'messages to be mixified', 'to mixify a message' and related variants are used informally throughout this document to refer to messages that either have the ",(0,n.kt)("inlineCode",{parentName:"p"},"mixify")," flag set or are selected to have it set.")),(0,n.kt)("li",{parentName:"ul"},(0,n.kt)("p",{parentName:"li"},(0,n.kt)("strong",{parentName:"p"},"Mix Entry Layer"),"\nA component that receives messages to be ",(0,n.kt)("em",{parentName:"p"},"mixified")," from an origin protocol and forwards them to the local Mix Protocol instance.\nThe Entry Layer is external to the Mix Protocol.")),(0,n.kt)("li",{parentName:"ul"},(0,n.kt)("p",{parentName:"li"},(0,n.kt)("strong",{parentName:"p"},"Mix Exit Layer"),"\nA component that receives decrypted messages from a Mix Protocol instance and delivers them to the appropriate origin protocol instance at the destination.\nLike the Entry Layer, it is external to the Mix Protocol.")),(0,n.kt)("li",{parentName:"ul"},(0,n.kt)("p",{parentName:"li"},(0,n.kt)("strong",{parentName:"p"},"Mixnet or Mix Network"),"\nA decentralized overlay network formed by all nodes that support the Mix Protocol.\nIt operates independently of libp2p's protocol-level routing and origin protocol behavior.")),(0,n.kt)("li",{parentName:"ul"},(0,n.kt)("p",{parentName:"li"},(0,n.kt)("strong",{parentName:"p"},"Sphinx Packet"),"\nA cryptographic packet format used by the Mix Protocol to encapsulate messages.\nIt uses layered encryption to hide routing information and protect message contents as packets are forwarded hop-by-hop.\nSphinx packets are fixed-size and indistinguishable from one another, providing unlinkability and metadata protection.")),(0,n.kt)("li",{parentName:"ul"},(0,n.kt)("p",{parentName:"li"},(0,n.kt)("strong",{parentName:"p"},"Initialization Vector (IV)"),"\nA fixed-length input used to initialize block ciphers to add randomness to the encryption process.\nIt ensures that encrypting the same plaintext with the same key produces different ciphertexts.\nThe IV is not secret but must be unique for each encryption.")),(0,n.kt)("li",{parentName:"ul"},(0,n.kt)("p",{parentName:"li"},(0,n.kt)("strong",{parentName:"p"},"Single-Use Reply Block (SURB)"),"\nA pre-computed Sphinx header that encodes a return path back to the sender.\nSURBs are generated by the sender and included in the Sphinx packet sent to the recipient.\nIt enables the recipient to send anonymous replies, without learning the sender's identity, the return path, or the forwarding delays."))),(0,n.kt)("h2",{id:"3-motivation-and-background"},"3. Motivation and Background"),(0,n.kt)("p",null,"libp2p enables modular peer-to-peer applications, but it lacks built-in support for sender anonymity.\nMost protocols expose persistent peer identifiers, transport metadata, or traffic patterns that can be exploited to deanonymize users through passive observation or correlation."),(0,n.kt)("p",null,"While libp2p supports NAT traversal mechanisms such as Circuit Relay, these focus on connectivity rather than anonymity.\nRelays may learn peer identities during stream setup and can observe traffic timing and volume, offering no protection against metadata analysis."),(0,n.kt)("p",null,"libp2p also supports a Tor transport for network-level anonymity, tunneling traffic through long-lived, encrypted circuits.\nHowever, Tor relies on session persistence and is ill-suited for protocols requiring per-message unlinkability."),(0,n.kt)("p",null,"The Mix Protocol addresses this gap with a decentralized message routing layer based on classical mix network principles.\nIt applies layered encryption and per-hop delays to obscure both routing paths and timing correlations.\nEach message is routed independently, providing resistance to traffic analysis and protection against metadata leakage"),(0,n.kt)("p",null,"By decoupling anonymity from connection state and transport negotiation, the Mix Protocol offers a modular privacy abstraction that existing libp2p protocols can adopt without altering their core behavior."),(0,n.kt)("p",null,"To better illustrate the differences in design goals and threat models, the following subsection contrasts the Mix Protocol with Tor, a widely known anonymity system."),(0,n.kt)("h3",{id:"31-comparison-with-tor"},"3.1 Comparison with Tor"),(0,n.kt)("p",null,"The Mix Protocol differs fundamentally from Tor in several ways:"),(0,n.kt)("ul",null,(0,n.kt)("li",{parentName:"ul"},(0,n.kt)("p",{parentName:"li"},(0,n.kt)("strong",{parentName:"p"},"Unlinkability"),": In the Mix Protocol, there is no direct connection between source and destination.\nEach message is routed independently, eliminating correlation through persistent circuits.")),(0,n.kt)("li",{parentName:"ul"},(0,n.kt)("p",{parentName:"li"},(0,n.kt)("strong",{parentName:"p"},"Delay-based mixing"),": Mix nodes introduce randomized delays (e.g., from an exponential distribution) before forwarding messages, making timing correlation significantly harder.")),(0,n.kt)("li",{parentName:"ul"},(0,n.kt)("p",{parentName:"li"},(0,n.kt)("strong",{parentName:"p"},"High-latency focus"),": Tor prioritizes low-latency communication for interactive web traffic, whereas the Mix Protocol is designed for scenarios where higher latency is acceptable in exchange for stronger anonymity.")),(0,n.kt)("li",{parentName:"ul"},(0,n.kt)("p",{parentName:"li"},(0,n.kt)("strong",{parentName:"p"},"Message-based design"),": Each message in the Mix Protocol is self-contained and independently routed.\nNo sessions or state are maintained between messages.")),(0,n.kt)("li",{parentName:"ul"},(0,n.kt)("p",{parentName:"li"},(0,n.kt)("strong",{parentName:"p"},"Resistance to endpoint attacks"),": The Mix Protocol is less susceptible to certain endpoint-level attacks, such as traffic volume correlation or targeted probing, since messages are delayed, reordered, and unlinkable at each hop."))),(0,n.kt)("p",null,"To understand the underlying anonymity properties of the Mix Protocol, we next describe the core components of a mix network."),(0,n.kt)("h2",{id:"4-mixing-strategy-and-packet-format"},"4. Mixing Strategy and Packet Format"),(0,n.kt)("p",null,"The Mix Protocol relies on two core design elements to achieve sender unlinkability and metadata protection:\na mixing strategy and a cryptographically secure mix packet format."),(0,n.kt)("h3",{id:"41-mixing-strategy"},"4.1 Mixing Strategy"),(0,n.kt)("p",null,"A mixing strategy defines how mix nodes delay and reorder incoming packets to resist timing correlation and input-output linkage.\nTwo commonly used approaches are batch-based mixing and continuous-time mixing."),(0,n.kt)("p",null,"In batching-based mixing, each mix node collects incoming packets over a fixed or adaptive interval, shuffles them, and forwards them in a batch.\nWhile this provides some unlinkability, it introduces high latency, requires synchronized flushing rounds, and may result in bursty output traffic.\nAnonymity is bounded by the batch size, and performance may degrade under variable message rates."),(0,n.kt)("p",null,"The Mix Protocol instead uses continuous-time mixing, where each mix node applies a randomized delay to every incoming packet, typically drawn from an exponential distribution.\nThis enables theoretically unbounded anonymity sets, since any packet may, with non-zero probability, be delayed arbitrarily long.\nIn practice, the distribution is truncated once the probability of delay falls below a negligible threshold.\nContinuous-time mixing also offers improved bandwidth utilization and smoother output traffic compared to batching-based approaches."),(0,n.kt)("p",null,"To make continuous-time mixing tunable and predictable, the sender MUST select the mean delay for each hop and encode it into the Sphinx packet header.\nThis allows top-level applications to balance latency and anonymity according to their requirements."),(0,n.kt)("h3",{id:"42-mix-packet-format"},"4.2 Mix Packet Format"),(0,n.kt)("p",null,"A mix packet format defines how messages are encapsulated and routed through a mix network.\nIt must ensure unlinkability between incoming and outgoing packets, prevent metadata leakage (e.g., path length, hop position, or payload size), and support uniform processing by mix nodes regardless of direction or content."),(0,n.kt)("p",null,"The Mix Protocol uses ",(0,n.kt)("a",{parentName:"p",href:"https://cypherpunks.ca/~iang/pubs/Sphinx_Oakland09.pdf"},"Sphinx packets")," to meet these goals.\nEach message is encrypted in layers corresponding to the selected mix path.\nAs a packet traverses the network, each mix node removes one encryption layer to obtain the next hop and delay, while the remaining payload remains encrypted and indistinguishable."),(0,n.kt)("p",null,"Sphinx packets are fixed in size and bit-wise unlinkable.\nThis ensures that they appear identical on the wire regardless of payload, direction, or route length, reducing opportunities for correlation based on packet size or format.\nEven mix nodes learn only the immediate routing information and the delay to be applied.\nThey do not learn their position in the path or the total number of hops."),(0,n.kt)("p",null,"The packet format is resistant to tagging and replay attacks and is compact and efficient to process.\nSphinx packets also include per-hop integrity checks and enforces a maximum path length.\nTogether with a constant-size header and payload, this provides bounded protection against endless routing and malformed packet propagation."),(0,n.kt)("p",null,"It also supports anonymous and indistinguishable reply messages through ",(0,n.kt)("a",{parentName:"p",href:"https://cypherpunks.ca/~iang/pubs/Sphinx_Oakland09.pdf"},"Single-Use Reply Blocks (SURBs)"),", although reply support is not implemented yet."),(0,n.kt)("p",null,"A complete specification of the Sphinx packet structure and fields is provided in ","[Section 6]","."),(0,n.kt)("h2",{id:"5-protocol-overview"},"5. Protocol Overview"),(0,n.kt)("p",null,"The Mix Protocol defines a decentralized, message-based routing layer that provides sender anonymity within the libp2p framework.\nIt is agnostic to message content and semantics.\nEach message is treated as an opaque payload, wrapped into a ",(0,n.kt)("a",{parentName:"p",href:"https://cypherpunks.ca/~iang/pubs/Sphinx_Oakland09.pdf"},"Sphinx packet")," and routed independently through a randomly selected mix path.\nAlong the path, each mix node removes one layer of encryption, adds a randomized delay, and forwards the packet to the next hop.\nThis combination of layered encryption and per-hop delay provides resistance to traffic analysis and enables message-level unlinkability."),(0,n.kt)("p",null,"Unlike typical custom libp2p protocols, the Mix Protocol is stateless","\u2014","it does not establish persistent streams, negotiate protocols, or maintain sessions.\nEach message is self-contained and routed independently."),(0,n.kt)("p",null,"The Mix Protocol sits above the transport layer and below the protocol layer in the libp2p stack.\nIt provides a modular anonymity layer that other libp2p protocols MAY invoke selectively on a per-message basis."),(0,n.kt)("p",null,"Integration with other libp2p protocols is handled through external components that mediate between the origin protocol and the Mix Protocol instances.\nThis enables selective anonymous routing without modifying protocol semantics or internal behavior."),(0,n.kt)("p",null,"The following subsections describe how the Mix Protocol integrates with origin protocols via the Mix Entry and Exit layers, how per-message anonymity is controlled through the ",(0,n.kt)("inlineCode",{parentName:"p"},"mixify")," flag, the rationale for defining Mix as a protocol rather than a transport, and the end-to-end message interaction flow."),(0,n.kt)("h3",{id:"51-integration-with-origin-protocols"},"5.1 Integration with Origin Protocols"),(0,n.kt)("p",null,"libp2p protocols that wish to anonymize messages MUST do so by integrating with the Mix Protocol via the Mix Entry and Exit layers."),(0,n.kt)("ul",null,(0,n.kt)("li",{parentName:"ul"},(0,n.kt)("p",{parentName:"li"},"The ",(0,n.kt)("strong",{parentName:"p"},"Mix Entry Layer")," receives messages to be ",(0,n.kt)("em",{parentName:"p"},"mixified")," from an origin protocol and forwards them to the local Mix Protocol instance.")),(0,n.kt)("li",{parentName:"ul"},(0,n.kt)("p",{parentName:"li"},"The ",(0,n.kt)("strong",{parentName:"p"},"Mix Exit Layer")," receives the final decrypted message from a Mix Protocol instance and forwards it to the appropriate origin protocol instance at the destination over a client-only connection."))),(0,n.kt)("p",null,"This integration is external to the Mix Protocol and is not handled by mix nodes themselves."),(0,n.kt)("h3",{id:"52-mixify-option"},"5.2 Mixify Option"),(0,n.kt)("p",null,"Some origin protocols may require selective anonymity, choosing to anonymize ",(0,n.kt)("em",{parentName:"p"},"only")," certain messages based on their content, context, or destination.\nFor example, a protocol may only anonymize messages containing sensitive metadata while delivering others directly to optimize performance."),(0,n.kt)("p",null,"To support this, origin protocols MAY implement a per-message ",(0,n.kt)("inlineCode",{parentName:"p"},"mixify")," flag that indicates whether a message should be routed using the Mix Protocol."),(0,n.kt)("ul",null,(0,n.kt)("li",{parentName:"ul"},"If the flag is set, the message MUST be handed off to the Mix Entry Layer for anonymous routing."),(0,n.kt)("li",{parentName:"ul"},"If the flag is not set, the message SHOULD be routed using the origin protocol's default mechanism.")),(0,n.kt)("p",null,"This design enables protocols to invoke the Mix Protocol only for selected messages, providing fine-grained control over privacy and performance trade-offs."),(0,n.kt)("h3",{id:"53-why-a-protocol-not-a-transport"},"5.3 Why a Protocol, Not a Transport"),(0,n.kt)("p",null,"The Mix Protocol is specified as a custom libp2p protocol rather than a transport to support selective anonymity while remaining compatible with libp2p's architecture."),(0,n.kt)("p",null,"As noted in ",(0,n.kt)("a",{parentName:"p",href:"#52-mixify-option"},"Section 5.2"),", origin protocols may anonymize only specific messages based on content or context.\nSupporting such selective behavior requires invoking Mix on a per-message basis."),(0,n.kt)("p",null,"libp2p transports, however, are negotiated per peer connection and apply globally to all messages exchanged between two peers.\nEnabling selective anonymity at the transport layer would therefore require changes to libp2p's core transport semantics."),(0,n.kt)("p",null,"Defining Mix as a protocol avoids these constraints and offers several benefits:"),(0,n.kt)("ul",null,(0,n.kt)("li",{parentName:"ul"},"Supports selective invocation on a per-message basis."),(0,n.kt)("li",{parentName:"ul"},"Works atop existing secure transports (",(0,n.kt)("em",{parentName:"li"},"e.g.,")," QUIC, TLS) without requiring changes to the transport stack."),(0,n.kt)("li",{parentName:"ul"},"Preserves a stateless, content-agnostic model focused on anonymous message routing."),(0,n.kt)("li",{parentName:"ul"},"Integrates seamlessly with origin protocols via the Mix Entry and Exit layers.")),(0,n.kt)("p",null,"This design preserves the modularity of the libp2p stack and allows Mix to be adopted without altering existing transport or protocol behavior."),(0,n.kt)("h3",{id:"54-protocol-interaction-flow"},"5.4 Protocol Interaction Flow"),(0,n.kt)("p",null,"A typical end-to-end Mix Protocol flow consists of the following three conceptual phases.\nOnly the second phase","\u2014","the anonymous routing performed by mix nodes","\u2014","is part of the core Mix Protocol.\nThe entry-side and exit-side integration steps are handled externally by the Mix Entry and Exit layers."),(0,n.kt)("ol",null,(0,n.kt)("li",{parentName:"ol"},(0,n.kt)("p",{parentName:"li"},(0,n.kt)("strong",{parentName:"p"},"Entry-side Integration (Mix Entry Layer):")),(0,n.kt)("ul",{parentName:"li"},(0,n.kt)("li",{parentName:"ul"},"The origin protocol generates a message and sets the ",(0,n.kt)("inlineCode",{parentName:"li"},"mixify")," flag."),(0,n.kt)("li",{parentName:"ul"},"The message is passed to the Mix Entry Layer, which invokes the local Mix Protocol instance with the message, destination, and origin protocol codec as input."))),(0,n.kt)("li",{parentName:"ol"},(0,n.kt)("p",{parentName:"li"},(0,n.kt)("strong",{parentName:"p"},"Anonymous Routing (Core Mix Protocol):")),(0,n.kt)("ul",{parentName:"li"},(0,n.kt)("li",{parentName:"ul"},"The Mix Protocol instance wraps the message in a Sphinx packet and selects a random mix path."),(0,n.kt)("li",{parentName:"ul"},"Each mix node along the path:",(0,n.kt)("ul",{parentName:"li"},(0,n.kt)("li",{parentName:"ul"},"Processes the Sphinx packet by removing one encryption layer."),(0,n.kt)("li",{parentName:"ul"},"Applies a delay and forwards the packet to the next hop."))),(0,n.kt)("li",{parentName:"ul"},"The final node in the path (exit node) decrypts the final layer, extracting the original plaintext message, destination, and origin protocol codec."))),(0,n.kt)("li",{parentName:"ol"},(0,n.kt)("p",{parentName:"li"},(0,n.kt)("strong",{parentName:"p"},"Exit-side Integration (Mix Exit Layer):")),(0,n.kt)("ul",{parentName:"li"},(0,n.kt)("li",{parentName:"ul"},"The Mix Exit Layer receives the plaintext message, destination, and origin protocol codec."),(0,n.kt)("li",{parentName:"ul"},"It routes the message to the destination origin protocol instance using a client-only connection.")))),(0,n.kt)("p",null,"The destination node does not need to support the Mix Protocol to receive or respond to anonymous messages."),(0,n.kt)("p",null,"The behavior described above represents the core Mix Protocol.\nIn addition, the protocol supports a set of pluggable components that extend its functionality.\nThese components cover areas such as node discovery, delay strategy, spam resistance, cover traffic generation, and incentivization.\nSome are REQUIRED for interoperability; others are OPTIONAL or deployment-specific.\nThe next section describes each component."),(0,n.kt)("h3",{id:"55-stream-management-and-multiplexing"},"5.5 Stream Management and Multiplexing"),(0,n.kt)("p",null,"Each Mix Protocol message is routed independently, and forwarding it to the next hop requires opening a new libp2p stream using the Mix Protocol.\nThis applies to both the initial Sphinx packet transmission and each hop along the mix path."),(0,n.kt)("p",null,"In high-throughput environments (",(0,n.kt)("em",{parentName:"p"},"e.g."),", messaging systems with continuous anonymous traffic), mix nodes may frequently communicate with a subset of mix nodes.\nOpening a new stream for each Sphinx packet in such scenarios can incur performance costs, as each stream setup requires a multistream handshake for protocol negotiation."),(0,n.kt)("p",null,"While libp2p supports multiplexing multiple streams over a single transport connection using stream muxers such as mplex and yamux, it does not natively support reusing the same stream over multiple message transmissions.\nHowever, stream reuse may be desirable in the mixnet setting to reduce overhead and avoid hitting per protocol stream limits between peers."),(0,n.kt)("p",null,"The lifecycle of streams, including their reuse, eviction, or pooling strategy, is outside the scope of this specification.\nIt SHOULD be handled by the libp2p host, connection manager, or transport stack."),(0,n.kt)("p",null,"Mix Protocol implementations MUST NOT assume persistent stream availability and SHOULD gracefully fall back to opening a new stream when reuse is not possible."),(0,n.kt)("h2",{id:"6-pluggable-components"},"6. Pluggable Components"),(0,n.kt)("p",null,"Pluggable components define functionality that extends or configures the behavior of the Mix Protocol beyond its core message routing logic.\nEach component in this section falls into one of two categories:"),(0,n.kt)("ul",null,(0,n.kt)("li",{parentName:"ul"},"Required for interoperability and path construction (",(0,n.kt)("em",{parentName:"li"},"e.g.,")," discovery, delay strategy)."),(0,n.kt)("li",{parentName:"ul"},"Optional or deployment-specific (",(0,n.kt)("em",{parentName:"li"},"e.g.")," spam protection, cover traffic, incentivization).")),(0,n.kt)("p",null,"The following subsections describe the role and expected behavior of each."),(0,n.kt)("h3",{id:"61-discovery"},"6.1 Discovery"),(0,n.kt)("p",null,"The Mix Protocol does not mandate a specific peer discovery mechanism.\nHowever, nodes participating in the mixnet MUST be discoverable so that other nodes can construct routing paths that include them."),(0,n.kt)("p",null,"To enable this, regardless of the discovery mechanism used, each mix node MUST make the following information available to peers:"),(0,n.kt)("ul",null,(0,n.kt)("li",{parentName:"ul"},"Indicate Mix Protocol support (",(0,n.kt)("em",{parentName:"li"},"e.g.,")," using a ",(0,n.kt)("inlineCode",{parentName:"li"},"mix")," field or bit)."),(0,n.kt)("li",{parentName:"ul"},"Its X25519 public key for Sphinx encryption."),(0,n.kt)("li",{parentName:"ul"},"One or more routable libp2p multiaddresses that identify the mix node's own network endpoints.")),(0,n.kt)("p",null,"To support sender anonymity at scale, discovery mechanism SHOULD support ",(0,n.kt)("em",{parentName:"p"},"unbiased random sampling")," from the set of live mix nodes.\nThis enables diverse path construction and reduces exposure to adversarial routing bias."),(0,n.kt)("p",null,"While no existing mechanism provides unbiased sampling by default, ",(0,n.kt)("a",{parentName:"p",href:"https://rfc.vac.dev/waku/standards/core/33/discv5/"},"Waku's ambient discovery"),"\u2014","an extension over ",(0,n.kt)("a",{parentName:"p",href:"https://github.com/ethereum/devp2p/blob/master/discv5/discv5.md"},"Discv5"),"\u2014","demonstrates an approximate solution.\nIt combines topic-based capability advertisement with periodic peer sampling.\nA similar strategy could potentially be adapted for the Mix Protocol."),(0,n.kt)("p",null,"A more robust solution would involve integrating capability-aware discovery directly into the libp2p stack, such as through extensions to ",(0,n.kt)("inlineCode",{parentName:"p"},"libp2p-kaddht"),".\nThis would enable direct lookup of mix nodes based on protocol support and eliminate reliance on external mechanisms such as Discv5.\nSuch an enhancement remains exploratory and is outside the scope of this specification."),(0,n.kt)("p",null,"Regardless of the mechanism, the goal is to ensure mix nodes are discoverable and that path selection is resistant to bias and node churn."),(0,n.kt)("h3",{id:"62-delay-strategy"},"6.2 Delay Strategy"),(0,n.kt)("p",null,"The Mix Protocol uses per-hop delay as a core mechanism for achieving timing unlinkability.\nFor each hop in the mix path, the sender MUST specify a mean delay value, which is embedded in the Sphinx packet header.\nThe mix node at each hop uses this value to sample a randomized delay before forwarding the packet."),(0,n.kt)("p",null,"By default, delays are sampled from an exponential distribution.\nThis supports continuous-time mixing, produces smooth output traffic, and enables tunable trade-offs between latency and anonymity.\nImportantly, it allows for unbounded anonymity sets: each packet may, with non-zero probability, be delayed arbitrarily long."),(0,n.kt)("p",null,"The delay strategy is considered pluggable, and other distributions MAY be used to match application-specific anonymity or performance requirements.\nHowever, any delay strategy MUST ensure that:"),(0,n.kt)("ul",null,(0,n.kt)("li",{parentName:"ul"},"Delays are sampled independently at each hop."),(0,n.kt)("li",{parentName:"ul"},"Delay sampling introduces sufficient variability to obscure timing correlation between packet arrival and forwarding across multiple hops.")),(0,n.kt)("p",null,"Strategies that produce deterministic or tightly clustered output delays are NOT RECOMMENDED, as they increase the risk of timing correlation.\nDelay strategies SHOULD introduce enough uncertainty to prevent adversaries from linking packet arrival and departure times, even when monitoring multiple hops concurrently."),(0,n.kt)("h3",{id:"63-spam-protection"},"6.3 Spam Protection"),(0,n.kt)("p",null,"The Mix Protocol supports an optional, pluggable spam protection mechanism to defend the mixnet against denial-of-service (DoS) or resource exhaustion attacks.\nWithout spam protection, malicious actors could flood mix nodes with valid Sphinx packets, exhausting computational resources or bandwidth of the mix nodes eventually making them unusable.\nSpam protection is critical to make the mixnet robust enough to be used in a production environment."),(0,n.kt)("p",null,"The spam protection mechanism is pluggable because different deployments may require different trade-offs between computational overhead, attack resistance, and Sybil resistance.\nFor a specific mix deployment, the same spam protection mechanism MUST be followed by all participating mix nodes to ensure interoperability."),(0,n.kt)("p",null,"Two primary architectural approaches exist for integrating spam protection: sender-generated proofs and per-hop generated proofs.\nEach approach has distinct implications for computational overhead, latency, security properties, Sybil resistance, and implementation complexity."),(0,n.kt)("p",null,"Detailed design requirements, architectural approaches, packet structure considerations, node responsibilities, and recommendations are specified in ",(0,n.kt)("a",{parentName:"p",href:"#9-spam-protection-architecture"},"Section 9"),"."),(0,n.kt)("p",null,"Note that application-level or origin-protocol spam protection mechanisms are out of scope for the Mix Protocol and MUST be handled by the appropriate protocol layer itself.\nFor example, Waku protocols use RLN (Rate Limiting Nullifiers) for spam protection, which is handled by ",(0,n.kt)("a",{parentName:"p",href:"https://rfc.vac.dev/waku/standards/core/17/rln-relay"},"Waku-Relay")," protocol, and the RLN proof would be included as part of the mix payload."),(0,n.kt)("h3",{id:"64-cover-traffic"},"6.4 Cover Traffic"),(0,n.kt)("p",null,"Cover traffic is an optional mechanism used to improve privacy by making the presence or absence of actual messages indistinguishable to observers.\nIt helps achieve ",(0,n.kt)("em",{parentName:"p"},"unobservability")," where a passive adversary cannot determine whether a node is sending real messages or not."),(0,n.kt)("p",null,"In the Mix Protocol, cover traffic is limited to ",(0,n.kt)("em",{parentName:"p"},"loop messages"),"\u2014","dummy Sphinx packets that follow a valid mix path and return to the originating node.\nThese messages carry no application payload but are indistinguishable from real messages in structure, size, and routing behavior."),(0,n.kt)("p",null,"Cover traffic MAY be generated by either mix nodes or senders.\nThe strategy for generating such traffic","\u2014","such as timing and frequency","\u2014","is pluggable and not specified in this document."),(0,n.kt)("p",null,"Implementations that support cover traffic SHOULD generate loop messages at randomized intervals.\nThis helps mask actual sending behavior and increases the effective anonymity set.\nTiming strategies such as Poisson processes or exponential delays are commonly used, but the choice is left to the implementation."),(0,n.kt)("p",null,"In addition to enhancing privacy, loop messages can be used to assess network liveness or path reliability without requiring explicit acknowledgments."),(0,n.kt)("h3",{id:"65-incentivization"},"6.5 Incentivization"),(0,n.kt)("p",null,"The Mix Protocol supports a simple tit-for-tat model to discourage free-riding and promote mix node participation.\nIn this model, nodes that wish to send anonymous messages using the Mix Protocol MUST also operate a mix node.\nThis requirement ensures that participants contribute to the anonymity set they benefit from, fostering a minimal form of fairness and reciprocity."),(0,n.kt)("p",null,"This tit-for-tat model is intentionally lightweight and decentralized.\nIt deters passive use of the mixnet by requiring each user to contribute bandwidth and processing capacity.\nHowever, it does not guarantee the quality of service provided by participating nodes.\nFor example, it does not prevent nodes from running low-quality or misbehaving mix instances, nor does it deter participation by compromised or transient peers."),(0,n.kt)("p",null,"The Mix Protocol does not mandate any form of payment, token exchange, or accounting.\nMore sophisticated economic models","\u2014","such as stake-based participation, credentialed relay networks, or zero-knowledge proof-of-contribution systems","\u2014","MAY be layered on top of the protocol or enforced via external coordination."),(0,n.kt)("p",null,"Additionally, network operators or application-layer policies MAY require nodes to maintain minimum uptime, prove their participation, or adhere to service-level guarantees."),(0,n.kt)("p",null,"While the Mix Protocol defines a minimum participation requirement, additional incentivization extensions are considered pluggable and experimental in this version of the specification.\nNo specific mechanism is standardized."),(0,n.kt)("h2",{id:"7-core-mix-protocol-responsibilities"},"7. Core Mix Protocol Responsibilities"),(0,n.kt)("p",null,"This section defines the core routing behavior of the Mix Protocol, which all conforming implementations MUST support."),(0,n.kt)("p",null,"The Mix Protocol defines the logic for anonymously routing messages through the decentralized mix network formed by participating libp2p nodes.\nEach mix node MUST implement support for:"),(0,n.kt)("ul",null,(0,n.kt)("li",{parentName:"ul"},"initiating anonymous routing when invoked with a message."),(0,n.kt)("li",{parentName:"ul"},"receiving and processing Sphinx packets when selected as a hop in a mix path.")),(0,n.kt)("p",null,"These roles and their required behaviors are defined in the following subsections."),(0,n.kt)("h3",{id:"71-protocol-identifier"},"7.1 Protocol Identifier"),(0,n.kt)("p",null,"The Mix Protocol is identified by the protocol string ",(0,n.kt)("inlineCode",{parentName:"p"},'"/mix/1.0.0"'),"."),(0,n.kt)("p",null,"All Mix Protocol interactions occur over libp2p streams negotiated using this identifier.\nEach Sphinx packet transmission","\u2014","whether initiated locally or forwarded as part of a mix path","\u2014","involves opening a new libp2p stream to the next hop.\nImplementations MAY optimize performance by reusing streams where appropriate;\nsee ",(0,n.kt)("a",{parentName:"p",href:"#55-stream-management-and-multiplexing"},"Section 5.5")," for more details on stream management."),(0,n.kt)("h3",{id:"72-initiation"},"7.2 Initiation"),(0,n.kt)("p",null,"A mix node initiates anonymous routing only when it is explicitly invoked with a message to be routed.\nAs specified in ",(0,n.kt)("a",{parentName:"p",href:"#52-mixify-option"},"Section 5.2"),", the decision to anonymize a message is made by the origin protocol.\nWhen anonymization is required, the origin protocol instance forwards the message to the Mix Entry Layer, which then passes the message to the local Mix Protocol instance for routing."),(0,n.kt)("p",null,"To perform message initiation, a mix node MUST:"),(0,n.kt)("ul",null,(0,n.kt)("li",{parentName:"ul"},"Select a random mix path."),(0,n.kt)("li",{parentName:"ul"},"Assign a delay value for each hop and encode it into the Sphinx packet header."),(0,n.kt)("li",{parentName:"ul"},"Wrap message in a Sphinx packet by applying layered encryption in reverse order of nodes in the selected mix path."),(0,n.kt)("li",{parentName:"ul"},"Forward the resulting packet to the first mix node in the mix path using the Mix Protocol.")),(0,n.kt)("p",null,"The Mix Protocol does not interpret message content or origin protocol context.\nEach invocation is stateless, and the implementation MUST NOT retain routing metadata or per-message state after the packet is forwarded."),(0,n.kt)("h3",{id:"73-sphinx-packet-receiving-and-processing"},"7.3 Sphinx Packet Receiving and Processing"),(0,n.kt)("p",null,"A mix node that receives a Sphinx packet is oblivious to its position in the path.\nThe first hop is indistinguishable from other intermediary hops in terms of processing and behavior."),(0,n.kt)("p",null,"After decrypting one layer of the Sphinx packet, the node MUST inspect the routing information.\nIf this layer indicates that the next hop is the final destination, the packet MUST be processed as an exit.\nOtherwise, it MUST be processed as an intermediary."),(0,n.kt)("h4",{id:"731-intermediary-processing"},"7.3.1 Intermediary Processing"),(0,n.kt)("p",null,"To process a Sphinx packet as an intermediary, a mix node MUST:"),(0,n.kt)("ul",null,(0,n.kt)("li",{parentName:"ul"},"Extract the next hop address and associated delay from the decrypted packet."),(0,n.kt)("li",{parentName:"ul"},"Wait for the specified delay."),(0,n.kt)("li",{parentName:"ul"},"Forward the updated packet to the next hop using the Mix Protocol.")),(0,n.kt)("p",null,"A mix node performing intermediary processing MUST treat each packet as stateless and self-contained."),(0,n.kt)("h4",{id:"732-exit-processing"},"7.3.2 Exit Processing"),(0,n.kt)("p",null,"To process a Sphinx packet as an exit, a mix node MUST:"),(0,n.kt)("ul",null,(0,n.kt)("li",{parentName:"ul"},"Extract the plaintext message from the final decrypted packet."),(0,n.kt)("li",{parentName:"ul"},"Forward the valid message to the Mix Exit Layer for delivery to the destination origin protocol instance.")),(0,n.kt)("p",null,"The node MUST NOT retain decrypted content after forwarding."),(0,n.kt)("p",null,"The routing behavior described in this section relies on the use of Sphinx packets to preserve unlinkability and confidentiality across hops.\nThe next section specifies their structure, cryptographic components, and construction."),(0,n.kt)("h2",{id:"8-sphinx-packet-format"},"8. Sphinx Packet Format"),(0,n.kt)("p",null,"The Mix Protocol uses the Sphinx packet format to enable unlinkable, multi-hop message routing with per-hop confidentiality and integrity.\nEach message transmitted through the mix network is encapsulated in a Sphinx packet constructed by the initiating mix node.\nThe packet is encrypted in layers such that each hop in the mix path can decrypt exactly one layer and obtain the next-hop routing information and forwarding delay, without learning the complete path or the message origin.\nOnly the final hop learns the destination, which is encoded in the innermost routing layer."),(0,n.kt)("p",null,"Sphinx packets are self-contained and indistinguishable on the wire, providing strong metadata protection.\nMix nodes forward packets without retaining state or requiring knowledge of the source or destination beyond their immediate routing target."),(0,n.kt)("p",null,"To ensure uniformity, each Sphinx packet consists of a fixed-length header and a payload that is padded to a fixed maximum size.\nAlthough the original message payload may vary in length, padding ensures that all packets are identical in size on the wire.\nThis ensures unlinkability and protects against correlation attacks based on message size."),(0,n.kt)("p",null,"If a message exceeds the maximum supported payload size, it MUST be fragmented before being passed to the Mix Protocol.\nFragmentation and reassembly are the responsibility of the origin protocol or the top-level application.\nThe Mix Protocol handles only messages that do not require fragmentation."),(0,n.kt)("p",null,"The structure, encoding, and size constraints of the Sphinx packet are detailed in the following subsections."),(0,n.kt)("h3",{id:"81-packet-structure-overview"},"8.1 Packet Structure Overview"),(0,n.kt)("p",null,"Each Sphinx packet consists of three fixed-length header fields","\u2014"," ",(0,n.kt)("span",{parentName:"p",className:"math math-inline"},(0,n.kt)("span",{parentName:"span",className:"katex"},(0,n.kt)("span",{parentName:"span",className:"katex-mathml"},(0,n.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,n.kt)("semantics",{parentName:"math"},(0,n.kt)("mrow",{parentName:"semantics"},(0,n.kt)("mi",{parentName:"mrow"},"\u03b1")),(0,n.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"\u03b1")))),(0,n.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"0.4306em"}}),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.0037em"}},"\u03b1"))))),", ",(0,n.kt)("span",{parentName:"p",className:"math math-inline"},(0,n.kt)("span",{parentName:"span",className:"katex"},(0,n.kt)("span",{parentName:"span",className:"katex-mathml"},(0,n.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,n.kt)("semantics",{parentName:"math"},(0,n.kt)("mrow",{parentName:"semantics"},(0,n.kt)("mi",{parentName:"mrow"},"\u03b2")),(0,n.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"\u03b2")))),(0,n.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"0.8889em",verticalAlign:"-0.1944em"}}),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.05278em"}},"\u03b2"))))),", and ",(0,n.kt)("span",{parentName:"p",className:"math math-inline"},(0,n.kt)("span",{parentName:"span",className:"katex"},(0,n.kt)("span",{parentName:"span",className:"katex-mathml"},(0,n.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,n.kt)("semantics",{parentName:"math"},(0,n.kt)("mrow",{parentName:"semantics"},(0,n.kt)("mi",{parentName:"mrow"},"\u03b3")),(0,n.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"\u03b3")))),(0,n.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"0.625em",verticalAlign:"-0.1944em"}}),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.05556em"}},"\u03b3")))))," ","\u2014","followed by a fixed-length encrypted payload ",(0,n.kt)("span",{parentName:"p",className:"math math-inline"},(0,n.kt)("span",{parentName:"span",className:"katex"},(0,n.kt)("span",{parentName:"span",className:"katex-mathml"},(0,n.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,n.kt)("semantics",{parentName:"math"},(0,n.kt)("mrow",{parentName:"semantics"},(0,n.kt)("mi",{parentName:"mrow"},"\u03b4")),(0,n.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"\u03b4")))),(0,n.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"0.6944em"}}),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.03785em"}},"\u03b4"))))),".\nTogether, these components enable per-hop message processing with strong confidentiality and integrity guarantees in a stateless and unlinkable manner."),(0,n.kt)("ul",null,(0,n.kt)("li",{parentName:"ul"},(0,n.kt)("strong",{parentName:"li"},(0,n.kt)("span",{parentName:"strong",className:"math math-inline"},(0,n.kt)("span",{parentName:"span",className:"katex"},(0,n.kt)("span",{parentName:"span",className:"katex-mathml"},(0,n.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,n.kt)("semantics",{parentName:"math"},(0,n.kt)("mrow",{parentName:"semantics"},(0,n.kt)("mi",{parentName:"mrow"},"\u03b1")),(0,n.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"\u03b1")))),(0,n.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"0.4306em"}}),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.0037em"}},"\u03b1")))))," (Alpha)"),": An ephemeral public value. Each mix node uses its private key and ",(0,n.kt)("span",{parentName:"li",className:"math math-inline"},(0,n.kt)("span",{parentName:"span",className:"katex"},(0,n.kt)("span",{parentName:"span",className:"katex-mathml"},(0,n.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,n.kt)("semantics",{parentName:"math"},(0,n.kt)("mrow",{parentName:"semantics"},(0,n.kt)("mi",{parentName:"mrow"},"\u03b1")),(0,n.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"\u03b1")))),(0,n.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"0.4306em"}}),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.0037em"}},"\u03b1")))))," to derive a shared session key for that hop. This session key is used to decrypt and process one layer of the packet."),(0,n.kt)("li",{parentName:"ul"},(0,n.kt)("strong",{parentName:"li"},(0,n.kt)("span",{parentName:"strong",className:"math math-inline"},(0,n.kt)("span",{parentName:"span",className:"katex"},(0,n.kt)("span",{parentName:"span",className:"katex-mathml"},(0,n.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,n.kt)("semantics",{parentName:"math"},(0,n.kt)("mrow",{parentName:"semantics"},(0,n.kt)("mi",{parentName:"mrow"},"\u03b2")),(0,n.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"\u03b2")))),(0,n.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"0.8889em",verticalAlign:"-0.1944em"}}),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.05278em"}},"\u03b2")))))," (Beta)"),": The nested encrypted routing information. It encodes the next hop address, the forwarding delay, integrity check ",(0,n.kt)("span",{parentName:"li",className:"math math-inline"},(0,n.kt)("span",{parentName:"span",className:"katex"},(0,n.kt)("span",{parentName:"span",className:"katex-mathml"},(0,n.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,n.kt)("semantics",{parentName:"math"},(0,n.kt)("mrow",{parentName:"semantics"},(0,n.kt)("mi",{parentName:"mrow"},"\u03b3")),(0,n.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"\u03b3")))),(0,n.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"0.625em",verticalAlign:"-0.1944em"}}),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.05556em"}},"\u03b3")))))," for the next hop, and the ",(0,n.kt)("span",{parentName:"li",className:"math math-inline"},(0,n.kt)("span",{parentName:"span",className:"katex"},(0,n.kt)("span",{parentName:"span",className:"katex-mathml"},(0,n.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,n.kt)("semantics",{parentName:"math"},(0,n.kt)("mrow",{parentName:"semantics"},(0,n.kt)("mi",{parentName:"mrow"},"\u03b2")),(0,n.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"\u03b2")))),(0,n.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"0.8889em",verticalAlign:"-0.1944em"}}),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.05278em"}},"\u03b2")))))," for subsequent hops. At the final hop, ",(0,n.kt)("span",{parentName:"li",className:"math math-inline"},(0,n.kt)("span",{parentName:"span",className:"katex"},(0,n.kt)("span",{parentName:"span",className:"katex-mathml"},(0,n.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,n.kt)("semantics",{parentName:"math"},(0,n.kt)("mrow",{parentName:"semantics"},(0,n.kt)("mi",{parentName:"mrow"},"\u03b2")),(0,n.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"\u03b2")))),(0,n.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"0.8889em",verticalAlign:"-0.1944em"}}),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.05278em"}},"\u03b2")))))," encodes the destination address and fixed-length zero padding to preserve uniform size."),(0,n.kt)("li",{parentName:"ul"},(0,n.kt)("strong",{parentName:"li"},(0,n.kt)("span",{parentName:"strong",className:"math math-inline"},(0,n.kt)("span",{parentName:"span",className:"katex"},(0,n.kt)("span",{parentName:"span",className:"katex-mathml"},(0,n.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,n.kt)("semantics",{parentName:"math"},(0,n.kt)("mrow",{parentName:"semantics"},(0,n.kt)("mi",{parentName:"mrow"},"\u03b3")),(0,n.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"\u03b3")))),(0,n.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"0.625em",verticalAlign:"-0.1944em"}}),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.05556em"}},"\u03b3")))))," (Gamma)"),": A message authentication code computed over ",(0,n.kt)("span",{parentName:"li",className:"math math-inline"},(0,n.kt)("span",{parentName:"span",className:"katex"},(0,n.kt)("span",{parentName:"span",className:"katex-mathml"},(0,n.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,n.kt)("semantics",{parentName:"math"},(0,n.kt)("mrow",{parentName:"semantics"},(0,n.kt)("mi",{parentName:"mrow"},"\u03b2")),(0,n.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"\u03b2")))),(0,n.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"0.8889em",verticalAlign:"-0.1944em"}}),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.05278em"}},"\u03b2")))))," using the session key derived from ",(0,n.kt)("span",{parentName:"li",className:"math math-inline"},(0,n.kt)("span",{parentName:"span",className:"katex"},(0,n.kt)("span",{parentName:"span",className:"katex-mathml"},(0,n.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,n.kt)("semantics",{parentName:"math"},(0,n.kt)("mrow",{parentName:"semantics"},(0,n.kt)("mi",{parentName:"mrow"},"\u03b1")),(0,n.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"\u03b1")))),(0,n.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"0.4306em"}}),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.0037em"}},"\u03b1"))))),". It ensures header integrity at each hop."),(0,n.kt)("li",{parentName:"ul"},(0,n.kt)("strong",{parentName:"li"},(0,n.kt)("span",{parentName:"strong",className:"math math-inline"},(0,n.kt)("span",{parentName:"span",className:"katex"},(0,n.kt)("span",{parentName:"span",className:"katex-mathml"},(0,n.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,n.kt)("semantics",{parentName:"math"},(0,n.kt)("mrow",{parentName:"semantics"},(0,n.kt)("mi",{parentName:"mrow"},"\u03b4")),(0,n.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"\u03b4")))),(0,n.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"0.6944em"}}),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.03785em"}},"\u03b4")))))," (Delta)"),": The encrypted payload. It consists of the message padded to a fixed maximum length and encrypted in layers corresponding to each hop in the mix path.")),(0,n.kt)("p",null,"At each hop, the mix node derives the session key from ",(0,n.kt)("span",{parentName:"p",className:"math math-inline"},(0,n.kt)("span",{parentName:"span",className:"katex"},(0,n.kt)("span",{parentName:"span",className:"katex-mathml"},(0,n.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,n.kt)("semantics",{parentName:"math"},(0,n.kt)("mrow",{parentName:"semantics"},(0,n.kt)("mi",{parentName:"mrow"},"\u03b1")),(0,n.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"\u03b1")))),(0,n.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"0.4306em"}}),(0,n.kt)("span",{parentName:"span",className:"mord 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math-inline"},(0,n.kt)("span",{parentName:"span",className:"katex"},(0,n.kt)("span",{parentName:"span",className:"katex-mathml"},(0,n.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,n.kt)("semantics",{parentName:"math"},(0,n.kt)("mrow",{parentName:"semantics"},(0,n.kt)("mi",{parentName:"mrow"},"\u03b2")),(0,n.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"\u03b2")))),(0,n.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"0.8889em",verticalAlign:"-0.1944em"}}),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.05278em"}},"\u03b2")))))," to extract the next hop and delay, and decrypts one layer of ",(0,n.kt)("span",{parentName:"p",className:"math math-inline"},(0,n.kt)("span",{parentName:"span",className:"katex"},(0,n.kt)("span",{parentName:"span",className:"katex-mathml"},(0,n.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,n.kt)("semantics",{parentName:"math"},(0,n.kt)("mrow",{parentName:"semantics"},(0,n.kt)("mi",{parentName:"mrow"},"\u03b4")),(0,n.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"\u03b4")))),(0,n.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"0.6944em"}}),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.03785em"}},"\u03b4"))))),".\nIt then constructs a new packet with updated values of ",(0,n.kt)("span",{parentName:"p",className:"math 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math-inline"},(0,n.kt)("span",{parentName:"span",className:"katex"},(0,n.kt)("span",{parentName:"span",className:"katex-mathml"},(0,n.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,n.kt)("semantics",{parentName:"math"},(0,n.kt)("mrow",{parentName:"semantics"},(0,n.kt)("mi",{parentName:"mrow"},"\u03b3")),(0,n.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"\u03b3")))),(0,n.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"0.625em",verticalAlign:"-0.1944em"}}),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.05556em"}},"\u03b3"))))),", and ",(0,n.kt)("span",{parentName:"p",className:"math math-inline"},(0,n.kt)("span",{parentName:"span",className:"katex"},(0,n.kt)("span",{parentName:"span",className:"katex-mathml"},(0,n.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,n.kt)("semantics",{parentName:"math"},(0,n.kt)("mrow",{parentName:"semantics"},(0,n.kt)("mi",{parentName:"mrow"},"\u03b4")),(0,n.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"\u03b4")))),(0,n.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"0.6944em"}}),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.03785em"}},"\u03b4"))))),", and forwards it to the next hop.\nAt the final hop, the mix node decrypts the innermost layer of ",(0,n.kt)("span",{parentName:"p",className:"math math-inline"},(0,n.kt)("span",{parentName:"span",className:"katex"},(0,n.kt)("span",{parentName:"span",className:"katex-mathml"},(0,n.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,n.kt)("semantics",{parentName:"math"},(0,n.kt)("mrow",{parentName:"semantics"},(0,n.kt)("mi",{parentName:"mrow"},"\u03b2")),(0,n.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"\u03b2")))),(0,n.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"0.8889em",verticalAlign:"-0.1944em"}}),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.05278em"}},"\u03b2")))))," and ",(0,n.kt)("span",{parentName:"p",className:"math math-inline"},(0,n.kt)("span",{parentName:"span",className:"katex"},(0,n.kt)("span",{parentName:"span",className:"katex-mathml"},(0,n.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,n.kt)("semantics",{parentName:"math"},(0,n.kt)("mrow",{parentName:"semantics"},(0,n.kt)("mi",{parentName:"mrow"},"\u03b4")),(0,n.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"\u03b4")))),(0,n.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"0.6944em"}}),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.03785em"}},"\u03b4"))))),", which yields the destination address and the original application message respectively."),(0,n.kt)("p",null,"All Sphinx packets are fixed in size and indistinguishable on the wire.\nThis uniform format, combined with layered encryption and per-hop integrity protection, ensures unlinkability, tamper resistance, and robustness against correlation attacks."),(0,n.kt)("p",null,"The structure and semantics of these fields, the cryptographic primitives used, and the construction and processing steps are defined in the following subsections."),(0,n.kt)("h3",{id:"82-cryptographic-primitives"},"8.2 Cryptographic Primitives"),(0,n.kt)("p",null,"This section defines the cryptographic primitives used in Sphinx packet construction and processing."),(0,n.kt)("ul",null,(0,n.kt)("li",{parentName:"ul"},(0,n.kt)("p",{parentName:"li"},(0,n.kt)("strong",{parentName:"p"},"Security Parameter"),": All cryptographic operations target a minimum of ",(0,n.kt)("span",{parentName:"p",className:"math 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design.")),(0,n.kt)("li",{parentName:"ul"},(0,n.kt)("p",{parentName:"li"},(0,n.kt)("strong",{parentName:"p"},"Per-hop ",(0,n.kt)("span",{parentName:"strong",className:"math math-inline"},(0,n.kt)("span",{parentName:"span",className:"katex"},(0,n.kt)("span",{parentName:"span",className:"katex-mathml"},(0,n.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,n.kt)("semantics",{parentName:"math"},(0,n.kt)("mrow",{parentName:"semantics"},(0,n.kt)("mi",{parentName:"mrow"},"\u03b3")),(0,n.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"\u03b3")))),(0,n.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"0.625em",verticalAlign:"-0.1944em"}}),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.05556em"}},"\u03b3")))))," size (",(0,n.kt)("span",{parentName:"strong",className:"math math-inline"},(0,n.kt)("span",{parentName:"span",className:"katex"},(0,n.kt)("span",{parentName:"span",className:"katex-mathml"},(0,n.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,n.kt)("semantics",{parentName:"math"},(0,n.kt)("mrow",{parentName:"semantics"},(0,n.kt)("mi",{parentName:"mrow"},"\u03ba")),(0,n.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"\u03ba")))),(0,n.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"0.4306em"}}),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal"},"\u03ba"))))),")")," (defined below): Accounts for the integrity tag included with each hop's routing information."))),(0,n.kt)("p",{parentName:"li"},"Using the recommended value of ",(0,n.kt)("span",{parentName:"p",className:"math 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mathnormal",style:{marginRight:"0.13889em"}},"lP"),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal"},"a"),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal"},"c"),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.03148em"}},"k"),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal"},"e"),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.05764em"}},"tS"),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal"},"i"),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal"},"ze"),(0,n.kt)("span",{parentName:"span",className:"mspace",style:{marginRight:"0.2222em"}}),(0,n.kt)("span",{parentName:"span",className:"mbin"},"\u2212"),(0,n.kt)("span",{parentName:"span",className:"mspace",style:{marginRight:"0.2222em"}}),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal"},"He"),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal"},"a"),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal"},"d"),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.02778em"}},"er"),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.05764em"}},"S"),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal"},"i"),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal"},"ze")))),(0,n.kt)("span",{parentName:"span",className:"vlist-s"},"\u200b")),(0,n.kt)("span",{parentName:"span",className:"vlist-r"},(0,n.kt)("span",{parentName:"span",className:"vlist",style:{height:"0.5em"}},(0,n.kt)("span",{parentName:"span"}))))))),(0,n.kt)("span",{parentName:"span",className:"mord"},"\u2018")))))),(0,n.kt)("p",null,"The recommended total packet size is ",(0,n.kt)("span",{parentName:"p",className:"math math-inline"},(0,n.kt)("span",{parentName:"span",className:"katex"},(0,n.kt)("span",{parentName:"span",className:"katex-mathml"},(0,n.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,n.kt)("semantics",{parentName:"math"},(0,n.kt)("mrow",{parentName:"semantics"},(0,n.kt)("mn",{parentName:"mrow"},"4608")),(0,n.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"4608")))),(0,n.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"0.6444em"}}),(0,n.kt)("span",{parentName:"span",className:"mord"},"4608")))))," bytes, chosen to:"),(0,n.kt)("ul",null,(0,n.kt)("li",{parentName:"ul"},"Accommodate larger libp2p application messages, such as those commonly observed in Status chat using Waku (typically ~4KB payloads),"),(0,n.kt)("li",{parentName:"ul"},"Allow inclusion of additional data such as SURBs without requiring fragmentation,"),(0,n.kt)("li",{parentName:"ul"},"Maintain reasonable per-hop processing and bandwidth overhead.")),(0,n.kt)("p",null,"This recommended total packet size of ","$","4608","$"," bytes yields:"),(0,n.kt)("p",null,(0,n.kt)("span",{parentName:"p",className:"math math-inline"},(0,n.kt)("span",{parentName:"span",className:"katex"},(0,n.kt)("span",{parentName:"span",className:"katex-mathml"},(0,n.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,n.kt)("semantics",{parentName:"math"},(0,n.kt)("mrow",{parentName:"semantics"},(0,n.kt)("mi",{parentName:"mrow",mathvariant:"normal"},"\u2018"),(0,n.kt)("mtable",{parentName:"mrow",rowspacing:"0.25em",columnalign:"right left",columnspacing:"0em"},(0,n.kt)("mtr",{parentName:"mtable"},(0,n.kt)("mtd",{parentName:"mtr"},(0,n.kt)("mstyle",{parentName:"mtd",scriptlevel:"0",displaystyle:"true"},(0,n.kt)("mrow",{parentName:"mstyle"},(0,n.kt)("mi",{parentName:"mrow"},"P"),(0,n.kt)("mi",{parentName:"mrow"},"a"),(0,n.kt)("mi",{parentName:"mrow"},"y"),(0,n.kt)("mi",{parentName:"mrow"},"l"),(0,n.kt)("mi",{parentName:"mrow"},"o"),(0,n.kt)("mi",{parentName:"mrow"},"a"),(0,n.kt)("mi",{parentName:"mrow"},"d")))),(0,n.kt)("mtd",{parentName:"mtr"},(0,n.kt)("mstyle",{parentName:"mtd",scriptlevel:"0",displaystyle:"true"},(0,n.kt)("mrow",{parentName:"mstyle"},(0,n.kt)("mrow",{parentName:"mrow"}),(0,n.kt)("mo",{parentName:"mrow"},"="),(0,n.kt)("mn",{parentName:"mrow"},"4608"),(0,n.kt)("mo",{parentName:"mrow"},"\u2212"),(0,n.kt)("mn",{parentName:"mrow"},"624"))))),(0,n.kt)("mtr",{parentName:"mtable"},(0,n.kt)("mtd",{parentName:"mtr"},(0,n.kt)("mstyle",{parentName:"mtd",scriptlevel:"0",displaystyle:"true"},(0,n.kt)("mrow",{parentName:"mstyle"}))),(0,n.kt)("mtd",{parentName:"mtr"},(0,n.kt)("mstyle",{parentName:"mtd",scriptlevel:"0",displaystyle:"true"},(0,n.kt)("mrow",{parentName:"mstyle"},(0,n.kt)("mrow",{parentName:"mrow"}),(0,n.kt)("mo",{parentName:"mrow"},"="),(0,n.kt)("mn",{parentName:"mrow"},"3984"),(0,n.kt)("mtext",{parentName:"mrow"},"\xa0"),(0,n.kt)("mi",{parentName:"mrow"},"b"),(0,n.kt)("mi",{parentName:"mrow"},"y"),(0,n.kt)("mi",{parentName:"mrow"},"t"),(0,n.kt)("mi",{parentName:"mrow"},"e"),(0,n.kt)("mi",{parentName:"mrow"},"s")))))),(0,n.kt)("mi",{parentName:"mrow",mathvariant:"normal"},"\u2018")),(0,n.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"` \\begin{aligned} Payload &= 4608 - 624 \\\\  &= 3984\\ bytes \\end{aligned} `")))),(0,n.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"3em",verticalAlign:"-1.25em"}}),(0,n.kt)("span",{parentName:"span",className:"mord"},"\u2018"),(0,n.kt)("span",{parentName:"span",className:"mord"},(0,n.kt)("span",{parentName:"span",className:"mtable"},(0,n.kt)("span",{parentName:"span",className:"col-align-r"},(0,n.kt)("span",{parentName:"span",className:"vlist-t vlist-t2"},(0,n.kt)("span",{parentName:"span",className:"vlist-r"},(0,n.kt)("span",{parentName:"span",className:"vlist",style:{height:"1.75em"}},(0,n.kt)("span",{parentName:"span",style:{top:"-3.91em"}},(0,n.kt)("span",{parentName:"span",className:"pstrut",style:{height:"3em"}}),(0,n.kt)("span",{parentName:"span",className:"mord"},(0,n.kt)("span",{parentName:"span",className:"mord 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mathnormal"},"d"))),(0,n.kt)("span",{parentName:"span",style:{top:"-2.41em"}},(0,n.kt)("span",{parentName:"span",className:"pstrut",style:{height:"3em"}}),(0,n.kt)("span",{parentName:"span",className:"mord"}))),(0,n.kt)("span",{parentName:"span",className:"vlist-s"},"\u200b")),(0,n.kt)("span",{parentName:"span",className:"vlist-r"},(0,n.kt)("span",{parentName:"span",className:"vlist",style:{height:"1.25em"}},(0,n.kt)("span",{parentName:"span"}))))),(0,n.kt)("span",{parentName:"span",className:"col-align-l"},(0,n.kt)("span",{parentName:"span",className:"vlist-t vlist-t2"},(0,n.kt)("span",{parentName:"span",className:"vlist-r"},(0,n.kt)("span",{parentName:"span",className:"vlist",style:{height:"1.75em"}},(0,n.kt)("span",{parentName:"span",style:{top:"-3.91em"}},(0,n.kt)("span",{parentName:"span",className:"pstrut",style:{height:"3em"}}),(0,n.kt)("span",{parentName:"span",className:"mord"},(0,n.kt)("span",{parentName:"span",className:"mord"}),(0,n.kt)("span",{parentName:"span",className:"mspace",style:{marginRight:"0.2778em"}}),(0,n.kt)("span",{parentName:"span",className:"mrel"},"="),(0,n.kt)("span",{parentName:"span",className:"mspace",style:{marginRight:"0.2778em"}}),(0,n.kt)("span",{parentName:"span",className:"mord"},"4608"),(0,n.kt)("span",{parentName:"span",className:"mspace",style:{marginRight:"0.2222em"}}),(0,n.kt)("span",{parentName:"span",className:"mbin"},"\u2212"),(0,n.kt)("span",{parentName:"span",className:"mspace",style:{marginRight:"0.2222em"}}),(0,n.kt)("span",{parentName:"span",className:"mord"},"624"))),(0,n.kt)("span",{parentName:"span",style:{top:"-2.41em"}},(0,n.kt)("span",{parentName:"span",className:"pstrut",style:{height:"3em"}}),(0,n.kt)("span",{parentName:"span",className:"mord"},(0,n.kt)("span",{parentName:"span",className:"mord"}),(0,n.kt)("span",{parentName:"span",className:"mspace",style:{marginRight:"0.2778em"}}),(0,n.kt)("span",{parentName:"span",className:"mrel"},"="),(0,n.kt)("span",{parentName:"span",className:"mspace",style:{marginRight:"0.2778em"}}),(0,n.kt)("span",{parentName:"span",className:"mord"},"3984"),(0,n.kt)("span",{parentName:"span",className:"mspace"},"\xa0"),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal"},"b"),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.03588em"}},"y"),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal"},"t"),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal"},"es")))),(0,n.kt)("span",{parentName:"span",className:"vlist-s"},"\u200b")),(0,n.kt)("span",{parentName:"span",className:"vlist-r"},(0,n.kt)("span",{parentName:"span",className:"vlist",style:{height:"1.25em"}},(0,n.kt)("span",{parentName:"span"}))))))),(0,n.kt)("span",{parentName:"span",className:"mord"},"\u2018")))))),(0,n.kt)("p",null,"Implementations MUST account for payload extensions, such as SURBs, when determining the maximum message size that can be encapsulated in a single Sphinx packet.\nDetails on SURBs are defined in ","[Section X.X]","."),(0,n.kt)("p",null,"The following subsection defines the padding and fragmentation requirements for ensuring this fixed-size constraint."),(0,n.kt)("h4",{id:"833-padding-and-fragmentation"},"8.3.3 Padding and Fragmentation"),(0,n.kt)("p",null,"Implementations MUST ensure that all messages shorter than the maximum payload size are padded before Sphinx encapsulation to ensure that all packets are indistinguishable on the wire.\nMessages larger than the maximum payload size MUST be fragmented by the origin protocol or top-level application before being passed to the Mix Protocol.\nReassembly is the responsibility of the consuming application, not the Mix Protocol."),(0,n.kt)("h4",{id:"834-anonymity-set-considerations"},"8.3.4 Anonymity Set Considerations"),(0,n.kt)("p",null,"The fixed maximum packet size is a configurable parameter.\nProtocols or applications that choose to configure a different packet size (either larger or smaller than the default) MUST be aware that using unique or uncommon packet sizes can reduce their effective anonymity set to only other users of the same size.\nImplementers SHOULD align with widely used defaults to maximize anonymity set size."),(0,n.kt)("p",null,"Similarly, parameters such as ",(0,n.kt)("span",{parentName:"p",className:"math math-inline"},(0,n.kt)("span",{parentName:"span",className:"katex"},(0,n.kt)("span",{parentName:"span",className:"katex-mathml"},(0,n.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,n.kt)("semantics",{parentName:"math"},(0,n.kt)("mrow",{parentName:"semantics"},(0,n.kt)("mi",{parentName:"mrow"},"r")),(0,n.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"r")))),(0,n.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"0.4306em"}}),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.02778em"}},"r")))))," and ",(0,n.kt)("span",{parentName:"p",className:"math math-inline"},(0,n.kt)("span",{parentName:"span",className:"katex"},(0,n.kt)("span",{parentName:"span",className:"katex-mathml"},(0,n.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,n.kt)("semantics",{parentName:"math"},(0,n.kt)("mrow",{parentName:"semantics"},(0,n.kt)("mi",{parentName:"mrow"},"t")),(0,n.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"t")))),(0,n.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"0.6151em"}}),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal"},"t")))))," are configurable.\nChanges to these parameters affect header size and therefore impact payload size if the total packet size remains fixed.\nHowever, if such changes alter the total packet size on the wire, the same anonymity set considerations apply."),(0,n.kt)("p",null,"The following subsection defines how the next-hop or destination address and forwarding delay are encoded within ",(0,n.kt)("span",{parentName:"p",className:"math math-inline"},(0,n.kt)("span",{parentName:"span",className:"katex"},(0,n.kt)("span",{parentName:"span",className:"katex-mathml"},(0,n.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,n.kt)("semantics",{parentName:"math"},(0,n.kt)("mrow",{parentName:"semantics"},(0,n.kt)("mi",{parentName:"mrow"},"\u03b2")),(0,n.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"\u03b2")))),(0,n.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"0.8889em",verticalAlign:"-0.1944em"}}),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.05278em"}},"\u03b2")))))," to enable correct routing and mixing behavior."),(0,n.kt)("h3",{id:"84-address-and-delay-encoding"},"8.4 Address and Delay Encoding"),(0,n.kt)("p",null,"Each hop's ",(0,n.kt)("span",{parentName:"p",className:"math math-inline"},(0,n.kt)("span",{parentName:"span",className:"katex"},(0,n.kt)("span",{parentName:"span",className:"katex-mathml"},(0,n.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,n.kt)("semantics",{parentName:"math"},(0,n.kt)("mrow",{parentName:"semantics"},(0,n.kt)("mi",{parentName:"mrow"},"\u03b2")),(0,n.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"\u03b2")))),(0,n.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"0.8889em",verticalAlign:"-0.1944em"}}),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.05278em"}},"\u03b2")))))," includes a fixed-size block containing the next-hop address and the forwarding delay, except for the final hop, which encodes the destination address and a delay-sized zero padding.\nThis section defines the structure and encoding of that block."),(0,n.kt)("p",null,"The combined address and delay block MUST be exactly ",(0,n.kt)("span",{parentName:"p",className:"math math-inline"},(0,n.kt)("span",{parentName:"span",className:"katex"},(0,n.kt)("span",{parentName:"span",className:"katex-mathml"},(0,n.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,n.kt)("semantics",{parentName:"math"},(0,n.kt)("mrow",{parentName:"semantics"},(0,n.kt)("mi",{parentName:"mrow"},"t"),(0,n.kt)("mi",{parentName:"mrow"},"\u03ba")),(0,n.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"t\u03ba")))),(0,n.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"0.6151em"}}),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal"},"t"),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal"},"\u03ba")))))," bytes in length, as defined in ",(0,n.kt)("a",{parentName:"p",href:"#831-header-field-sizes"},"Section 8.3.1"),", regardless of the actual address or delay values.\nThe first ",(0,n.kt)("span",{parentName:"p",className:"math math-inline"},(0,n.kt)("span",{parentName:"span",className:"katex"},(0,n.kt)("span",{parentName:"span",className:"katex-mathml"},(0,n.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,n.kt)("semantics",{parentName:"math"},(0,n.kt)("mrow",{parentName:"semantics"},(0,n.kt)("mo",{parentName:"mrow",stretchy:"false"},"("),(0,n.kt)("mi",{parentName:"mrow"},"t"),(0,n.kt)("mi",{parentName:"mrow"},"\u03ba"),(0,n.kt)("mo",{parentName:"mrow"},"\u2212"),(0,n.kt)("mn",{parentName:"mrow"},"2"),(0,n.kt)("mo",{parentName:"mrow",stretchy:"false"},")")),(0,n.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"(t\u03ba - 2)")))),(0,n.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"1em",verticalAlign:"-0.25em"}}),(0,n.kt)("span",{parentName:"span",className:"mopen"},"("),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal"},"t"),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal"},"\u03ba"),(0,n.kt)("span",{parentName:"span",className:"mspace",style:{marginRight:"0.2222em"}}),(0,n.kt)("span",{parentName:"span",className:"mbin"},"\u2212"),(0,n.kt)("span",{parentName:"span",className:"mspace",style:{marginRight:"0.2222em"}})),(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"1em",verticalAlign:"-0.25em"}}),(0,n.kt)("span",{parentName:"span",className:"mord"},"2"),(0,n.kt)("span",{parentName:"span",className:"mclose"},")")))))," bytes MUST encode the address, and the final ",(0,n.kt)("span",{parentName:"p",className:"math math-inline"},(0,n.kt)("span",{parentName:"span",className:"katex"},(0,n.kt)("span",{parentName:"span",className:"katex-mathml"},(0,n.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,n.kt)("semantics",{parentName:"math"},(0,n.kt)("mrow",{parentName:"semantics"},(0,n.kt)("mn",{parentName:"mrow"},"2")),(0,n.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"2")))),(0,n.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"0.6444em"}}),(0,n.kt)("span",{parentName:"span",className:"mord"},"2")))))," bytes MUST encode the forwarding delay.\nThis fixed-length encoding ensures that packets remain indistinguishable on the wire and prevents correlation attacks based on routing metadata structure."),(0,n.kt)("p",null,"Implementations MAY use any address and delay encoding format agreed upon by all participating mix nodes, as long as the combined length is exactly ",(0,n.kt)("span",{parentName:"p",className:"math math-inline"},(0,n.kt)("span",{parentName:"span",className:"katex"},(0,n.kt)("span",{parentName:"span",className:"katex-mathml"},(0,n.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,n.kt)("semantics",{parentName:"math"},(0,n.kt)("mrow",{parentName:"semantics"},(0,n.kt)("mi",{parentName:"mrow"},"t"),(0,n.kt)("mi",{parentName:"mrow"},"\u03ba")),(0,n.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"t\u03ba")))),(0,n.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"0.6151em"}}),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal"},"t"),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal"},"\u03ba")))))," bytes.\nThe encoding format MUST be interpreted consistently by all nodes within a deployment."),(0,n.kt)("p",null,"For interoperability, a recommended default encoding format involves:"),(0,n.kt)("ul",null,(0,n.kt)("li",{parentName:"ul"},(0,n.kt)("p",{parentName:"li"},"Encoding the next-hop or destination address as a libp2p multi-address:"),(0,n.kt)("ul",{parentName:"li"},(0,n.kt)("li",{parentName:"ul"},"To keep the address block compact while allowing relay connectivity, each mix node is limited to one IPv4 circuit relay multiaddress. This ensures that most nodes can act as mix nodes, including those behind NATs or firewalls."),(0,n.kt)("li",{parentName:"ul"},"In libp2p terms, this combines transport addresses with multiple peer identities to form an address that describes a relay circuit:\n",(0,n.kt)("inlineCode",{parentName:"li"},"/ip4/<ipv4>/tcp/<port>/p2p/<relayPeerID>/p2p-circuit/p2p/<relayedPeerID>"),"\nVariants may include directly reachable peers and transports such as ",(0,n.kt)("inlineCode",{parentName:"li"},"/quic-v1"),", depending on the mix node's supported stack."),(0,n.kt)("li",{parentName:"ul"},"IPv6 support is deferred, as it adds ",(0,n.kt)("span",{parentName:"li",className:"math math-inline"},(0,n.kt)("span",{parentName:"span",className:"katex"},(0,n.kt)("span",{parentName:"span",className:"katex-mathml"},(0,n.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,n.kt)("semantics",{parentName:"math"},(0,n.kt)("mrow",{parentName:"semantics"},(0,n.kt)("mn",{parentName:"mrow"},"16")),(0,n.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"16")))),(0,n.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"0.6444em"}}),(0,n.kt)("span",{parentName:"span",className:"mord"},"16")))))," bytes just for the IP field."),(0,n.kt)("li",{parentName:"ul"},"Future revisions may extend this format to support IPv6 or DNS-based multiaddresses.")),(0,n.kt)("p",{parentName:"li"},"With these constraints, the recommended encoding layout is:"),(0,n.kt)("ul",{parentName:"li"},(0,n.kt)("li",{parentName:"ul"},"IPv4 address (4 bytes)"),(0,n.kt)("li",{parentName:"ul"},"Protocol identifier ",(0,n.kt)("em",{parentName:"li"},"e.g.,")," TCP or QUIC (1 byte)"),(0,n.kt)("li",{parentName:"ul"},"Port number (2 bytes)"),(0,n.kt)("li",{parentName:"ul"},"Peer IDs (39 bytes, post-Base58 decoding)"))),(0,n.kt)("li",{parentName:"ul"},(0,n.kt)("p",{parentName:"li"},"Encoding the forwarding delay as an unsigned 16-bit integer (2 bytes), representing the mean delay in milliseconds for the configured delay distribution, using big endian network byte order.\nThe delay distribution is pluggable, as defined in ",(0,n.kt)("a",{parentName:"p",href:"#62-delay-strategy"},"Section 6.2"),"."))),(0,n.kt)("p",null,"If the encoded address or delay is shorter than its respective allocated field, it MUST be padded with zeros.\nIf it exceeds the allocated size, it MUST be rejected or truncated according to the implementation policy."),(0,n.kt)("p",null,"Note:\nFuture versions of the Mix Protocol may support address compression by encoding only the peer identifier and relying on external peer discovery mechanisms to retrieve full multiaddresses at runtime.\nThis would allow for more compact headers and greater address flexibility, but requires fast and reliable lookup support across deployments.\nThis design is out of scope for the current version."),(0,n.kt)("p",null,"With the field sizes and encoding conventions established, the next section describes how a mix node constructs a complete Sphinx packet when initiating the Mix Protocol."),(0,n.kt)("h3",{id:"85-packet-construction"},"8.5 Packet Construction"),(0,n.kt)("p",null,"This section defines how a mix node constructs a Sphinx packet when initiating the Mix Protocol on behalf of a local origin protocol instance.\nThe construction process wraps the message in a sequence of encryption layers","\u2014","one for each hop","\u2014","such that only the corresponding mix node can decrypt its layer and retrieve the routing instructions for that hop."),(0,n.kt)("h4",{id:"851-inputs"},"8.5.1 Inputs"),(0,n.kt)("p",null,"To initiate the Mix Protocol, the origin protocol instance submits a message to the Mix Entry Layer on the same node.\nThis layer forwards it to the local Mix Protocol instance, which constructs a Sphinx packet using the following REQUIRED inputs:"),(0,n.kt)("ul",null,(0,n.kt)("li",{parentName:"ul"},(0,n.kt)("strong",{parentName:"li"},"Application message"),": The serialized message provided by the origin protocol instance. The Mix Protocol instance attaches one or two SURBs prior to encapsulating the message in the Sphinx packet. The initiating node MUST ensure that the resulting payload size does not exceed the maximum supported size defined in ",(0,n.kt)("a",{parentName:"li",href:"#832-payload-size"},"Section 8.3.2"),"."),(0,n.kt)("li",{parentName:"ul"},(0,n.kt)("strong",{parentName:"li"},"Origin protocol codec"),": The libp2p protocol string corresponding to the origin protocol instance. This is included in the payload so that the exit node can route the message to the intended destination protocol after decryption."),(0,n.kt)("li",{parentName:"ul"},(0,n.kt)("strong",{parentName:"li"},"Mix Path length ",(0,n.kt)("span",{parentName:"strong",className:"math math-inline"},(0,n.kt)("span",{parentName:"span",className:"katex"},(0,n.kt)("span",{parentName:"span",className:"katex-mathml"},(0,n.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,n.kt)("semantics",{parentName:"math"},(0,n.kt)("mrow",{parentName:"semantics"},(0,n.kt)("mi",{parentName:"mrow"},"L")),(0,n.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"L")))),(0,n.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"0.6833em"}}),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal"},"L")))))),": The number of mix nodes to include in the path. The mix path MUST consist of at least three hops, each representing a distinct mix node."),(0,n.kt)("li",{parentName:"ul"},(0,n.kt)("strong",{parentName:"li"},"Destination address ",(0,n.kt)("span",{parentName:"strong",className:"math math-inline"},(0,n.kt)("span",{parentName:"span",className:"katex"},(0,n.kt)("span",{parentName:"span",className:"katex-mathml"},(0,n.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,n.kt)("semantics",{parentName:"math"},(0,n.kt)("mrow",{parentName:"semantics"},(0,n.kt)("mi",{parentName:"mrow",mathvariant:"normal"},"\u0394")),(0,n.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"\u0394")))),(0,n.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"0.6833em"}}),(0,n.kt)("span",{parentName:"span",className:"mord"},"\u0394")))))),": The routing address of the intended recipient of the message. This address is encoded in ",(0,n.kt)("span",{parentName:"li",className:"math math-inline"},(0,n.kt)("span",{parentName:"span",className:"katex"},(0,n.kt)("span",{parentName:"span",className:"katex-mathml"},(0,n.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,n.kt)("semantics",{parentName:"math"},(0,n.kt)("mrow",{parentName:"semantics"},(0,n.kt)("mo",{parentName:"mrow",stretchy:"false"},"("),(0,n.kt)("mi",{parentName:"mrow"},"t"),(0,n.kt)("mi",{parentName:"mrow"},"\u03ba"),(0,n.kt)("mo",{parentName:"mrow"},"\u2212"),(0,n.kt)("mn",{parentName:"mrow"},"2"),(0,n.kt)("mo",{parentName:"mrow",stretchy:"false"},")")),(0,n.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"(t\u03ba - 2)")))),(0,n.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"1em",verticalAlign:"-0.25em"}}),(0,n.kt)("span",{parentName:"span",className:"mopen"},"("),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal"},"t"),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal"},"\u03ba"),(0,n.kt)("span",{parentName:"span",className:"mspace",style:{marginRight:"0.2222em"}}),(0,n.kt)("span",{parentName:"span",className:"mbin"},"\u2212"),(0,n.kt)("span",{parentName:"span",className:"mspace",style:{marginRight:"0.2222em"}})),(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"1em",verticalAlign:"-0.25em"}}),(0,n.kt)("span",{parentName:"span",className:"mord"},"2"),(0,n.kt)("span",{parentName:"span",className:"mclose"},")")))))," bytes as defined in ",(0,n.kt)("a",{parentName:"li",href:"#84-address-and-delay-encoding"},"Section 8.4")," and revealed only at the last hop.")),(0,n.kt)("h4",{id:"852-construction-steps"},"8.5.2 Construction Steps"),(0,n.kt)("p",null,"This subsection defines how the initiating mix node constructs a complete Sphinx packet using the inputs defined in ",(0,n.kt)("a",{parentName:"p",href:"#851-inputs"},"Section 8.5.1"),".\nThe construction MUST follow the cryptographic structure defined in ",(0,n.kt)("a",{parentName:"p",href:"#81-packet-structure-overview"},"Section 8.1"),", use the primitives specified in ",(0,n.kt)("a",{parentName:"p",href:"#82-cryptographic-primitives"},"Section 8.2"),", and adhere to the component sizes and encoding formats from ",(0,n.kt)("a",{parentName:"p",href:"#83-packet-component-sizes"},"Section 8.3")," and ",(0,n.kt)("a",{parentName:"p",href:"#84-address-and-delay-encoding"},"Section 8.4"),"."),(0,n.kt)("p",null,"The construction MUST proceed as follows:"),(0,n.kt)("ol",null,(0,n.kt)("li",{parentName:"ol"},(0,n.kt)("p",{parentName:"li"},(0,n.kt)("strong",{parentName:"p"},"Prepare Application Message")),(0,n.kt)("ul",{parentName:"li"},(0,n.kt)("li",{parentName:"ul"},"Attach one or more SURBs, if required. Their format and processing are specified in ","[Section X.X]","."),(0,n.kt)("li",{parentName:"ul"},"Append the origin protocol codec in a format that enables the exit node to reliably extract it during parsing. A recommended encoding approach is to prefix the codec string with its length, encoded as a compact varint field limited to two bytes. Regardless of the scheme used, implementations MUST agree on the format within a deployment to ensure deterministic decoding."),(0,n.kt)("li",{parentName:"ul"},"Pad the result to the maximum application message length of ",(0,n.kt)("span",{parentName:"li",className:"math math-inline"},(0,n.kt)("span",{parentName:"span",className:"katex"},(0,n.kt)("span",{parentName:"span",className:"katex-mathml"},(0,n.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,n.kt)("semantics",{parentName:"math"},(0,n.kt)("mrow",{parentName:"semantics"},(0,n.kt)("mn",{parentName:"mrow"},"3968")),(0,n.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"3968")))),(0,n.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"0.6444em"}}),(0,n.kt)("span",{parentName:"span",className:"mord"},"3968")))))," bytes using a deterministic padding scheme. This value is derived from the fixed payload size in ",(0,n.kt)("a",{parentName:"li",href:"#832-payload-size"},"Section 8.3.2")," (",(0,n.kt)("span",{parentName:"li",className:"math math-inline"},(0,n.kt)("span",{parentName:"span",className:"katex"},(0,n.kt)("span",{parentName:"span",className:"katex-mathml"},(0,n.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,n.kt)("semantics",{parentName:"math"},(0,n.kt)("mrow",{parentName:"semantics"},(0,n.kt)("mn",{parentName:"mrow"},"3984")),(0,n.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"3984")))),(0,n.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"0.6444em"}}),(0,n.kt)("span",{parentName:"span",className:"mord"},"3984")))))," bytes) minus the security parameter ",(0,n.kt)("span",{parentName:"li",className:"math math-inline"},(0,n.kt)("span",{parentName:"span",className:"katex"},(0,n.kt)("span",{parentName:"span",className:"katex-mathml"},(0,n.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,n.kt)("semantics",{parentName:"math"},(0,n.kt)("mrow",{parentName:"semantics"},(0,n.kt)("mi",{parentName:"mrow"},"\u03ba"),(0,n.kt)("mo",{parentName:"mrow"},"="),(0,n.kt)("mn",{parentName:"mrow"},"16")),(0,n.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"\u03ba = 16")))),(0,n.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"0.4306em"}}),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal"},"\u03ba"),(0,n.kt)("span",{parentName:"span",className:"mspace",style:{marginRight:"0.2778em"}}),(0,n.kt)("span",{parentName:"span",className:"mrel"},"="),(0,n.kt)("span",{parentName:"span",className:"mspace",style:{marginRight:"0.2778em"}})),(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"0.6444em"}}),(0,n.kt)("span",{parentName:"span",className:"mord"},"16")))))," bytes defined in ",(0,n.kt)("a",{parentName:"li",href:"#82-cryptographic-primitives"},"Section 8.2"),". The chosen scheme MUST yield a fixed-size padded output and MUST be consistent across all mix nodes to ensure correct interpretation during unpadding. For example, schemes that explicitly encode the padding length and prepend zero-valued padding bytes MAY be used."),(0,n.kt)("li",{parentName:"ul"},"Let the resulting message be ",(0,n.kt)("span",{parentName:"li",className:"math math-inline"},(0,n.kt)("span",{parentName:"span",className:"katex"},(0,n.kt)("span",{parentName:"span",className:"katex-mathml"},(0,n.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,n.kt)("semantics",{parentName:"math"},(0,n.kt)("mrow",{parentName:"semantics"},(0,n.kt)("mi",{parentName:"mrow"},"m")),(0,n.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"m")))),(0,n.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"0.4306em"}}),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal"},"m"))))),"."))),(0,n.kt)("li",{parentName:"ol"},(0,n.kt)("p",{parentName:"li"},(0,n.kt)("strong",{parentName:"p"},"Select A Mix Path")),(0,n.kt)("ul",{parentName:"li"},(0,n.kt)("li",{parentName:"ul"},"First obtain an unbiased random sample of live, routable mix nodes using some discovery mechanism. The choice of discovery mechanism is deployment-specific as defined in ",(0,n.kt)("a",{parentName:"li",href:"#61-discovery"},"Section 6.1"),". The discovery mechanism MUST be unbiased and provide, at a minimum, the multiaddress and X25519 public key of each mix node."),(0,n.kt)("li",{parentName:"ul"},"From this sample, choose a random mix path of length ",(0,n.kt)("span",{parentName:"li",className:"math math-inline"},(0,n.kt)("span",{parentName:"span",className:"katex"},(0,n.kt)("span",{parentName:"span",className:"katex-mathml"},(0,n.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,n.kt)("semantics",{parentName:"math"},(0,n.kt)("mrow",{parentName:"semantics"},(0,n.kt)("mi",{parentName:"mrow"},"L"),(0,n.kt)("mo",{parentName:"mrow"},"\u2265"),(0,n.kt)("mn",{parentName:"mrow"},"3")),(0,n.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"L \\geq 3")))),(0,n.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"0.8193em",verticalAlign:"-0.136em"}}),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal"},"L"),(0,n.kt)("span",{parentName:"span",className:"mspace",style:{marginRight:"0.2778em"}}),(0,n.kt)("span",{parentName:"span",className:"mrel"},"\u2265"),(0,n.kt)("span",{parentName:"span",className:"mspace",style:{marginRight:"0.2778em"}})),(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"0.6444em"}}),(0,n.kt)("span",{parentName:"span",className:"mord"},"3"))))),". As defined in ",(0,n.kt)("a",{parentName:"li",href:"#2-terminology"},"Section 2"),", a mix path is a non-repeating sequence of mix nodes."),(0,n.kt)("li",{parentName:"ul"},"For each hop ",(0,n.kt)("span",{parentName:"li",className:"math 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bytes as defined in Step 1."))),(0,n.kt)("p",{parentName:"li"},"e. 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",(0,n.kt)("strong",{parentName:"p"},"Transmit Packet")),(0,n.kt)("ul",{parentName:"li"},(0,n.kt)("li",{parentName:"ul"},"Sample a randomized delay from the same distribution family used for per-hop delays (in Step 3.e.) with an independently chosen mean.")),(0,n.kt)("p",{parentName:"li"},"This delay prevents timing correlation when multiple Sphinx packets are sent in quick succession.\nSuch bursts may occur when an upstream protocol fragments a large message, or when several messages are sent close together."),(0,n.kt)("ul",{parentName:"li"},(0,n.kt)("li",{parentName:"ul"},"After the randomized delay elapses, transmit the serialized packet to the first hop via a libp2p stream negotiated under the ",(0,n.kt)("inlineCode",{parentName:"li"},'"/mix/1.0.0"')," protocol identifier.")),(0,n.kt)("p",{parentName:"li"},"Implementations MAY reuse an existing stream to the first hop as described in ",(0,n.kt)("a",{parentName:"p",href:"#55-stream-management-and-multiplexing"},"Section 5.5"),", if doing so does not introduce any observable linkability between the packets."))),(0,n.kt)("p",null,"Once a Sphinx packet is constructed and transmitted by the initiating node, it is processed hop-by-hop by the remaining mix nodes in the path.\nEach node receives the packet over a libp2p stream negotiated under the ",(0,n.kt)("inlineCode",{parentName:"p"},'"/mix/1.0.0"')," protocol.\nThe following subsection defines the per-hop packet handling logic expected of each mix node, depending on whether it acts as an intermediary or an exit."),(0,n.kt)("h3",{id:"86-sphinx-packet-handling"},"8.6 Sphinx Packet Handling"),(0,n.kt)("p",null,"Each mix node MUST implement a handler for incoming data received over libp2p streams negotiated under the ",(0,n.kt)("inlineCode",{parentName:"p"},'"/mix/1.0.0"')," protocol identifier.\nThe incoming stream may have been reused by the previous hop, as described in ",(0,n.kt)("a",{parentName:"p",href:"#55-stream-management-and-multiplexing"},"Section 5.5"),".\nImplementations MUST ensure that packet handling remains stateless and unlinkable, regardless of stream reuse."),(0,n.kt)("p",null,"Upon receiving the stream payload, the node MUST interpret it as a Sphinx packet and process it in one of two roles","\u2014","intermediary or exit","\u2014"," as defined in ",(0,n.kt)("a",{parentName:"p",href:"#73-sphinx-packet-receiving-and-processing"},"Section 7.3"),".\nThis section defines the exact behavior for both roles."),(0,n.kt)("h4",{id:"861-shared-preprocessing"},"8.6.1 Shared Preprocessing"),(0,n.kt)("p",null,"Upon receiving a stream payload over a libp2p stream, the mix node MUST first deserialize it into a Sphinx packet ",(0,n.kt)("inlineCode",{parentName:"p"},"(\u03b1, \u03b2, \u03b3, \u03b4)"),"."),(0,n.kt)("p",null,"The deserialized fields MUST match the sizes defined in ",(0,n.kt)("a",{parentName:"p",href:"#852-construction-steps"},"Section 8.5.2")," step 3.e., and the total packet length MUST match the fixed packet size defined in ",(0,n.kt)("a",{parentName:"p",href:"#832-payload-size"},"Section 8.3.2"),"."),(0,n.kt)("p",null,"If the stream payload does not match the expected length, it MUST be discarded and the processing MUST terminate."),(0,n.kt)("p",null,"After successful deserialization, the mix node performs the following steps:"),(0,n.kt)("ol",null,(0,n.kt)("li",{parentName:"ol"},(0,n.kt)("p",{parentName:"li"},(0,n.kt)("strong",{parentName:"p"},"Derive Session Key")),(0,n.kt)("p",{parentName:"li"},"Let ",(0,n.kt)("span",{parentName:"p",className:"math 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vlist-t2"},(0,n.kt)("span",{parentName:"span",className:"vlist-r"},(0,n.kt)("span",{parentName:"span",className:"vlist",style:{height:"0.6887em"}},(0,n.kt)("span",{parentName:"span",style:{top:"-2.453em",marginLeft:"0em",marginRight:"0.05em"}},(0,n.kt)("span",{parentName:"span",className:"pstrut",style:{height:"2.7em"}}),(0,n.kt)("span",{parentName:"span",className:"sizing reset-size6 size3 mtight"},(0,n.kt)("span",{parentName:"span",className:"mord mathnormal mtight",style:{marginRight:"0.03588em"}},"q"))),(0,n.kt)("span",{parentName:"span",style:{top:"-3.063em",marginRight:"0.05em"}},(0,n.kt)("span",{parentName:"span",className:"pstrut",style:{height:"2.7em"}}),(0,n.kt)("span",{parentName:"span",className:"sizing reset-size6 size3 mtight"},(0,n.kt)("span",{parentName:"span",className:"mbin 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\u03b1^x")))),(0,n.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"0.4306em"}}),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal"},"s"),(0,n.kt)("span",{parentName:"span",className:"mspace",style:{marginRight:"0.2778em"}}),(0,n.kt)("span",{parentName:"span",className:"mrel"},"="),(0,n.kt)("span",{parentName:"span",className:"mspace",style:{marginRight:"0.2778em"}})),(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"0.6644em"}}),(0,n.kt)("span",{parentName:"span",className:"mord"},(0,n.kt)("span",{parentName:"span",className:"mord 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math-inline"},(0,n.kt)("span",{parentName:"span",className:"katex"},(0,n.kt)("span",{parentName:"span",className:"katex-mathml"},(0,n.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,n.kt)("semantics",{parentName:"math"},(0,n.kt)("mrow",{parentName:"semantics"},(0,n.kt)("mi",{parentName:"mrow"},"H"),(0,n.kt)("mo",{parentName:"mrow",stretchy:"false"},"("),(0,n.kt)("mi",{parentName:"mrow"},"s"),(0,n.kt)("mo",{parentName:"mrow",stretchy:"false"},")")),(0,n.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"H(s)")))),(0,n.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"1em",verticalAlign:"-0.25em"}}),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.08125em"}},"H"),(0,n.kt)("span",{parentName:"span",className:"mopen"},"("),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal"},"s"),(0,n.kt)("span",{parentName:"span",className:"mclose"},")"))))),"."),(0,n.kt)("li",{parentName:"ul"},"If the tag exists in the node's table of previously seen tags, discard the packet and terminate processing."),(0,n.kt)("li",{parentName:"ul"},"Otherwise, store the tag in the table.")),(0,n.kt)("p",{parentName:"li"},"The table MAY be flushed when the node rotates its private key.\nImplementations SHOULD perform this cleanup securely and automatically.")),(0,n.kt)("li",{parentName:"ol"},(0,n.kt)("p",{parentName:"li"},(0,n.kt)("strong",{parentName:"p"},"Check Header Integrity")),(0,n.kt)("ul",{parentName:"li"},(0,n.kt)("li",{parentName:"ul"},(0,n.kt)("p",{parentName:"li"},"Derive the MAC key from the session secret ",(0,n.kt)("span",{parentName:"p",className:"math 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text"},(0,n.kt)("span",{parentName:"span",className:"mord"},"\xa0to\xa0the\xa0end\xa0of\xa0the\xa0string\xa0using\xa0zero-based\xa0indexing."))))),(0,n.kt)("span",{parentName:"span",className:"vlist-s"},"\u200b")),(0,n.kt)("span",{parentName:"span",className:"vlist-r"},(0,n.kt)("span",{parentName:"span",className:"vlist",style:{height:"0.4185em"}},(0,n.kt)("span",{parentName:"span"}))))),(0,n.kt)("span",{parentName:"span",className:"arraycolsep",style:{width:"0.5em"}}))),(0,n.kt)("span",{parentName:"span",className:"mord"},"\u2018"))))))))),(0,n.kt)("li",{parentName:"ol"},(0,n.kt)("p",{parentName:"li"},(0,n.kt)("strong",{parentName:"p"},"Extract Application Message")),(0,n.kt)("p",{parentName:"li"},"Interpret recovered ",(0,n.kt)("span",{parentName:"p",className:"math math-inline"},(0,n.kt)("span",{parentName:"span",className:"katex"},(0,n.kt)("span",{parentName:"span",className:"katex-mathml"},(0,n.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,n.kt)("semantics",{parentName:"math"},(0,n.kt)("mrow",{parentName:"semantics"},(0,n.kt)("mi",{parentName:"mrow"},"m")),(0,n.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"m")))),(0,n.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"0.4306em"}}),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal"},"m")))))," according to the construction steps defined in ",(0,n.kt)("a",{parentName:"p",href:"#852-construction-steps"},"Section 8.5.2")," step 1.:"),(0,n.kt)("ul",{parentName:"li"},(0,n.kt)("li",{parentName:"ul"},(0,n.kt)("p",{parentName:"li"},"First, unpad ",(0,n.kt)("span",{parentName:"p",className:"math math-inline"},(0,n.kt)("span",{parentName:"span",className:"katex"},(0,n.kt)("span",{parentName:"span",className:"katex-mathml"},(0,n.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,n.kt)("semantics",{parentName:"math"},(0,n.kt)("mrow",{parentName:"semantics"},(0,n.kt)("mi",{parentName:"mrow"},"m")),(0,n.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"m")))),(0,n.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"0.4306em"}}),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal"},"m")))))," using the deterministic padding scheme defined during construction.")),(0,n.kt)("li",{parentName:"ul"},(0,n.kt)("p",{parentName:"li"},"Next, parse the unpadded message deterministically to extract:"),(0,n.kt)("ul",{parentName:"li"},(0,n.kt)("li",{parentName:"ul"},"zero or more SURBs"),(0,n.kt)("li",{parentName:"ul"},"the origin protocol codec"),(0,n.kt)("li",{parentName:"ul"},"the serialized application message"))),(0,n.kt)("li",{parentName:"ul"},(0,n.kt)("p",{parentName:"li"},"Extract SURBs , and identify protocol codec , consistent with the format and extensions applied by the initiator.\nThe application message itself MUST remain serialized.")),(0,n.kt)("li",{parentName:"ul"},(0,n.kt)("p",{parentName:"li"},"If parsing fails at any stage, discard ",(0,n.kt)("span",{parentName:"p",className:"math math-inline"},(0,n.kt)("span",{parentName:"span",className:"katex"},(0,n.kt)("span",{parentName:"span",className:"katex-mathml"},(0,n.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,n.kt)("semantics",{parentName:"math"},(0,n.kt)("mrow",{parentName:"semantics"},(0,n.kt)("mi",{parentName:"mrow"},"m")),(0,n.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"m")))),(0,n.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"0.4306em"}}),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal"},"m")))))," and terminate processing.")))),(0,n.kt)("li",{parentName:"ol"},(0,n.kt)("p",{parentName:"li"},(0,n.kt)("strong",{parentName:"p"},"Handoff to Exit Layer")),(0,n.kt)("ul",{parentName:"li"},(0,n.kt)("li",{parentName:"ul"},(0,n.kt)("p",{parentName:"li"},"Hand off the serialized application message, the origin protocol codec, and destination address ",(0,n.kt)("span",{parentName:"p",className:"math math-inline"},(0,n.kt)("span",{parentName:"span",className:"katex"},(0,n.kt)("span",{parentName:"span",className:"katex-mathml"},(0,n.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,n.kt)("semantics",{parentName:"math"},(0,n.kt)("mrow",{parentName:"semantics"},(0,n.kt)("mi",{parentName:"mrow",mathvariant:"normal"},"\u0394")),(0,n.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"\u0394")))),(0,n.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"0.6833em"}}),(0,n.kt)("span",{parentName:"span",className:"mord"},"\u0394")))))," (extracted in step 1.) to the local Exit layer for further processing and delivery.")),(0,n.kt)("li",{parentName:"ul"},(0,n.kt)("p",{parentName:"li"},"The Exit Layer is responsible for establishing a client-only connection and forwarding the message to the destination. Implementations MAY reuse an existing stream to the destination, if doing so does not introduce any observable linkability between forwarded messages."))))),(0,n.kt)("h2",{id:"9-spam-protection-architecture"},"9. Spam Protection Architecture"),(0,n.kt)("p",null,"This section provides detailed specifications for integrating a spam protection mechanism with the Mix Protocol.\nAs introduced in ",(0,n.kt)("a",{parentName:"p",href:"#63-spam-protection"},"Section 6.3"),", Mix protocol supports a pluggable spam protection mechanism.\nThis section defines design requirements, architectural approaches, packet structure modifications, and node responsibilities for spam protection.\nThis section also defines the interfaces between the Mix Protocol and spam protection mechanisms."),(0,n.kt)("h3",{id:"91-spam-protection-mechanism-requirements"},"9.1 Spam Protection Mechanism Requirements"),(0,n.kt)("p",null,"Any spam protection mechanism integrated with the Mix Protocol MUST satisfy the following requirements:"),(0,n.kt)("ul",null,(0,n.kt)("li",{parentName:"ul"},(0,n.kt)("p",{parentName:"li"},"Each mix node in the path MUST verify proofs before applying delay and forwarding or taking further action (in the case of exit nodes).")),(0,n.kt)("li",{parentName:"ul"},(0,n.kt)("p",{parentName:"li"},"Spam protection data and verification MUST NOT enable linking or correlating packets across hops.\nTherefore, spam protection proofs MUST be unique per hop.")),(0,n.kt)("li",{parentName:"ul"},(0,n.kt)("p",{parentName:"li"},"Spam protection proofs MUST NOT be reusable across different packets or hops.\nEach hop SHOULD be able to detect replayed or forged proofs (e.g., via cryptographic binding to packet-specific or hop-specific data).")),(0,n.kt)("li",{parentName:"ul"},(0,n.kt)("p",{parentName:"li"},"Proofs SHOULD be bound to unique signals per message that cannot be known in advance, preventing adversaries from pre-computing large batches of proofs offline for spam attacks.")),(0,n.kt)("li",{parentName:"ul"},(0,n.kt)("p",{parentName:"li"},"Verification overhead MUST be low to minimise per-hop delays.\nOtherwise, the spam protection mechanism would add substantial delay at each hop.")),(0,n.kt)("li",{parentName:"ul"},(0,n.kt)("p",{parentName:"li"},"Proof generation and verification methods MUST preserve unlinkability of the sender and MUST NOT leak any additional metadata about the sender or node.")),(0,n.kt)("li",{parentName:"ul"},(0,n.kt)("p",{parentName:"li"},"The mechanism SHOULD provide a way to punish spammers or detect misuse."))),(0,n.kt)("h3",{id:"92-integration-architecture"},"9.2 Integration Architecture"),(0,n.kt)("p",null,"Two primary architectural approaches exist for integrating spam protection with the Mix Protocol, each with distinct trade-offs.\nThis section elaborates on each approach and also lists down trade-offs and provides a comparison which helps in making a decision for deployments."),(0,n.kt)("h4",{id:"921-sender-generated-proofs"},"9.2.1 Sender-Generated Proofs"),(0,n.kt)("p",null,"In this approach, the sender generates spam protection proofs for all hops in the mix path during Sphinx packet construction.\nProofs are embedded within each hop's routing block in the encrypted header ",(0,n.kt)("span",{parentName:"p",className:"math math-inline"},(0,n.kt)("span",{parentName:"span",className:"katex"},(0,n.kt)("span",{parentName:"span",className:"katex-mathml"},(0,n.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,n.kt)("semantics",{parentName:"math"},(0,n.kt)("mrow",{parentName:"semantics"},(0,n.kt)("mi",{parentName:"mrow"},"\u03b2")),(0,n.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"\\beta")))),(0,n.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"0.8889em",verticalAlign:"-0.1944em"}}),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.05278em"}},"\u03b2"))))),"."),(0,n.kt)("h5",{id:"9211-how-it-works"},"9.2.1.1 How It Works"),(0,n.kt)("p",null,"During Sphinx packet construction, as defined in ",(0,n.kt)("a",{parentName:"p",href:"#852-construction-steps"},"Section 8.5.2"),", the sender follows the standard construction process (computing ephemeral secrets in step 3.a and encrypted payloads in step 3.d).\nAfter steps 3.a and 3.d, the sender additionally performs the following spam protection steps:"),(0,n.kt)("ol",null,(0,n.kt)("li",{parentName:"ol"},(0,n.kt)("p",{parentName:"li"},(0,n.kt)("strong",{parentName:"p"},"Generate and Embed Proofs:"),"\nFor each hop ",(0,n.kt)("span",{parentName:"p",className:"math 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hop."),(0,n.kt)("li",{parentName:"ul"},"Each hop's proof is encrypted in a separate layer of ",(0,n.kt)("span",{parentName:"li",className:"math math-inline"},(0,n.kt)("span",{parentName:"span",className:"katex"},(0,n.kt)("span",{parentName:"span",className:"katex-mathml"},(0,n.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,n.kt)("semantics",{parentName:"math"},(0,n.kt)("mrow",{parentName:"semantics"},(0,n.kt)("mi",{parentName:"mrow"},"\u03b2")),(0,n.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"\\beta")))),(0,n.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"0.8889em",verticalAlign:"-0.1944em"}}),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.05278em"}},"\u03b2"))))),", making proofs unique per hop and cryptographically isolated."),(0,n.kt)("li",{parentName:"ul"},"Aligned with Sphinx philosophy wherein complexity is at the sender while intermediate nodes perform lightweight operations.")),(0,n.kt)("h5",{id:"9213-disadvantages"},"9.2.1.3 Disadvantages"),(0,n.kt)("ul",null,(0,n.kt)("li",{parentName:"ul"},"Sender must generate ",(0,n.kt)("span",{parentName:"li",className:"math 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cannot reuse the proofs if two different paths are chosen for the same message."),(0,n.kt)("li",{parentName:"ul"},"Proofs can only be verified AFTER expensive Sphinx processing operations (session key derivation, replay checking, header integrity verification, and decryption), since they are encrypted within the ",(0,n.kt)("span",{parentName:"li",className:"math math-inline"},(0,n.kt)("span",{parentName:"span",className:"katex"},(0,n.kt)("span",{parentName:"span",className:"katex-mathml"},(0,n.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,n.kt)("semantics",{parentName:"math"},(0,n.kt)("mrow",{parentName:"semantics"},(0,n.kt)("mi",{parentName:"mrow"},"\u03b2")),(0,n.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"\\beta")))),(0,n.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"0.8889em",verticalAlign:"-0.1944em"}}),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.05278em"}},"\u03b2")))))," field and bound to the decrypted payload state ",(0,n.kt)("span",{parentName:"li",className:"math math-inline"},(0,n.kt)("span",{parentName:"span",className:"katex"},(0,n.kt)("span",{parentName:"span",className:"katex-mathml"},(0,n.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,n.kt)("semantics",{parentName:"math"},(0,n.kt)("mrow",{parentName:"semantics"},(0,n.kt)("msup",{parentName:"mrow"},(0,n.kt)("mi",{parentName:"msup"},"\u03b4"),(0,n.kt)("mo",{parentName:"msup",mathvariant:"normal",lspace:"0em",rspace:"0em"},"\u2032"))),(0,n.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"\\delta'")))),(0,n.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"0.7519em"}}),(0,n.kt)("span",{parentName:"span",className:"mord"},(0,n.kt)("span",{parentName:"span",className:"mord 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\\times |\\mathrm{spam\\_proof}|")))),(0,n.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"0.7278em",verticalAlign:"-0.0833em"}}),(0,n.kt)("span",{parentName:"span",className:"mord"},"5"),(0,n.kt)("span",{parentName:"span",className:"mspace",style:{marginRight:"0.2222em"}}),(0,n.kt)("span",{parentName:"span",className:"mbin"},"\xd7"),(0,n.kt)("span",{parentName:"span",className:"mspace",style:{marginRight:"0.2222em"}})),(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"1.06em",verticalAlign:"-0.31em"}}),(0,n.kt)("span",{parentName:"span",className:"mord"},"\u2223"),(0,n.kt)("span",{parentName:"span",className:"mord"},(0,n.kt)("span",{parentName:"span",className:"mord 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math-inline"},(0,n.kt)("span",{parentName:"span",className:"katex"},(0,n.kt)("span",{parentName:"span",className:"katex-mathml"},(0,n.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,n.kt)("semantics",{parentName:"math"},(0,n.kt)("mrow",{parentName:"semantics"},(0,n.kt)("mi",{parentName:"mrow"},"\u03b3")),(0,n.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"\\gamma")))),(0,n.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"0.625em",verticalAlign:"-0.1944em"}}),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.05556em"}},"\u03b3")))))," are transformed during Sphinx processing.\nThe proof MAY be bound to all the components of outgoing sphinx packet ",(0,n.kt)("span",{parentName:"p",className:"math 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better DoS protection by allowing nodes to reject invalid packets earlier, before performing costly cryptographic operations."),(0,n.kt)("li",{parentName:"ul"},"If a membership-based spam protection mechanism is used (",(0,n.kt)("em",{parentName:"li"},"e.g.,")," Rate Limiting Nullifiers), the same mechanism can provide Sybil resistance.\nNodes must prove membership or ownership of resources at each hop, making it economically infeasible to operate large numbers of Sybil nodes.")),(0,n.kt)("h5",{id:"9223-disadvantages"},"9.2.2.3 Disadvantages"),(0,n.kt)("ul",null,(0,n.kt)("li",{parentName:"ul"},"Each node must generate fresh proofs, adding additional latency and processing cost at each hop.\nThe proof generation latency can be overcome by doing pre-computation of proofs but the proofs would not be bound to message contents rather some other means to add uniqueness."),(0,n.kt)("li",{parentName:"ul"},"When using rate-limiting mechanisms (such as RLN), intermediate nodes may exhaust their rate limits due to random path selection by multiple independent senders, causing legitimate packets to be dropped even when no individual sender is misbehaving.\nThis creates availability bottlenecks at popular nodes and unpredictable message delivery.\nThis can be mitigated by assigning higher rate-limits to intermediate or popular nodes(e.g. tied to reputation).")),(0,n.kt)("h5",{id:"9224-impact-on-header-size"},"9.2.2.4 Impact on Header Size"),(0,n.kt)("p",null,"A new header field ",(0,n.kt)("span",{parentName:"p",className:"math 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\u03b4     |\n| 32 B   | variable | 16 B   | variable | variable |\n+--------+----------+--------+----------+----------+\n")),(0,n.kt)("p",null,"The size of ",(0,n.kt)("span",{parentName:"p",className:"math math-inline"},(0,n.kt)("span",{parentName:"span",className:"katex"},(0,n.kt)("span",{parentName:"span",className:"katex-mathml"},(0,n.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,n.kt)("semantics",{parentName:"math"},(0,n.kt)("mrow",{parentName:"semantics"},(0,n.kt)("mi",{parentName:"mrow"},"\u03c3")),(0,n.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"\\sigma")))),(0,n.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"0.4306em"}}),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.03588em"}},"\u03c3")))))," depends on the spam protection method."),(0,n.kt)("p",null,"With the current recommended values:"),(0,n.kt)("ul",null,(0,n.kt)("li",{parentName:"ul"},"Original header size: ",(0,n.kt)("span",{parentName:"li",className:"math math-inline"},(0,n.kt)("span",{parentName:"span",className:"katex"},(0,n.kt)("span",{parentName:"span",className:"katex-mathml"},(0,n.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,n.kt)("semantics",{parentName:"math"},(0,n.kt)("mrow",{parentName:"semantics"},(0,n.kt)("mn",{parentName:"mrow"},"624")),(0,n.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"624")))),(0,n.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"0.6444em"}}),(0,n.kt)("span",{parentName:"span",className:"mord"},"624")))))," bytes"),(0,n.kt)("li",{parentName:"ul"},"Header size increase: ",(0,n.kt)("span",{parentName:"li",className:"math math-inline"},(0,n.kt)("span",{parentName:"span",className:"katex"},(0,n.kt)("span",{parentName:"span",className:"katex-mathml"},(0,n.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,n.kt)("semantics",{parentName:"math"},(0,n.kt)("mrow",{parentName:"semantics"},(0,n.kt)("mi",{parentName:"mrow",mathvariant:"normal"},"\u2223"),(0,n.kt)("mi",{parentName:"mrow"},"\u03c3"),(0,n.kt)("mi",{parentName:"mrow",mathvariant:"normal"},"\u2223")),(0,n.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"|\\sigma|")))),(0,n.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"1em",verticalAlign:"-0.25em"}}),(0,n.kt)("span",{parentName:"span",className:"mord"},"\u2223"),(0,n.kt)("span",{parentName:"span",className:"mord 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Header size becomes: ",(0,n.kt)("span",{parentName:"p",className:"math math-inline"},(0,n.kt)("span",{parentName:"span",className:"katex"},(0,n.kt)("span",{parentName:"span",className:"katex-mathml"},(0,n.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,n.kt)("semantics",{parentName:"math"},(0,n.kt)("mrow",{parentName:"semantics"},(0,n.kt)("mn",{parentName:"mrow"},"624"),(0,n.kt)("mo",{parentName:"mrow"},"+"),(0,n.kt)("mn",{parentName:"mrow"},"300"),(0,n.kt)("mo",{parentName:"mrow"},"="),(0,n.kt)("mn",{parentName:"mrow"},"924")),(0,n.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"624 + 300 = 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bytes"),(0,n.kt)("h4",{id:"923-comparison"},"9.2.3 Comparison"),(0,n.kt)("p",null,"The following table provides a brief comparison between both integration approaches."),(0,n.kt)("table",null,(0,n.kt)("thead",{parentName:"table"},(0,n.kt)("tr",{parentName:"thead"},(0,n.kt)("th",{parentName:"tr",align:null},"Aspect"),(0,n.kt)("th",{parentName:"tr",align:null},"Sender-Generated Proofs"),(0,n.kt)("th",{parentName:"tr",align:null},"Per-Hop Generated Proofs"))),(0,n.kt)("tbody",{parentName:"table"},(0,n.kt)("tr",{parentName:"tbody"},(0,n.kt)("td",{parentName:"tr",align:null},(0,n.kt)("strong",{parentName:"td"},"DoS protection")),(0,n.kt)("td",{parentName:"tr",align:null},"Weaker (verify after Sphinx decryption)"),(0,n.kt)("td",{parentName:"tr",align:null},"Stronger (verify before Sphinx decryption)")),(0,n.kt)("tr",{parentName:"tbody"},(0,n.kt)("td",{parentName:"tr",align:null},(0,n.kt)("strong",{parentName:"td"},"Sender burden")),(0,n.kt)("td",{parentName:"tr",align:null},"High (generates 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overhead")),(0,n.kt)("td",{parentName:"tr",align:null},"Low (verify only)"),(0,n.kt)("td",{parentName:"tr",align:null},"High (verify + generate)")),(0,n.kt)("tr",{parentName:"tbody"},(0,n.kt)("td",{parentName:"tr",align:null},(0,n.kt)("strong",{parentName:"td"},"Per-hop latency")),(0,n.kt)("td",{parentName:"tr",align:null},"Minimal (fast verification)"),(0,n.kt)("td",{parentName:"tr",align:null},"Higher (mitigated with pre-computation)")),(0,n.kt)("tr",{parentName:"tbody"},(0,n.kt)("td",{parentName:"tr",align:null},(0,n.kt)("strong",{parentName:"td"},"Total end-to-end latency")),(0,n.kt)("td",{parentName:"tr",align:null},"Lower"),(0,n.kt)("td",{parentName:"tr",align:null},"Higher (mitigated with pre-computation)")),(0,n.kt)("tr",{parentName:"tbody"},(0,n.kt)("td",{parentName:"tr",align:null},(0,n.kt)("strong",{parentName:"td"},"Sybil resistance")),(0,n.kt)("td",{parentName:"tr",align:null},"Requires separate mechanism"),(0,n.kt)("td",{parentName:"tr",align:null},"Can be 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math-inline"},(0,n.kt)("span",{parentName:"span",className:"katex"},(0,n.kt)("span",{parentName:"span",className:"katex-mathml"},(0,n.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,n.kt)("semantics",{parentName:"math"},(0,n.kt)("mrow",{parentName:"semantics"},(0,n.kt)("mi",{parentName:"mrow"},"L"),(0,n.kt)("mo",{parentName:"mrow"},"\xd7"),(0,n.kt)("mrow",{parentName:"mrow"},(0,n.kt)("mi",{parentName:"mrow",mathvariant:"normal"},"s"),(0,n.kt)("mi",{parentName:"mrow",mathvariant:"normal"},"p"),(0,n.kt)("mi",{parentName:"mrow",mathvariant:"normal"},"a"),(0,n.kt)("mi",{parentName:"mrow",mathvariant:"normal"},"m"),(0,n.kt)("mi",{parentName:"mrow",mathvariant:"normal"},"_"),(0,n.kt)("mi",{parentName:"mrow",mathvariant:"normal"},"p"),(0,n.kt)("mi",{parentName:"mrow",mathvariant:"normal"},"r"),(0,n.kt)("mi",{parentName:"mrow",mathvariant:"normal"},"o"),(0,n.kt)("mi",{parentName:"mrow",mathvariant:"normal"},"o"),(0,n.kt)("mi",{parentName:"mrow",mathvariant:"normal"},"f"))),(0,n.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"L \\times \\mathrm{spam\\_proof}")))),(0,n.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"0.7667em",verticalAlign:"-0.0833em"}}),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal"},"L"),(0,n.kt)("span",{parentName:"span",className:"mspace",style:{marginRight:"0.2222em"}}),(0,n.kt)("span",{parentName:"span",className:"mbin"},"\xd7"),(0,n.kt)("span",{parentName:"span",className:"mspace",style:{marginRight:"0.2222em"}})),(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"1.0044em",verticalAlign:"-0.31em"}}),(0,n.kt)("span",{parentName:"span",className:"mord"},(0,n.kt)("span",{parentName:"span",className:"mord mathrm",style:{marginRight:"0.07778em"}},"spam_proof"))))))),(0,n.kt)("td",{parentName:"tr",align:null},(0,n.kt)("span",{parentName:"td",className:"math math-inline"},(0,n.kt)("span",{parentName:"span",className:"katex"},(0,n.kt)("span",{parentName:"span",className:"katex-mathml"},(0,n.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,n.kt)("semantics",{parentName:"math"},(0,n.kt)("mrow",{parentName:"semantics"},(0,n.kt)("mi",{parentName:"mrow",mathvariant:"normal"},"\u2225"),(0,n.kt)("mi",{parentName:"mrow"},"\u03c3"),(0,n.kt)("mi",{parentName:"mrow",mathvariant:"normal"},"\u2225")),(0,n.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"\\|\\sigma\\|")))),(0,n.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"1em",verticalAlign:"-0.25em"}}),(0,n.kt)("span",{parentName:"span",className:"mord"},"\u2225"),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.03588em"}},"\u03c3"),(0,n.kt)("span",{parentName:"span",className:"mord"},"\u2225"))))))))),(0,n.kt)("p",null,"Separate specifications defining concrete spam protection mechanisms SHOULD specify recommended approaches and provide detailed integration instructions."),(0,n.kt)("h3",{id:"93-node-responsibilities"},"9.3 Node Responsibilities"),(0,n.kt)("p",null,"In addition to the standard Sphinx processing responsibilities described in ",(0,n.kt)("a",{parentName:"p",href:"#8-sphinx-packet-format"},"Section 8"),", nodes MUST implement the following spam protection responsibilities based on the chosen architectural approach."),(0,n.kt)("h4",{id:"931-for-sender-generated-proofs"},"9.3.1 For Sender-Generated Proofs"),(0,n.kt)("ul",null,(0,n.kt)("li",{parentName:"ul"},(0,n.kt)("p",{parentName:"li"},(0,n.kt)("strong",{parentName:"p"},"Sender nodes"),": MUST generate spam protection proofs for each hop during packet construction as described in ",(0,n.kt)("a",{parentName:"p",href:"#9211-how-it-works"},"Section 9.2.1.1"),".\nThe sender MUST NOT include any identifying information in the proofs.")),(0,n.kt)("li",{parentName:"ul"},(0,n.kt)("p",{parentName:"li"},(0,n.kt)("strong",{parentName:"p"},"Intermediate and exit nodes"),": MUST verify the spam protection proof during packet processing as described in ",(0,n.kt)("a",{parentName:"p",href:"#9211-how-it-works"},"Section 9.2.1.1"),".\nVerification occurs after decrypting ",(0,n.kt)("span",{parentName:"p",className:"math math-inline"},(0,n.kt)("span",{parentName:"span",className:"katex"},(0,n.kt)("span",{parentName:"span",className:"katex-mathml"},(0,n.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,n.kt)("semantics",{parentName:"math"},(0,n.kt)("mrow",{parentName:"semantics"},(0,n.kt)("mi",{parentName:"mrow"},"\u03b2")),(0,n.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"\\beta")))),(0,n.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"0.8889em",verticalAlign:"-0.1944em"}}),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.05278em"}},"\u03b2")))))," and ",(0,n.kt)("span",{parentName:"p",className:"math math-inline"},(0,n.kt)("span",{parentName:"span",className:"katex"},(0,n.kt)("span",{parentName:"span",className:"katex-mathml"},(0,n.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,n.kt)("semantics",{parentName:"math"},(0,n.kt)("mrow",{parentName:"semantics"},(0,n.kt)("mi",{parentName:"mrow"},"\u03b4")),(0,n.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"\\delta")))),(0,n.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"0.6944em"}}),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.03785em"}},"\u03b4")))))," during the shared preprocessing steps in ",(0,n.kt)("a",{parentName:"p",href:"#861-shared-preprocessing"},"Section 8.6.1"),".\nIf verification fails, nodes MUST discard the packet and MAY apply penalties or rate-limiting measures."))),(0,n.kt)("h4",{id:"932-for-per-hop-generated-proofs"},"9.3.2 For Per-Hop Generated Proofs"),(0,n.kt)("ul",null,(0,n.kt)("li",{parentName:"ul"},(0,n.kt)("p",{parentName:"li"},(0,n.kt)("strong",{parentName:"p"},"Sender nodes"),": MUST generate the initial spam protection proof ",(0,n.kt)("span",{parentName:"p",className:"math math-inline"},(0,n.kt)("span",{parentName:"span",className:"katex"},(0,n.kt)("span",{parentName:"span",className:"katex-mathml"},(0,n.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,n.kt)("semantics",{parentName:"math"},(0,n.kt)("mrow",{parentName:"semantics"},(0,n.kt)("msub",{parentName:"mrow"},(0,n.kt)("mi",{parentName:"msub"},"\u03c3"),(0,n.kt)("mn",{parentName:"msub"},"0"))),(0,n.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"\\sigma_0")))),(0,n.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"0.5806em",verticalAlign:"-0.15em"}}),(0,n.kt)("span",{parentName:"span",className:"mord"},(0,n.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.03588em"}},"\u03c3"),(0,n.kt)("span",{parentName:"span",className:"msupsub"},(0,n.kt)("span",{parentName:"span",className:"vlist-t vlist-t2"},(0,n.kt)("span",{parentName:"span",className:"vlist-r"},(0,n.kt)("span",{parentName:"span",className:"vlist",style:{height:"0.3011em"}},(0,n.kt)("span",{parentName:"span",style:{top:"-2.55em",marginLeft:"-0.0359em",marginRight:"0.05em"}},(0,n.kt)("span",{parentName:"span",className:"pstrut",style:{height:"2.7em"}}),(0,n.kt)("span",{parentName:"span",className:"sizing reset-size6 size3 mtight"},(0,n.kt)("span",{parentName:"span",className:"mord mtight"},"0")))),(0,n.kt)("span",{parentName:"span",className:"vlist-s"},"\u200b")),(0,n.kt)("span",{parentName:"span",className:"vlist-r"},(0,n.kt)("span",{parentName:"span",className:"vlist",style:{height:"0.15em"}},(0,n.kt)("span",{parentName:"span"}))))))))))," for the first hop as described in ",(0,n.kt)("a",{parentName:"p",href:"#9221-how-it-works"},"Section 9.2.2.1"),".\nThe proof MAY be bound to the outgoing Sphinx packet and MUST NOT contain identifying information.")),(0,n.kt)("li",{parentName:"ul"},(0,n.kt)("p",{parentName:"li"},(0,n.kt)("strong",{parentName:"p"},"Intermediate nodes"),": MUST verify the incoming proof ",(0,n.kt)("span",{parentName:"p",className:"math math-inline"},(0,n.kt)("span",{parentName:"span",className:"katex"},(0,n.kt)("span",{parentName:"span",className:"katex-mathml"},(0,n.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,n.kt)("semantics",{parentName:"math"},(0,n.kt)("mrow",{parentName:"semantics"},(0,n.kt)("mi",{parentName:"mrow"},"\u03c3")),(0,n.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"\\sigma")))),(0,n.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"0.4306em"}}),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.03588em"}},"\u03c3")))))," BEFORE any other Sphinx processing.\nIf verification fails, nodes MUST discard the packet and MAY apply penalties or rate-limiting measures to the previous hop.\nIf incoming proof is valid, nodes MUST generate a fresh proof ",(0,n.kt)("span",{parentName:"p",className:"math math-inline"},(0,n.kt)("span",{parentName:"span",className:"katex"},(0,n.kt)("span",{parentName:"span",className:"katex-mathml"},(0,n.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,n.kt)("semantics",{parentName:"math"},(0,n.kt)("mrow",{parentName:"semantics"},(0,n.kt)("msup",{parentName:"mrow"},(0,n.kt)("mi",{parentName:"msup"},"\u03c3"),(0,n.kt)("mo",{parentName:"msup",mathvariant:"normal",lspace:"0em",rspace:"0em"},"\u2032"))),(0,n.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"\\sigma'")))),(0,n.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"0.7519em"}}),(0,n.kt)("span",{parentName:"span",className:"mord"},(0,n.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.03588em"}},"\u03c3"),(0,n.kt)("span",{parentName:"span",className:"msupsub"},(0,n.kt)("span",{parentName:"span",className:"vlist-t"},(0,n.kt)("span",{parentName:"span",className:"vlist-r"},(0,n.kt)("span",{parentName:"span",className:"vlist",style:{height:"0.7519em"}},(0,n.kt)("span",{parentName:"span",style:{top:"-3.063em",marginRight:"0.05em"}},(0,n.kt)("span",{parentName:"span",className:"pstrut",style:{height:"2.7em"}}),(0,n.kt)("span",{parentName:"span",className:"sizing reset-size6 size3 mtight"},(0,n.kt)("span",{parentName:"span",className:"mord mtight"},(0,n.kt)("span",{parentName:"span",className:"mord mtight"},"\u2032")))))))))))))," for the next hop that is unlinkable from ",(0,n.kt)("span",{parentName:"p",className:"math math-inline"},(0,n.kt)("span",{parentName:"span",className:"katex"},(0,n.kt)("span",{parentName:"span",className:"katex-mathml"},(0,n.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,n.kt)("semantics",{parentName:"math"},(0,n.kt)("mrow",{parentName:"semantics"},(0,n.kt)("mi",{parentName:"mrow"},"\u03c3")),(0,n.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"\\sigma")))),(0,n.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"0.4306em"}}),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.03588em"}},"\u03c3"))))),".")),(0,n.kt)("li",{parentName:"ul"},(0,n.kt)("p",{parentName:"li"},(0,n.kt)("strong",{parentName:"p"},"Exit nodes"),": MUST verify the incoming proof ",(0,n.kt)("span",{parentName:"p",className:"math math-inline"},(0,n.kt)("span",{parentName:"span",className:"katex"},(0,n.kt)("span",{parentName:"span",className:"katex-mathml"},(0,n.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,n.kt)("semantics",{parentName:"math"},(0,n.kt)("mrow",{parentName:"semantics"},(0,n.kt)("mi",{parentName:"mrow"},"\u03c3")),(0,n.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"\\sigma")))),(0,n.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"0.4306em"}}),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.03588em"}},"\u03c3")))))," before decrypting the final payload.\nExit nodes do not generate new proofs."))),(0,n.kt)("h3",{id:"94-anonymity-and-security-considerations"},"9.4 Anonymity and Security Considerations"),(0,n.kt)("p",null,"Spam protection mechanisms MUST be carefully designed to avoid introducing correlation risks:"),(0,n.kt)("ul",null,(0,n.kt)("li",{parentName:"ul"},(0,n.kt)("p",{parentName:"li"},(0,n.kt)("strong",{parentName:"p"},"Timing side channels"),": Proof verification and generation time SHOULD be constant to prevent packet fingerprinting through timing analysis.")),(0,n.kt)("li",{parentName:"ul"},(0,n.kt)("p",{parentName:"li"},(0,n.kt)("strong",{parentName:"p"},"Proof uniqueness and unlinkability"),": Each hop's proof MUST be unique and unlinkable from other hops' proofs.")),(0,n.kt)("li",{parentName:"ul"},(0,n.kt)("p",{parentName:"li"},(0,n.kt)("strong",{parentName:"p"},"Verification failure handling"),": Nodes MUST handle failures in a manner such that probing attacks can be prevented.")),(0,n.kt)("li",{parentName:"ul"},(0,n.kt)("p",{parentName:"li"},(0,n.kt)("strong",{parentName:"p"},"Global state and coordination"),": Mechanisms requiring global state MUST ensure access/updates don't leak any additional information.\nState lookups SHOULD use privacy-preserving techniques.")),(0,n.kt)("li",{parentName:"ul"},(0,n.kt)("p",{parentName:"li"},(0,n.kt)("strong",{parentName:"p"},"Sybil attacks"),": For sender-generated proofs, Sybil resistance cannot be included and nodes can still perform Sybil attacks by colluding.\nFor per-hop generation, membership-based methods can provide Sybil resistance."))),(0,n.kt)("h3",{id:"95-recommended-methods"},"9.5 Recommended Methods"),(0,n.kt)("p",null,"Specific spam protection methods fall outside this specification's scope.\nCommon strategies that MAY be adapted include:"),(0,n.kt)("ul",null,(0,n.kt)("li",{parentName:"ul"},(0,n.kt)("p",{parentName:"li"},(0,n.kt)("strong",{parentName:"p"},"PoW style approaches"),": Approaches like ",(0,n.kt)("a",{parentName:"p",href:"https://github.com/khovratovich/equihash"},"EquiHash")," or ",(0,n.kt)("a",{parentName:"p",href:"https://www.researchgate.net/publication/356450648_Non-Interactive_VDF_Client_Puzzle_for_DoS_Mitigation"},"VDF Client puzzles")," that satisfy spam protection requirements can be used.\nThese, however, do not provide Sybil resistance, which would require a separate mechanism.")),(0,n.kt)("li",{parentName:"ul"},(0,n.kt)("p",{parentName:"li"},(0,n.kt)("strong",{parentName:"p"},"Privacy preserving Rate-limiting"),": Rate limiting approaches like ",(0,n.kt)("a",{parentName:"p",href:"https://rate-limiting-nullifier.github.io/rln-docs/rln_in_details.html"},"RLN")," with zero-knowledge cryptography that preserve user's privacy can be used.\nRequires careful design of state access patterns.\nMay need to be augmented with staking and slashing to add Sybil resistance."))),(0,n.kt)("p",null,"Deployments MUST evaluate each method's computational overhead, latency impact, anonymity implications, infrastructure requirements, attack resistance, Sybil resistance, pre-computation resistance, economic cost, and architectural fit."),(0,n.kt)("h3",{id:"96-spam-protection-interface"},"9.6 Spam Protection Interface"),(0,n.kt)("p",null,"This section defines the standardized interface that spam protection mechanisms MUST implement to integrate with the Mix Protocol.\nThe interface is designed to be architecture-agnostic, supporting both sender-generated proofs and Per-Hop Generated Proofs approaches described in ",(0,n.kt)("a",{parentName:"p",href:"#92-integration-architecture"},"Section 9.2"),"."),(0,n.kt)("p",null,"Initialization and configuration of spam protection mechanisms is out of scope for this interface specification.\nImplementations are expected to handle their own initialization, configuration management, and runtime state independently before being integrated with the Mix Protocol."),(0,n.kt)("p",null,"Any spam protection mechanism integrated with the Mix Protocol MUST provide implementations of the procedures defined in this section.\nThe specific cryptographic constructions, proof systems, and verification logic are left to the mechanism's specification, but the interface signatures and the behavior defined here MUST be adhered to for interoperability."),(0,n.kt)("h4",{id:"961-deployment-configuration"},"9.6.1 Deployment Configuration"),(0,n.kt)("p",null,"The following parameters MUST be agreed upon and configured consistently across all nodes in a deployment:"),(0,n.kt)("ul",null,(0,n.kt)("li",{parentName:"ul"},(0,n.kt)("p",{parentName:"li"},(0,n.kt)("strong",{parentName:"p"},"Proof Size"),": The fixed size in bytes of ",(0,n.kt)("inlineCode",{parentName:"p"},"encoded_proof_data")," produced by ",(0,n.kt)("inlineCode",{parentName:"p"},"GenerateProof"),".\nThis value is used by Mix Protocol implementations to calculate header sizes and payload capacity.")),(0,n.kt)("li",{parentName:"ul"},(0,n.kt)("p",{parentName:"li"},(0,n.kt)("strong",{parentName:"p"},"Integration Architecture"),": The spam protection integration architecture used by the deployment.\nMust be one of:"),(0,n.kt)("ul",{parentName:"li"},(0,n.kt)("li",{parentName:"ul"},(0,n.kt)("inlineCode",{parentName:"li"},"SENDER_GENERATED_PER_HOP"),": Sender generates proofs for each hop (see ",(0,n.kt)("a",{parentName:"li",href:"#9631-for-sender-generated-proofs"},"Section 9.6.3.1"),")"),(0,n.kt)("li",{parentName:"ul"},(0,n.kt)("inlineCode",{parentName:"li"},"PER_HOP_GENERATION"),": Each node generates a fresh proof for the next hop (see ",(0,n.kt)("a",{parentName:"li",href:"#9632-for-per-hop-generated-proofs"},"Section 9.6.3.2"),")")))),(0,n.kt)("p",null,"All nodes in a deployment MUST use the same integration architecture.\nNodes MUST refuse to process packets that do not conform to the deployment's configured architecture."),(0,n.kt)("h4",{id:"962-interface-procedures"},"9.6.2 Interface Procedures"),(0,n.kt)("p",null,"All spam protection mechanisms MUST implement the following procedures."),(0,n.kt)("h5",{id:"9621-proof-generation"},"9.6.2.1 Proof Generation"),(0,n.kt)("p",null,(0,n.kt)("inlineCode",{parentName:"p"},"GenerateProof(binding_data) -> encoded_proof_data")),(0,n.kt)("p",null,"Generate a spam protection proof bound to specific packet data."),(0,n.kt)("p",null,(0,n.kt)("strong",{parentName:"p"},"Parameters"),":"),(0,n.kt)("ul",null,(0,n.kt)("li",{parentName:"ul"},(0,n.kt)("inlineCode",{parentName:"li"},"binding_data"),": The packet-specific data to which the proof MAY be cryptographically bound.\nFor sender-generated proofs, this is ",(0,n.kt)("span",{parentName:"li",className:"math math-inline"},(0,n.kt)("span",{parentName:"span",className:"katex"},(0,n.kt)("span",{parentName:"span",className:"katex-mathml"},(0,n.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,n.kt)("semantics",{parentName:"math"},(0,n.kt)("mrow",{parentName:"semantics"},(0,n.kt)("msub",{parentName:"mrow"},(0,n.kt)("mi",{parentName:"msub"},"\u03b4"),(0,n.kt)("mrow",{parentName:"msub"},(0,n.kt)("mi",{parentName:"mrow"},"i"),(0,n.kt)("mo",{parentName:"mrow"},"+"),(0,n.kt)("mn",{parentName:"mrow"},"1")))),(0,n.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"\\delta_{i+1}")))),(0,n.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"0.9028em",verticalAlign:"-0.2083em"}}),(0,n.kt)("span",{parentName:"span",className:"mord"},(0,n.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.03785em"}},"\u03b4"),(0,n.kt)("span",{parentName:"span",className:"msupsub"},(0,n.kt)("span",{parentName:"span",className:"vlist-t vlist-t2"},(0,n.kt)("span",{parentName:"span",className:"vlist-r"},(0,n.kt)("span",{parentName:"span",className:"vlist",style:{height:"0.3117em"}},(0,n.kt)("span",{parentName:"span",style:{top:"-2.55em",marginLeft:"-0.0379em",marginRight:"0.05em"}},(0,n.kt)("span",{parentName:"span",className:"pstrut",style:{height:"2.7em"}}),(0,n.kt)("span",{parentName:"span",className:"sizing reset-size6 size3 mtight"},(0,n.kt)("span",{parentName:"span",className:"mord mtight"},(0,n.kt)("span",{parentName:"span",className:"mord mathnormal mtight"},"i"),(0,n.kt)("span",{parentName:"span",className:"mbin mtight"},"+"),(0,n.kt)("span",{parentName:"span",className:"mord mtight"},"1"))))),(0,n.kt)("span",{parentName:"span",className:"vlist-s"},"\u200b")),(0,n.kt)("span",{parentName:"span",className:"vlist-r"},(0,n.kt)("span",{parentName:"span",className:"vlist",style:{height:"0.2083em"}},(0,n.kt)("span",{parentName:"span"}))))))))))," (the decrypted payload that hop ",(0,n.kt)("span",{parentName:"li",className:"math math-inline"},(0,n.kt)("span",{parentName:"span",className:"katex"},(0,n.kt)("span",{parentName:"span",className:"katex-mathml"},(0,n.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,n.kt)("semantics",{parentName:"math"},(0,n.kt)("mrow",{parentName:"semantics"},(0,n.kt)("mi",{parentName:"mrow"},"i")),(0,n.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"i")))),(0,n.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"0.6595em"}}),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal"},"i")))))," will see).\nFor per-hop generated proofs, this is the complete outgoing Sphinx packet state ",(0,n.kt)("span",{parentName:"li",className:"math math-inline"},(0,n.kt)("span",{parentName:"span",className:"katex"},(0,n.kt)("span",{parentName:"span",className:"katex-mathml"},(0,n.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,n.kt)("semantics",{parentName:"math"},(0,n.kt)("mrow",{parentName:"semantics"},(0,n.kt)("mo",{parentName:"mrow",stretchy:"false"},"("),(0,n.kt)("msup",{parentName:"mrow"},(0,n.kt)("mi",{parentName:"msup"},"\u03b1"),(0,n.kt)("mo",{parentName:"msup",mathvariant:"normal",lspace:"0em",rspace:"0em"},"\u2032")),(0,n.kt)("mo",{parentName:"mrow",separator:"true"},","),(0,n.kt)("msup",{parentName:"mrow"},(0,n.kt)("mi",{parentName:"msup"},"\u03b2"),(0,n.kt)("mo",{parentName:"msup",mathvariant:"normal",lspace:"0em",rspace:"0em"},"\u2032")),(0,n.kt)("mo",{parentName:"mrow",separator:"true"},","),(0,n.kt)("msup",{parentName:"mrow"},(0,n.kt)("mi",{parentName:"msup"},"\u03b3"),(0,n.kt)("mo",{parentName:"msup",mathvariant:"normal",lspace:"0em",rspace:"0em"},"\u2032")),(0,n.kt)("mo",{parentName:"mrow",separator:"true"},","),(0,n.kt)("msup",{parentName:"mrow"},(0,n.kt)("mi",{parentName:"msup"},"\u03b4"),(0,n.kt)("mo",{parentName:"msup",mathvariant:"normal",lspace:"0em",rspace:"0em"},"\u2032")),(0,n.kt)("mo",{parentName:"mrow",stretchy:"false"},")")),(0,n.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"(\\alpha', \\beta', \\gamma', \\delta')")))),(0,n.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"1.0019em",verticalAlign:"-0.25em"}}),(0,n.kt)("span",{parentName:"span",className:"mopen"},"("),(0,n.kt)("span",{parentName:"span",className:"mord"},(0,n.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.0037em"}},"\u03b1"),(0,n.kt)("span",{parentName:"span",className:"msupsub"},(0,n.kt)("span",{parentName:"span",className:"vlist-t"},(0,n.kt)("span",{parentName:"span",className:"vlist-r"},(0,n.kt)("span",{parentName:"span",className:"vlist",style:{height:"0.7519em"}},(0,n.kt)("span",{parentName:"span",style:{top:"-3.063em",marginRight:"0.05em"}},(0,n.kt)("span",{parentName:"span",className:"pstrut",style:{height:"2.7em"}}),(0,n.kt)("span",{parentName:"span",className:"sizing reset-size6 size3 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mtight"},(0,n.kt)("span",{parentName:"span",className:"mord mtight"},"\u2032"))))))))),(0,n.kt)("span",{parentName:"span",className:"mpunct"},","),(0,n.kt)("span",{parentName:"span",className:"mspace",style:{marginRight:"0.1667em"}}),(0,n.kt)("span",{parentName:"span",className:"mord"},(0,n.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.05556em"}},"\u03b3"),(0,n.kt)("span",{parentName:"span",className:"msupsub"},(0,n.kt)("span",{parentName:"span",className:"vlist-t"},(0,n.kt)("span",{parentName:"span",className:"vlist-r"},(0,n.kt)("span",{parentName:"span",className:"vlist",style:{height:"0.7519em"}},(0,n.kt)("span",{parentName:"span",style:{top:"-3.063em",marginRight:"0.05em"}},(0,n.kt)("span",{parentName:"span",className:"pstrut",style:{height:"2.7em"}}),(0,n.kt)("span",{parentName:"span",className:"sizing reset-size6 size3 mtight"},(0,n.kt)("span",{parentName:"span",className:"mord mtight"},(0,n.kt)("span",{parentName:"span",className:"mord mtight"},"\u2032"))))))))),(0,n.kt)("span",{parentName:"span",className:"mpunct"},","),(0,n.kt)("span",{parentName:"span",className:"mspace",style:{marginRight:"0.1667em"}}),(0,n.kt)("span",{parentName:"span",className:"mord"},(0,n.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.03785em"}},"\u03b4"),(0,n.kt)("span",{parentName:"span",className:"msupsub"},(0,n.kt)("span",{parentName:"span",className:"vlist-t"},(0,n.kt)("span",{parentName:"span",className:"vlist-r"},(0,n.kt)("span",{parentName:"span",className:"vlist",style:{height:"0.7519em"}},(0,n.kt)("span",{parentName:"span",style:{top:"-3.063em",marginRight:"0.05em"}},(0,n.kt)("span",{parentName:"span",className:"pstrut",style:{height:"2.7em"}}),(0,n.kt)("span",{parentName:"span",className:"sizing reset-size6 size3 mtight"},(0,n.kt)("span",{parentName:"span",className:"mord mtight"},(0,n.kt)("span",{parentName:"span",className:"mord mtight"},"\u2032"))))))))),(0,n.kt)("span",{parentName:"span",className:"mclose"},")"))))),".")),(0,n.kt)("p",null,(0,n.kt)("strong",{parentName:"p"},"Returns"),":"),(0,n.kt)("ul",null,(0,n.kt)("li",{parentName:"ul"},(0,n.kt)("inlineCode",{parentName:"li"},"encoded_proof_data"),": Serialized bytes containing the spam protection proof and any required verification metadata.\nThis is treated as opaque data by the Mix Protocol layer.")),(0,n.kt)("p",null,(0,n.kt)("strong",{parentName:"p"},"Requirements"),":"),(0,n.kt)("ul",null,(0,n.kt)("li",{parentName:"ul"},"The spam protection mechanism is responsible for managing its own runtime state (",(0,n.kt)("em",{parentName:"li"},"e.g.,")," current epochs, difficulty levels, merkle tree states).\nThe Mix Protocol layer does not provide or track mechanism-specific runtime context."),(0,n.kt)("li",{parentName:"ul"},"The encoding MUST produce a fixed-length output, or include a length prefix if variable-length encoding is used.")),(0,n.kt)("h5",{id:"9622-proof-verification"},"9.6.2.2 Proof Verification"),(0,n.kt)("p",null,(0,n.kt)("inlineCode",{parentName:"p"},"VerifyProof(encoded_proof_data, binding_data) -> valid")),(0,n.kt)("p",null,"Verify that a spam protection proof is valid and correctly bound to the provided packet data."),(0,n.kt)("p",null,(0,n.kt)("strong",{parentName:"p"},"Parameters"),":"),(0,n.kt)("ul",null,(0,n.kt)("li",{parentName:"ul"},(0,n.kt)("inlineCode",{parentName:"li"},"encoded_proof_data"),": Serialized bytes containing the spam protection proof and verification metadata, extracted from the routing block ",(0,n.kt)("span",{parentName:"li",className:"math 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math-inline"},(0,n.kt)("span",{parentName:"span",className:"katex"},(0,n.kt)("span",{parentName:"span",className:"katex-mathml"},(0,n.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,n.kt)("semantics",{parentName:"math"},(0,n.kt)("mrow",{parentName:"semantics"},(0,n.kt)("mi",{parentName:"mrow"},"\u03c3")),(0,n.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"\\sigma")))),(0,n.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"0.4306em"}}),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.03588em"}},"\u03c3")))))," (for per-hop generation approach)."),(0,n.kt)("li",{parentName:"ul"},(0,n.kt)("inlineCode",{parentName:"li"},"binding_data"),": The packet-specific data against which the proof SHOULD be verified.\nFor nodes verifying sender-generated proofs, this is ",(0,n.kt)("span",{parentName:"li",className:"math math-inline"},(0,n.kt)("span",{parentName:"span",className:"katex"},(0,n.kt)("span",{parentName:"span",className:"katex-mathml"},(0,n.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,n.kt)("semantics",{parentName:"math"},(0,n.kt)("mrow",{parentName:"semantics"},(0,n.kt)("msup",{parentName:"mrow"},(0,n.kt)("mi",{parentName:"msup"},"\u03b4"),(0,n.kt)("mo",{parentName:"msup",mathvariant:"normal",lspace:"0em",rspace:"0em"},"\u2032"))),(0,n.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"\\delta'")))),(0,n.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"0.7519em"}}),(0,n.kt)("span",{parentName:"span",className:"mord"},(0,n.kt)("span",{parentName:"span",className:"mord 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math-inline"},(0,n.kt)("span",{parentName:"span",className:"katex"},(0,n.kt)("span",{parentName:"span",className:"katex-mathml"},(0,n.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,n.kt)("semantics",{parentName:"math"},(0,n.kt)("mrow",{parentName:"semantics"},(0,n.kt)("mo",{parentName:"mrow",stretchy:"false"},"("),(0,n.kt)("msup",{parentName:"mrow"},(0,n.kt)("mi",{parentName:"msup"},"\u03b1"),(0,n.kt)("mo",{parentName:"msup",mathvariant:"normal",lspace:"0em",rspace:"0em"},"\u2032")),(0,n.kt)("mo",{parentName:"mrow",separator:"true"},","),(0,n.kt)("msup",{parentName:"mrow"},(0,n.kt)("mi",{parentName:"msup"},"\u03b2"),(0,n.kt)("mo",{parentName:"msup",mathvariant:"normal",lspace:"0em",rspace:"0em"},"\u2032")),(0,n.kt)("mo",{parentName:"mrow",separator:"true"},","),(0,n.kt)("msup",{parentName:"mrow"},(0,n.kt)("mi",{parentName:"msup"},"\u03b3"),(0,n.kt)("mo",{parentName:"msup",mathvariant:"normal",lspace:"0em",rspace:"0em"},"\u2032")),(0,n.kt)("mo",{parentName:"mrow",separator:"true"},","),(0,n.kt)("msup",{parentName:"mrow"},(0,n.kt)("mi",{parentName:"msup"},"\u03b4"),(0,n.kt)("mo",{parentName:"msup",mathvariant:"normal",lspace:"0em",rspace:"0em"},"\u2032")),(0,n.kt)("mo",{parentName:"mrow",stretchy:"false"},")")),(0,n.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"(\\alpha', 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mtight"},"\u2032"))))))))),(0,n.kt)("span",{parentName:"span",className:"mclose"},")"))))),".")),(0,n.kt)("p",null,(0,n.kt)("strong",{parentName:"p"},"Returns"),":"),(0,n.kt)("ul",null,(0,n.kt)("li",{parentName:"ul"},(0,n.kt)("inlineCode",{parentName:"li"},"valid"),": Boolean indicating whether the proof is valid.")),(0,n.kt)("p",null,(0,n.kt)("strong",{parentName:"p"},"Requirements"),":"),(0,n.kt)("ul",null,(0,n.kt)("li",{parentName:"ul"},"Implementations MUST handle malformed or truncated ",(0,n.kt)("inlineCode",{parentName:"li"},"encoded_proof_data")," gracefully and return ",(0,n.kt)("inlineCode",{parentName:"li"},"false"),"."),(0,n.kt)("li",{parentName:"ul"},"For mechanisms that maintain global state (",(0,n.kt)("em",{parentName:"li"},"e.g.,")," nullifier sets, rate-limit counters, membership trees), this procedure MUST update the internal state atomically when verification succeeds.\nState updates (",(0,n.kt)("em",{parentName:"li"},"e.g.,")," recording nullifiers, updating rate-limit counters) and state cleanup (",(0,n.kt)("em",{parentName:"li"},"e.g.,")," removing expired epochs, old nullifiers) are managed internally by the spam protection mechanism.")),(0,n.kt)("h4",{id:"963-integration-points-in-sphinx-processing"},"9.6.3 Integration Points in Sphinx Processing"),(0,n.kt)("p",null,"The Mix Protocol invokes spam protection procedures at specific points in Sphinx packet construction and processing:"),(0,n.kt)("h5",{id:"9631-for-sender-generated-proofs"},"9.6.3.1 For Sender-Generated Proofs"),(0,n.kt)("p",null,(0,n.kt)("strong",{parentName:"p"},"Sender Nodes - During Packet Construction")," (",(0,n.kt)("a",{parentName:"p",href:"#852-construction-steps"},"Section 8.5.2"),"):"),(0,n.kt)("p",null,"After computing encrypted payloads ",(0,n.kt)("span",{parentName:"p",className:"math 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each hop ",(0,n.kt)("span",{parentName:"li",className:"math math-inline"},(0,n.kt)("span",{parentName:"span",className:"katex"},(0,n.kt)("span",{parentName:"span",className:"katex-mathml"},(0,n.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,n.kt)("semantics",{parentName:"math"},(0,n.kt)("mrow",{parentName:"semantics"},(0,n.kt)("mi",{parentName:"mrow"},"i")),(0,n.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"i")))),(0,n.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"0.6595em"}}),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal"},"i")))))," in path (from ",(0,n.kt)("span",{parentName:"li",className:"math math-inline"},(0,n.kt)("span",{parentName:"span",className:"katex"},(0,n.kt)("span",{parentName:"span",className:"katex-mathml"},(0,n.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,n.kt)("semantics",{parentName:"math"},(0,n.kt)("mrow",{parentName:"semantics"},(0,n.kt)("mi",{parentName:"mrow"},"i"),(0,n.kt)("mo",{parentName:"mrow"},"="),(0,n.kt)("mn",{parentName:"mrow"},"0")),(0,n.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"i = 0")))),(0,n.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"0.6595em"}}),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal"},"i"),(0,n.kt)("span",{parentName:"span",className:"mspace",style:{marginRight:"0.2778em"}}),(0,n.kt)("span",{parentName:"span",className:"mrel"},"="),(0,n.kt)("span",{parentName:"span",className:"mspace",style:{marginRight:"0.2778em"}})),(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"0.6444em"}}),(0,n.kt)("span",{parentName:"span",className:"mord"},"0")))))," to ",(0,n.kt)("span",{parentName:"li",className:"math math-inline"},(0,n.kt)("span",{parentName:"span",className:"katex"},(0,n.kt)("span",{parentName:"span",className:"katex-mathml"},(0,n.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,n.kt)("semantics",{parentName:"math"},(0,n.kt)("mrow",{parentName:"semantics"},(0,n.kt)("mi",{parentName:"mrow"},"L"),(0,n.kt)("mo",{parentName:"mrow"},"\u2212"),(0,n.kt)("mn",{parentName:"mrow"},"1")),(0,n.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"L-1")))),(0,n.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"0.7667em",verticalAlign:"-0.0833em"}}),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal"},"L"),(0,n.kt)("span",{parentName:"span",className:"mspace",style:{marginRight:"0.2222em"}}),(0,n.kt)("span",{parentName:"span",className:"mbin"},"\u2212"),(0,n.kt)("span",{parentName:"span",className:"mspace",style:{marginRight:"0.2222em"}})),(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"0.6444em"}}),(0,n.kt)("span",{parentName:"span",className:"mord"},"1"))))),"):",(0,n.kt)("ul",{parentName:"li"},(0,n.kt)("li",{parentName:"ul"},"Call ",(0,n.kt)("inlineCode",{parentName:"li"},"GenerateProof(binding_data = \u03b4_{i+1})")," to generate ",(0,n.kt)("inlineCode",{parentName:"li"},"encoded_proof_data")," for hop ",(0,n.kt)("span",{parentName:"li",className:"math math-inline"},(0,n.kt)("span",{parentName:"span",className:"katex"},(0,n.kt)("span",{parentName:"span",className:"katex-mathml"},(0,n.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,n.kt)("semantics",{parentName:"math"},(0,n.kt)("mrow",{parentName:"semantics"},(0,n.kt)("mi",{parentName:"mrow"},"i")),(0,n.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"i")))),(0,n.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"0.6595em"}}),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal"},"i")))))),(0,n.kt)("li",{parentName:"ul"},"Embed the ",(0,n.kt)("inlineCode",{parentName:"li"},"encoded_proof_data")," in hop ",(0,n.kt)("span",{parentName:"li",className:"math math-inline"},(0,n.kt)("span",{parentName:"span",className:"katex"},(0,n.kt)("span",{parentName:"span",className:"katex-mathml"},(0,n.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,n.kt)("semantics",{parentName:"math"},(0,n.kt)("mrow",{parentName:"semantics"},(0,n.kt)("mi",{parentName:"mrow"},"i")),(0,n.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"i")))),(0,n.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"0.6595em"}}),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal"},"i"))))),"'s routing block within ",(0,n.kt)("span",{parentName:"li",className:"math 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Packet Processing")," (",(0,n.kt)("a",{parentName:"p",href:"#86-sphinx-packet-handling"},"Section 8.6"),"):"),(0,n.kt)("p",null,(0,n.kt)("strong",{parentName:"p"},"Before")," any Sphinx decryption operations, the node MUST:"),(0,n.kt)("ol",null,(0,n.kt)("li",{parentName:"ol"},"Call ",(0,n.kt)("inlineCode",{parentName:"li"},"VerifyProof(encoded_proof_data, binding_data)")," where ",(0,n.kt)("inlineCode",{parentName:"li"},"binding_data")," is the received packet state ",(0,n.kt)("span",{parentName:"li",className:"math math-inline"},(0,n.kt)("span",{parentName:"span",className:"katex"},(0,n.kt)("span",{parentName:"span",className:"katex-mathml"},(0,n.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,n.kt)("semantics",{parentName:"math"},(0,n.kt)("mrow",{parentName:"semantics"},(0,n.kt)("mo",{parentName:"mrow",stretchy:"false"},"("),(0,n.kt)("mi",{parentName:"mrow"},"\u03b1"),(0,n.kt)("mo",{parentName:"mrow",separator:"true"},","),(0,n.kt)("mi",{parentName:"mrow"},"\u03b2"),(0,n.kt)("mo",{parentName:"mrow",separator:"true"},","),(0,n.kt)("mi",{parentName:"mrow"},"\u03b3"),(0,n.kt)("mo",{parentName:"mrow",separator:"true"},","),(0,n.kt)("mi",{parentName:"mrow"},"\u03b4"),(0,n.kt)("mo",{parentName:"mrow",stretchy:"false"},")")),(0,n.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"(\\alpha, \\beta, \\gamma, \\delta)")))),(0,n.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"1em",verticalAlign:"-0.25em"}}),(0,n.kt)("span",{parentName:"span",className:"mopen"},"("),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.0037em"}},"\u03b1"),(0,n.kt)("span",{parentName:"span",className:"mpunct"},","),(0,n.kt)("span",{parentName:"span",className:"mspace",style:{marginRight:"0.1667em"}}),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.05278em"}},"\u03b2"),(0,n.kt)("span",{parentName:"span",className:"mpunct"},","),(0,n.kt)("span",{parentName:"span",className:"mspace",style:{marginRight:"0.1667em"}}),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.05556em"}},"\u03b3"),(0,n.kt)("span",{parentName:"span",className:"mpunct"},","),(0,n.kt)("span",{parentName:"span",className:"mspace",style:{marginRight:"0.1667em"}}),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.03785em"}},"\u03b4"),(0,n.kt)("span",{parentName:"span",className:"mclose"},")")))))),(0,n.kt)("li",{parentName:"ol"},"If the proof is not valid, discard the packet and terminate processing immediately (before session key derivation)"),(0,n.kt)("li",{parentName:"ol"},"If the proof is valid, generate fresh proof for next hop as explained above.")),(0,n.kt)("p",null,(0,n.kt)("strong",{parentName:"p"},"Exit nodes")," verify the incoming proof but do not generate a new proof."),(0,n.kt)("h2",{id:"10-security-considerations"},"10. Security Considerations"),(0,n.kt)("p",null,"This section describes the security guarantees and limitations of the Mix Protocol.\nIt begins by outlining the anonymity properties provided by the core protocol when routing messages through the mix network.\nIt then discusses the trust assumptions required at the edges of the network, particularly at the final hop.\nFinally, it presents an alternative trust model for destinations that support Mix Protocol directly, followed by a summary of broader limitations and areas that may be addressed in future iterations."),(0,n.kt)("h3",{id:"101-security-guarantees-of-the-core-mix-protocol"},"10.1 Security Guarantees of the Core Mix Protocol"),(0,n.kt)("p",null,"The core Mix Protocol","\u2014","comprising anonymous routing through a sequence of mix nodes using Sphinx packets","\u2014","provides the following security guarantees:"),(0,n.kt)("ul",null,(0,n.kt)("li",{parentName:"ul"},(0,n.kt)("strong",{parentName:"li"},"Sender anonymity"),": Each message is wrapped in layered encryption and routed independently, making it unlinkable to the sender even if multiple mix nodes are colluding."),(0,n.kt)("li",{parentName:"ul"},(0,n.kt)("strong",{parentName:"li"},"Metadata protection"),": All messages are fixed in size and indistinguishable on the wire. Sphinx packets reveal only the immediate next hop and delay to each mix node. No intermediate node learns its position in the path or the total pathlength."),(0,n.kt)("li",{parentName:"ul"},(0,n.kt)("strong",{parentName:"li"},"Traffic analysis resistance"),": Continuous-time mixing with randomized per-hop delays reduces the risk of timing correlation and input-output linkage."),(0,n.kt)("li",{parentName:"ul"},(0,n.kt)("strong",{parentName:"li"},"Per-hop confidentiality and integrity"),": Each hop decrypts only its assigned layer of the Sphinx packet and verifies header integrity via a per-hop MAC."),(0,n.kt)("li",{parentName:"ul"},(0,n.kt)("strong",{parentName:"li"},"No long-term state"),": All routing is stateless. Mix nodes do not maintain per-message metadata, reducing the surface for correlation attacks.")),(0,n.kt)("p",null,"These guarantees hold only within the boundaries of the Mix Protocol.\nAdditional trust assumptions are introduced at the edges, particularly at the final hop, where the decrypted message is handed off to the Mix Exit Layer for delivery to the destination outside the mixnet.\nThe next subsection discusses these trust assumptions in detail."),(0,n.kt)("h3",{id:"102-exit-node-trust-model"},"10.2 Exit Node Trust Model"),(0,n.kt)("p",null,"The Mix Protocol ensures strong sender anonymity and metadata protection between the Mix Entry and Exit layers.\nHowever, once a Sphinx packet is decrypted at the final hop, additional trust assumptions are introduced.\nThe node processing the final layer of encryption is trusted to forward the correct message to the destination and return any reply using the provided reply key.\nThis section outlines the resulting trust boundaries."),(0,n.kt)("h4",{id:"1021-message-delivery-and-origin-trust"},"10.2.1 Message Delivery and Origin Trust"),(0,n.kt)("p",null,"At the final hop, the decrypted Sphinx packet reveals the plaintext message and destination address.\nThe exit node is then trusted to deliver this message to the destination application, and","\u2014","if a reply is expected","\u2014","to return the response using the embedded reply key."),(0,n.kt)("p",null,"In this model, the exit node becomes a privileged middleman.\nIt has full visibility into the decrypted payload.\nSpecifically, the exit node could tamper with either direction of communication without detection:"),(0,n.kt)("ul",null,(0,n.kt)("li",{parentName:"ul"},"It may alter or drop the forwarded message."),(0,n.kt)("li",{parentName:"ul"},"It may fabricate a reply instead of forwarding the actual response from the destination.")),(0,n.kt)("p",null,"This limitation is consistent with the broader mixnet trust model.\nWhile intermediate nodes are constrained by layered encryption, edge nodes","\u2014","specifically the initiating and the exit nodes in the path","\u2014","are inherently more privileged and operate outside the cryptographic protections of the mixnet."),(0,n.kt)("p",null,"In systems like Tor, such exit-level tampering is mitigated by long-lived circuits that allow endpoints to negotiate shared session keys (",(0,n.kt)("em",{parentName:"p"},"e.g.,")," via TLS).\nA malicious exit cannot forge a valid forward message or response without access to these session secrets."),(0,n.kt)("p",null,"The Mix Protocol, by contrast, is stateless and message-based.\nEach message is routed independently, with no persistent circuit or session context.\nAs a result, endpoints cannot correlate messages, establish session keys, or validate message origin.\nThat is, the exit remains a necessary point of trust for message delivery and response handling."),(0,n.kt)("p",null,"The next subsection describes a related limitation:\nthe exit's ability to pose as a legitimate client to the destination's origin protocol, and how that can be abused to bypass application-layer expectations."),(0,n.kt)("h4",{id:"1022-origin-protocol-trust-and-client-role-abuse"},"10.2.2 Origin Protocol Trust and Client Role Abuse"),(0,n.kt)("p",null,"In addition to the message delivery and origin trust assumption, the exit node also initiates a client-side connection to the origin protocol instance at the destination.\nFrom the destination's perspective, this appears indistinguishable from a conventional peer connection, and the exit is accepted as a legitimate peer."),(0,n.kt)("p",null,"As a result, any protocol-level safeguards and integrity checks are applied to the exit node as well.\nHowever, since the exit node is not a verifiable peer and may open fresh connections at will, such protections are limited in their effectiveness.\nA malicious exit may repeatedly initiate new connections, send well-formed fabricated messages and circumvent any peer scoring mechanisms by reconnecting.\nThese messages are indistinguishable from legitimate peer messages from the destination's point of view."),(0,n.kt)("p",null,"This class of attack is distinct from basic message tampering.\nEven if the message content is well-formed and semantically valid, the exit's role as an unaccountable client allows it to bypass application-level assumptions about peer behavior.\nThis results in protocol misuse, targeted disruption, or spoofed message injection that the destination cannot attribute."),(0,n.kt)("p",null,"Despite these limitations, this model is compatible with legacy protocols and destinations that do not support the Mix Protocol.\nIt allows applications to preserve sender anonymity without requiring any participation from the recipient."),(0,n.kt)("p",null,"However, in scenarios that demand stronger end-to-end guarantees","\u2014","such as verifiable message delivery, origin authentication, or control over client access","\u2014","it may be beneficial for the destination itself to operate a Mix instance.\nThis alternative model is described in the next subsection."),(0,n.kt)("h3",{id:"103-destination-as-final-hop"},"10.3 Destination as Final Hop"),(0,n.kt)("p",null,"In some deployments, it may be desirable for the destination node to participate in the Mix Protocol directly.\nIn this model, the destination operates its own Mix instance and is selected as the final node in the mix path.\nThe decrypted message is then delivered by the Mix Exit Layer directly to the destination's local origin protocol instance, without relying on a separate exit node."),(0,n.kt)("p",null,"From a security standpoint, this model provides end-to-end integrity guarantees.\nIt removes the trust assumption on an external exit.\nThe message is decrypted and delivered entirely within the destination node, eliminating the risk of tampering during the final delivery step.\nThe response, if used, is also encrypted and returned by the destination itself, avoiding reliance on a third-party node to apply the reply key."),(0,n.kt)("p",null,"This model also avoids client role abuse.\nSince the Mix Exit Layer delivers the message locally, the destination need not accept arbitrary inbound connections from external clients.\nThis removes the risk of an adversarial exit posing as a peer and injecting protocol-compliant but unauthorized messages."),(0,n.kt)("p",null,"This approach does require the destination to support the Mix Protocol.\nHowever, this requirement can be minimized by supporting a lightweight mode in which the destination only sends and receives messages via Mix, without participating in message routing for other nodes.\nThis is similar to the model adopted by Waku, where edge nodes are not required to relay traffic but still interact with the network.\nIn practice, this tradeoff is often acceptable."),(0,n.kt)("p",null,"The core Mix Protocol does not mandate destination participation.\nHowever, implementations MAY support this model as an optional mode for use in deployments that require stronger end-to-end security guarantees.\nThe discovery mechanism MAY include a flag to advertise support for routing versus receive-only participation.\nAdditional details on discovery configurations are out of scope for this specification."),(0,n.kt)("p",null,"This trust model is not required for interoperability, but is recommended when assessing deployment-specific threat models, especially in protocols that require message integrity or authenticated replies."),(0,n.kt)("h3",{id:"104-known-protocol-limitations"},"10.4 Known Protocol Limitations"),(0,n.kt)("p",null,"The Mix Protocol provides strong sender anonymity and metadata protection guarantees within the mix network.\nHowever, it does not address all classes of network-level disruption or application-layer abuse.\nThis section outlines known limitations that deployments MUST consider when evaluating system resilience and reliability."),(0,n.kt)("h4",{id:"1041-undetectable-node-misbehavior"},"10.4.1 Undetectable Node Misbehavior"),(0,n.kt)("p",null,"The Mix Protocol in its current version does not include mechanisms to detect or attribute misbehavior by mix nodes.\nSince Sphinx packets are unlinkable and routing is stateless, malicious or faulty nodes may delay, drop, or selectively forward packets without detection."),(0,n.kt)("p",null,"This behavior is indistinguishable from benign network failure.\nThere is no native support for feedback, acknowledgment, or proof-of-relay.\nAs a result, unreliable nodes cannot be penalized or excluded based on observed reliability."),(0,n.kt)("p",null,"Future versions may explore accountability mechanisms.\nFor now, deployments MAY improve robustness by sending each packet along multiple paths as defined in ","[Section X.X]",", but MUST treat message loss as a possibility."),(0,n.kt)("h4",{id:"1042-no-built-in-retry-or-acknowledgment"},"10.4.2 No Built-in Retry or Acknowledgment"),(0,n.kt)("p",null,"The Mix protocol does not support retransmission, delivery acknowledgments, or automated fallback logic.\nEach message is sent once and routed independently through the mixnet.\nIf a message is lost or a node becomes unavailable, recovery is the responsibility of the top-level application."),(0,n.kt)("p",null,"Single-Use Reply Blocks (SURBs) (defined in Section","[X.X]",") enable destinations to send responses back to the sender via a fresh mix path.\nHowever, SURBs are optional, and their usage for acknowledgments or retries must be coordinated by the application."),(0,n.kt)("p",null,"Applications using the Mix Protocol MUST treat delivery as probabilistic.\nTo improve reliability, the sender MAY:"),(0,n.kt)("ul",null,(0,n.kt)("li",{parentName:"ul"},"Use parallel transmission across ",(0,n.kt)("inlineCode",{parentName:"li"},"D")," disjoint paths."),(0,n.kt)("li",{parentName:"ul"},"Estimate end-to-end delay bounds based on chosen per-hop delays (defined in ",(0,n.kt)("a",{parentName:"li",href:"#62-delay-strategy"},"Section 6.2"),"), and retry using different paths if a response is not received within the expected window.")),(0,n.kt)("p",null,"These strategies MUST be implemented at the origin protocol layer or through Mix integration logic and are not enforced by the Mix Protocol itself."),(0,n.kt)("h4",{id:"1043-no-sybil-resistance"},"10.4.3 No Sybil Resistance"),(0,n.kt)("p",null,"The Mix Protocol does not include any built-in defenses against Sybil attacks.\nAll nodes that support the protocol and are discoverable via peer discovery are equally eligible for path selection.\nAn adversary that operates a large number of Sybil nodes may be selected into mix paths more often than expected, increasing the likelihood of partial or full path compromise."),(0,n.kt)("p",null,"In the worst case, if an adversary controls a significant fraction of nodes (",(0,n.kt)("em",{parentName:"p"},"e.g.,")," one-third of the network), the probability that a given path includes only adversarial nodes increases sharply.\nThis raises the risk of deanonymization through end-to-end traffic correlation or timing analysis."),(0,n.kt)("p",null,"Deployments concerned with Sybil resistance MAY implement passive defenses such as minimum path length constraints.\nMore advanced mitigations such as stake-based participation or resource proofs typically require some form of trusted setup or blockchain-based coordination."),(0,n.kt)("p",null,"Such defenses are out of scope in the current version of the Mix Protocol, but are critical to ensuring anonymity at scale and may be explored in future iterations."),(0,n.kt)("h4",{id:"1044-vulnerability-to-denial-of-service-attacks"},"10.4.4 Vulnerability to Denial-of-Service Attacks"),(0,n.kt)("p",null,"The Mix Protocol does not provide built-in defenses against denial-of-service (DoS) attacks targeting mix nodes.\nA malicious mix node may generate a high volume of valid Sphinx packets to exhaust computational, memory, or bandwidth resources along random paths through the network."),(0,n.kt)("p",null,"This risk stems from the protocol's stateless and sender-anonymous design.\nMix nodes process each packet independently and cannot distinguish honest users from attackers.\nThere is no mechanism to attribute packets, limit per-sender usage, or apply network-wide fairness constraints."),(0,n.kt)("p",null,"Mix nodes remain vulnerable to volumetric attacks even when destinations are protected."),(0,n.kt)("p",null,"While the Mix Protocol includes safeguards such as layered encryption, per-hop integrity checks, and fixed-size headers, these primarily defend against tagging attacks and structurally invalid or malformed traffic.\nThe Sphinx packet format also enforces a maximum path length ",(0,n.kt)("span",{parentName:"p",className:"math math-inline"},(0,n.kt)("span",{parentName:"span",className:"katex"},(0,n.kt)("span",{parentName:"span",className:"katex-mathml"},(0,n.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,n.kt)("semantics",{parentName:"math"},(0,n.kt)("mrow",{parentName:"semantics"},(0,n.kt)("mo",{parentName:"mrow",stretchy:"false"},"("),(0,n.kt)("mi",{parentName:"mrow"},"L"),(0,n.kt)("mo",{parentName:"mrow"},"\u2264"),(0,n.kt)("mi",{parentName:"mrow"},"r"),(0,n.kt)("mo",{parentName:"mrow",stretchy:"false"},")")),(0,n.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"(L \\leq r)")))),(0,n.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"1em",verticalAlign:"-0.25em"}}),(0,n.kt)("span",{parentName:"span",className:"mopen"},"("),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal"},"L"),(0,n.kt)("span",{parentName:"span",className:"mspace",style:{marginRight:"0.2778em"}}),(0,n.kt)("span",{parentName:"span",className:"mrel"},"\u2264"),(0,n.kt)("span",{parentName:"span",className:"mspace",style:{marginRight:"0.2778em"}})),(0,n.kt)("span",{parentName:"span",className:"base"},(0,n.kt)("span",{parentName:"span",className:"strut",style:{height:"1em",verticalAlign:"-0.25em"}}),(0,n.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.02778em"}},"r"),(0,n.kt)("span",{parentName:"span",className:"mclose"},")"))))),", which prevents infinite loops or excessively long paths being embedded.\nHowever, these protections do not prevent adversaries from injecting large volumes of short, well-formed messages to exhaust mix node resources."),(0,n.kt)("p",null,"DoS protection","\u2014","such as admission control, rate-limiting, or resource-bound access","\u2014","can be plugged in as explained in 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