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<title data-rh="true">Waku Privacy and Anonymity Analysis Part I: Definitions and Waku Relay | Vac Research</title><meta data-rh="true" name="viewport" content="width=device-width,initial-scale=1"><meta data-rh="true" name="twitter:card" content="summary_large_image"><meta data-rh="true" property="og:url" content="https://vac.dev/rlog/wakuv2-relay-anon"><meta data-rh="true" property="og:locale" content="en"><meta data-rh="true" name="docusaurus_locale" content="en"><meta data-rh="true" name="docusaurus_tag" content="default"><meta data-rh="true" name="docsearch:language" content="en"><meta data-rh="true" name="docsearch:docusaurus_tag" content="default"><meta data-rh="true" name="image" content="https://vac.dev/_og/2eaefa509b1537dbc62430b0dc25b8a535d24983.png"><meta data-rh="true" property="og:title" content="Waku Privacy and Anonymity Analysis Part I: Definitions and Waku Relay | Vac Research"><meta data-rh="true" name="description" content="Introducing a basic threat model and privacy/anonymity analysis for the Waku v2 relay protocol."><meta data-rh="true" property="og:description" content="Introducing a basic threat model and privacy/anonymity analysis for the Waku v2 relay protocol."><meta data-rh="true" property="og:image" content="https://vac.dev/_og/2eaefa509b1537dbc62430b0dc25b8a535d24983.png"><meta data-rh="true" name="twitter:image" content="https://vac.dev/_og/2eaefa509b1537dbc62430b0dc25b8a535d24983.png"><meta data-rh="true" property="og:type" content="article"><meta data-rh="true" property="article:published_time" content="2022-07-22T10:00:00.000Z"><link data-rh="true" rel="icon" href="/theme/image/favicon.ico"><link data-rh="true" rel="canonical" href="https://vac.dev/rlog/wakuv2-relay-anon"><link data-rh="true" rel="alternate" href="https://vac.dev/rlog/wakuv2-relay-anon" hreflang="en"><link data-rh="true" rel="alternate" href="https://vac.dev/rlog/wakuv2-relay-anon" hreflang="x-default"><script data-rh="true" type="application/ld+json">{"@context":"https://schema.org","@type":"BlogPosting","@id":"https://vac.dev/rlog/wakuv2-relay-anon","mainEntityOfPage":"https://vac.dev/rlog/wakuv2-relay-anon","url":"https://vac.dev/rlog/wakuv2-relay-anon","headline":"Waku Privacy and Anonymity Analysis Part I: Definitions and Waku Relay","name":"Waku Privacy and Anonymity Analysis Part I: Definitions and Waku Relay","description":"Introducing a basic threat model and privacy/anonymity analysis for the Waku v2 relay protocol.","datePublished":"2022-07-22T10:00:00.000Z","author":{"@type":"Person","name":"Daniel"},"image":{"@type":"ImageObject","@id":"https://vac.dev/img/anonymity_trilemma.svg","url":"https://vac.dev/img/anonymity_trilemma.svg","contentUrl":"https://vac.dev/img/anonymity_trilemma.svg","caption":"title image for the blog post: Waku Privacy and Anonymity Analysis Part I: Definitions and Waku Relay"},"keywords":[],"isPartOf":{"@type":"Blog","@id":"https://vac.dev/rlog","name":"Research Blog"}}</script><link rel="alternate icon" type="image/png" href="/theme/image/favicon.png">
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class="col col--9 col--offset-1" itemscope="" itemtype="http://schema.org/Blog"><article class=""><header><nav class="theme-doc-breadcrumbs breadcrumbsContainer_RLvU" aria-label="Breadcrumbs"><ul class="breadcrumbs" itemscope="" itemtype="https://schema.org/BreadcrumbList"><a class="breadcrumbs__item" href="/blog"><span class="lsd-typography lsd-typography--body3">All posts</span></a><li itemscope="" itemprop="itemListElement" itemtype="https://schema.org/ListItem" class="breadcrumbs__item breadcrumbs__item--active"><span class="lsd-typography lsd-typography--body3 breadcrumbs__link" itemprop="name">Waku Privacy and Anonymity Analysis Part I: Definitions and Waku Relay</span><meta itemprop="position" content="1"></li></ul></nav><h1 class="title_f1Hy">Waku Privacy and Anonymity Analysis Part I: Definitions and Waku Relay</h1><div class="container_PkUo margin-vert--md"><time datetime="2022-07-22T10:00:00.000Z" itemprop="datePublished">July 22, 2022</time><div class="authors_dZ4g"><span class="lsd-typography lsd-typography--body2">by </span><div class="col col--6 authorCol_y4tx"><div class="avatar margin-bottom--sm"><div class="avatar__intro" itemprop="author" itemscope="" itemtype="https://schema.org/Person"><div class="avatar__name"><span class="lsd-typography lsd-typography--body2" itemprop="name">Daniel</span></div></div></div></div></div><div>17 min read</div></div><hr class="blog-divider"></header><div id="__blog-post-container" class="markdown"><p>Introducing a basic threat model and privacy/anonymity analysis for the Waku v2 relay protocol.</p>
<p><a href="https://rfc.vac.dev/waku/standards/core/10/waku2" target="_blank" rel="noopener noreferrer">Waku v2</a> enables secure, privacy preserving communication using a set of modular P2P protocols.
Waku v2 also aims at protecting the user&#x27;s anonymity.
This post is the first in a series about Waku v2 security, privacy, and anonymity.
The goal is to eventually have a full privacy and anonymity analysis for each of the Waku v2 protocols, as well as covering the interactions of various Waku v2 protocols.
This provides transparency with respect to Waku&#x27;s current privacy and anonymity guarantees, and also identifies weak points that we have to address.</p>
<p>In this post, we first give an informal description of security, privacy and anonymity in the context of Waku v2.
For each definition, we summarize Waku&#x27;s current guarantees regarding the respective property.
We also provide attacker models, an attack-based threat model, and a first anonymity analysis of <a href="https://rfc.vac.dev/waku/standards/core/11/relay" target="_blank" rel="noopener noreferrer">Waku v2 relay</a> within the respective models.</p>
<p>Waku comprises many protocols that can be combined in a modular way.
For our privacy and anonymity analysis, we start with the relay protocol because it is at the core of Waku v2 enabling Waku&#x27;s publish subscribe approach to P2P messaging.
In its current form, Waku relay is a minor extension of <a href="https://github.com/libp2p/specs/blob/master/pubsub/gossipsub/README.md" target="_blank" rel="noopener noreferrer">libp2p GossipSub</a>.</p>
<p></p><div class="wrapper_SWrM active_qZD5"><img decoding="async" loading="lazy" alt="Figure 1: The Waku v2 relay mesh is based on the GossipSub mesh" src="/assets/images/libp2p_gossipsub_types_of_peering-d0772153a5d11dea7b24c0bdc307a93d.png" width="800" height="305" class="img_ev3q"><button class="fullscreenButton_Bocn lsd-icon-button lsd-icon-button--medium lsd-icon-button--outlined"><div class="icon_S7Kx m_thRi"><svg xmlns="http://www.w3.org/2000/svg" width="14" height="14" fill="none" viewBox="0 0 14 14"><path fill="#fff" d="M1.75 2.917V5.25h1.167V2.917H5.25V1.75H2.917A1.17 1.17 0 0 0 1.75 2.917M2.917 8.75H1.75v2.333a1.17 1.17 0 0 0 1.167 1.167H5.25v-1.167H2.917zm8.166 2.333H8.75v1.167h2.333a1.17 1.17 0 0 0 1.167-1.167V8.75h-1.167zm0-9.333H8.75v1.167h2.333V5.25h1.167V2.917a1.17 1.17 0 0 0-1.167-1.167"></path></svg></div></button></div><p></p>
<h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="informal-definitions-security-privacy-and-anonymity">Informal Definitions: Security, Privacy, and Anonymity<a href="#informal-definitions-security-privacy-and-anonymity" class="hash-link" aria-label="Direct link to Informal Definitions: Security, Privacy, and Anonymity" title="Direct link to Informal Definitions: Security, Privacy, and Anonymity">​</a></h2>
<p>The concepts of security, privacy, and anonymity are linked and have quite a bit of overlap.</p>
<h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="security">Security<a href="#security" class="hash-link" aria-label="Direct link to Security" title="Direct link to Security">​</a></h3>
<p>Of the three, <a href="https://en.wikipedia.org/wiki/Information_security" target="_blank" rel="noopener noreferrer">Security</a> has the clearest agreed upon definition,
at least regarding its key concepts: <em>confidentiality</em>, <em>integrity</em>, and <em>availability</em>.</p>
<ul>
<li>confidentiality: data is not disclosed to unauthorized entities.</li>
<li>integrity: data is not modified by unauthorized entities.</li>
<li>availability: data is available, i.e. accessible by authorized entities.</li>
</ul>
<p>While these are the key concepts, the definition of information security has been extended over time including further concepts,
e.g. <a href="https://en.wikipedia.org/wiki/Authentication" target="_blank" rel="noopener noreferrer">authentication</a> and <a href="https://en.wikipedia.org/wiki/Non-repudiation" target="_blank" rel="noopener noreferrer">non-repudiation</a>.
We might cover these in future posts.</p>
<h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="privacy">Privacy<a href="#privacy" class="hash-link" aria-label="Direct link to Privacy" title="Direct link to Privacy">​</a></h3>
<p>Privacy allows users to choose which data and information</p>
<ul>
<li>they want to share</li>
<li>and with whom they want to share it.</li>
</ul>
<p>This includes data and information that is associated with and/or generated by users.
Protected data also comprises metadata that might be generated without users being aware of it.
This means, no further information about the sender or the message is leaked.
Metadata that is protected as part of the privacy-preserving property does not cover protecting the identities of sender and receiver.
Identities are protected by the <a href="#anonymity">anonymity property</a>.</p>
<p>Often privacy is realized by the confidentiality property of security.
This neither makes privacy and security the same, nor the one a sub category of the other.
While security is abstract itself (its properties can be realized in various ways), privacy lives on a more abstract level using security properties.
Privacy typically does not use integrity and availability.
An adversary who has no access to the private data, because the message has been encrypted, could still alter the message.</p>
<p>Waku offers confidentiality via secure channels set up with the help of the <a href="https://noiseprotocol.org/" target="_blank" rel="noopener noreferrer">Noise Protocol Framework</a>.
Using these secure channels, message content is only disclosed to the intended receivers.
They also provide good metadata protection properties.
However, we do not have a metadata protection analysis as of yet,
which is part of our privacy/anonymity roadmap.</p>
<h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="anonymity">Anonymity<a href="#anonymity" class="hash-link" aria-label="Direct link to Anonymity" title="Direct link to Anonymity">​</a></h3>
<p>Privacy and anonymity are closely linked.
Both the identity of a user and data that allows inferring a user&#x27;s identity should be part of the privacy policy.
For the purpose of analysis, we want to have a clearer separation between these concepts.</p>
<p>We define anonymity as <em>unlinkablity of users&#x27; identities and their shared data and/or actions</em>.</p>
<p>We subdivide anonymity into <em>receiver anonymity</em> and <em>sender anonymity</em>.</p>
<h4 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="receiver-anonymity">Receiver Anonymity<a href="#receiver-anonymity" class="hash-link" aria-label="Direct link to Receiver Anonymity" title="Direct link to Receiver Anonymity">​</a></h4>
<p>We define receiver anonymity as <em>unlinkability of users&#x27; identities and the data they receive and/or related actions</em>.
The data transmitted via Waku relay must be a <a href="https://rfc.vac.dev/waku/standards/core/14/message" target="_blank" rel="noopener noreferrer">Waku message</a>, which contains a content topic field.
Because each message is associated with a content topic, and each receiver is interested in messages with specific content topics,
receiver anonymity in the context of Waku corresponds to <em>subscriber-topic unlinkability</em>.
An example for the &quot;action&quot; part of our receiver anonymity definition is subscribing to a specific topic.</p>
<p>The Waku message&#x27;s content topic is not related to the libp2p pubsub topic.
For now, Waku uses a single libp2p pubsub topic, which means messages are propagated via a single mesh of peers.
With this, the receiver discloses its participation in Waku on the gossipsub layer.
We will leave the analysis of libp2p gossipsub to a future article within this series, and only provide a few hints and pointers here.</p>
<p>Waku offers k-anonymity regarding content topic interest in the global adversary model.
<a href="https://en.wikipedia.org/wiki/K-anonymity" target="_blank" rel="noopener noreferrer">K-anonymity</a> in the context of Waku means an attacker can link receivers to content topics with a maximum certainty of <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn><mi mathvariant="normal">/</mi><mi>k</mi></mrow><annotation encoding="application/x-tex">1/k</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em"></span><span class="mord">1/</span><span class="mord mathnormal" style="margin-right:0.03148em">k</span></span></span></span>.
The larger <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>k</mi></mrow><annotation encoding="application/x-tex">k</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em"></span><span class="mord mathnormal" style="margin-right:0.03148em">k</span></span></span></span>, the less certainty the attacker gains.
Receivers basically hide in a pool of <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>k</mi></mrow><annotation encoding="application/x-tex">k</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em"></span><span class="mord mathnormal" style="margin-right:0.03148em">k</span></span></span></span> content topics, any subset of which could be topics they subscribed to.
The attacker does not know which of those the receiver actually subscribed to,
and the receiver enjoys <a href="https://en.wikipedia.org/wiki/Plausible_deniability#Use_in_cryptography" target="_blank" rel="noopener noreferrer">plausible deniability</a> regarding content topic subscription.
Assuming there are <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi></mrow><annotation encoding="application/x-tex">n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em"></span><span class="mord mathnormal">n</span></span></span></span> Waku content topics, a receiver has <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi></mrow><annotation encoding="application/x-tex">n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em"></span><span class="mord mathnormal">n</span></span></span></span>-anonymity with respect to association to a specific content topic.</p>
<p>Technically, Waku allows distributing messages over several libp2p pubsub topics.
This yields <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>k</mi></mrow><annotation encoding="application/x-tex">k</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em"></span><span class="mord mathnormal" style="margin-right:0.03148em">k</span></span></span></span>-anonymity, assuming <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>k</mi></mrow><annotation encoding="application/x-tex">k</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em"></span><span class="mord mathnormal" style="margin-right:0.03148em">k</span></span></span></span> content topics share the same pubsub topic.
However, if done wrongly, such sharding of pubsub topics can breach anonymity.
A formal specification of anonymity-preserving topic sharding building on the concepts of <a href="https://rfc.vac.dev/status/deprecated/10/waku-usage#partitioned-topic" target="_blank" rel="noopener noreferrer">partitioned topics</a> is part of our roadmap.</p>
<p>Also, Waku is not directly concerned with 1:1 communication, so for this post, 1:1 communication is out of scope.
Channels for 1:1 communication can be implemented on top of Waku relay.
In the future, a 1:1 communication protocol might be added to Waku.
Similar to topic sharding, it would maintain receiver anonymity leveraging <a href="https://rfc.vac.dev/status/deprecated/10/waku-usage/#partitioned-topic" target="_blank" rel="noopener noreferrer">partitioned topics</a>.</p>
<h4 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="sender-anonymity">Sender Anonymity<a href="#sender-anonymity" class="hash-link" aria-label="Direct link to Sender Anonymity" title="Direct link to Sender Anonymity">​</a></h4>
<p>We define sender anonymity as <em>unlinkability of users&#x27; identities and the data they send and/or related actions</em>.
Because the data in the context of Waku is Waku messages, sender anonymity corresponds to <em>sender-message unlinkability</em>.</p>
<p>In summary, Waku offers weak sender anonymity because of <a href="https://rfc.vac.dev/waku/standards/core/11/relay" target="_blank" rel="noopener noreferrer">Waku&#x27;s strict no sign policy</a>,
which has its origins in the <a href="https://github.com/ethereum/consensus-specs/blob/dev/specs/phase0/p2p-interface.md#why-are-we-using-the-strictnosign-signature-policy" target="_blank" rel="noopener noreferrer">Ethereum consensus specs</a>.
<a href="https://rfc.vac.dev/waku/standards/core/17/rln-relay" target="_blank" rel="noopener noreferrer">17/WAKU-RLN-RELAY</a> and <a href="https://rfc.vac.dev/waku/deprecated/18/swap" target="_blank" rel="noopener noreferrer">18/WAKU2-SWAP</a> mitigate replay and injection attacks.</p>
<p>Waku currently does not offer sender anonymity in stronger attacker models, as well as cannot protect against targeted attacks in weaker attacker models like the single or multi node attacker.
We will cover this in more detail in later sections.</p>
<h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="anonymity-trilemma">Anonymity Trilemma<a href="#anonymity-trilemma" class="hash-link" aria-label="Direct link to Anonymity Trilemma" title="Direct link to Anonymity Trilemma">​</a></h3>
<p><a href="https://freedom.cs.purdue.edu/projects/trilemma.html" target="_blank" rel="noopener noreferrer">The Anonymity trilemma</a> states that only two out of <em>strong anonymity</em>, <em>low bandwidth</em>, and <em>low latency</em> can be guaranteed in the global on-net attacker model.
Waku&#x27;s goal, being a modular set of protocols, is to offer any combination of two out of these three properties, as well as blends.
An example for blending is an adjustable number of pubsub topics and peers in the respective pubsub topic mesh; this allows tuning the trade-off between anonymity and bandwidth.</p>
<p></p><div class="wrapper_SWrM active_qZD5"><img decoding="async" loading="lazy" alt="Figure 2: Anonymity Trilemma: pick two. " src="data:image/svg+xml;base64,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" width="81" height="94" class="img_ev3q"><button class="fullscreenButton_Bocn lsd-icon-button lsd-icon-button--medium lsd-icon-button--outlined"><div class="icon_S7Kx m_thRi"><svg xmlns="http://www.w3.org/2000/svg" width="14" height="14" fill="none" viewBox="0 0 14 14"><path fill="#fff" d="M1.75 2.917V5.25h1.167V2.917H5.25V1.75H2.917A1.17 1.17 0 0 0 1.75 2.917M2.917 8.75H1.75v2.333a1.17 1.17 0 0 0 1.167 1.167H5.25v-1.167H2.917zm8.166 2.333H8.75v1.167h2.333a1.17 1.17 0 0 0 1.167-1.167V8.75h-1.167zm0-9.333H8.75v1.167h2.333V5.25h1.167V2.917a1.17 1.17 0 0 0-1.167-1.167"></path></svg></div></button></div><p></p>
<p>A fourth factor that influences <a href="https://freedom.cs.purdue.edu/projects/trilemma.html" target="_blank" rel="noopener noreferrer">the anonymity trilemma</a> is <em>frequency and patterns</em> of messages.
The more messages there are, and the more randomly distributed they are, the better the anonymity protection offered by a given anonymous communication protocol.
So, incentivising users to use the protocol, for instance by lowering entry barriers, helps protecting the anonymity of all users.
The frequency/patterns factor is also related to the above described k-anonymity.</p>
<h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="censorship-resistance">Censorship Resistance<a href="#censorship-resistance" class="hash-link" aria-label="Direct link to Censorship Resistance" title="Direct link to Censorship Resistance">​</a></h3>
<p>Another security related property that Waku aims to offer is censorship resistance.
Censorship resistance guarantees that users can participate even if an attacker tries to deny them access.
So, censorship resistance ties into the availability aspect of security.
In the context of Waku that means users should be able to send messages as well as receive all messages they are interested in,
even if an attacker tries to prevent them from disseminating messages or tries to deny them access to messages.</p>
<p>Currently, Waku only guarantees censorship resistance in the weak single node attacker model.
While currently employed secure channels mitigate targeted censorship, e.g. blocking specific content topics,
general censorship resistance in strong attacker models is part of our roadmap.
Among other options, we will investigate <a href="https://www.pluggabletransports.info/about/" target="_blank" rel="noopener noreferrer">Pluggable Transports</a> in future articles.</p>
<h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="attacker-types">Attacker Types<a href="#attacker-types" class="hash-link" aria-label="Direct link to Attacker Types" title="Direct link to Attacker Types">​</a></h2>
<p>The following lists various attacker types with varying degrees of power.
The more power an attacker has, the more difficult it is to gain the respective attacker position.</p>
<p>Each attacker type comes in a passive and an active variant.
While a passive attacker can stay hidden and is not suspicious,
the respective active attacker has more (or at least the same) deanonymization power.</p>
<p>We also distinguish between internal and external attackers.</p>
<h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="internal">Internal<a href="#internal" class="hash-link" aria-label="Direct link to Internal" title="Direct link to Internal">​</a></h3>
<p>With respect to Waku relay, an internal attacker participates in the same pubsub topic as its victims.
Without additional measures on higher layer protocols, access to an internal position is easy to get.</p>
<h4 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="single-node">Single Node<a href="#single-node" class="hash-link" aria-label="Direct link to Single Node" title="Direct link to Single Node">​</a></h4>
<p>This attacker controls a single node.
Because this position corresponds to normal usage of Waku relay, it is trivial to obtain.</p>
<h4 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="multi-node">Multi Node<a href="#multi-node" class="hash-link" aria-label="Direct link to Multi Node" title="Direct link to Multi Node">​</a></h4>
<p>This attacker controls several nodes. We assume a smaller static number of controlled nodes.
The multi node position can be achieved relatively easily by setting up multiple nodes.
Botnets might be leveraged to increase the number of available hosts.
Multi node attackers could use <a href="https://en.wikipedia.org/wiki/Sybil_attack" target="_blank" rel="noopener noreferrer">Sybil attacks</a> to increase the number of controlled nodes.
A countermeasure is for nodes to only accept libp2p gossipsub graft requests from peers with different IP addresses, or even different subnets.</p>
<h4 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="linearly-scaling-nodes">Linearly Scaling Nodes<a href="#linearly-scaling-nodes" class="hash-link" aria-label="Direct link to Linearly Scaling Nodes" title="Direct link to Linearly Scaling Nodes">​</a></h4>
<p>This attacker controls a number of nodes that scales linearly with the number of nodes in the network.
This attacker is especially interesting to investigate in the context of DHT security,
which Waku uses for ambient peer discovery.</p>
<h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="external">External<a href="#external" class="hash-link" aria-label="Direct link to External" title="Direct link to External">​</a></h3>
<p>An external attacker can only see encrypted traffic (protected by a secure channel set up with <a href="https://github.com/waku-org/specs/blob/master/standards/application/noise.md" target="_blank" rel="noopener noreferrer">WAKU2-NOISE</a>).
Because an internal position can be easily obtained,
in practice external attackers would mount combined attacks that leverage both internal an external attacks.
We cover this more below when describing attacks.</p>
<h4 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="local">Local<a href="#local" class="hash-link" aria-label="Direct link to Local" title="Direct link to Local">​</a></h4>
<p>A local attacker has access to communication links in a local network segment.
This could be a rogue access point (with routing capability).</p>
<h4 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="as">AS<a href="#as" class="hash-link" aria-label="Direct link to AS" title="Direct link to AS">​</a></h4>
<p>An AS attacker controls a single AS (autonomous system).
A passive AS attacker can listen to traffic on arbitrary links within the AS.
An active AS attacker can drop, inject, and alter traffic on arbitrary links within the AS.</p>
<p>In practice, a malicious ISP would be considered as an AS attacker.
A malicious ISP could also easily setup a set of nodes at specific points in the network,
gaining internal attack power similar to a strong multi node attacker.</p>
<h4 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="global-on-net">Global On-Net<a href="#global-on-net" class="hash-link" aria-label="Direct link to Global On-Net" title="Direct link to Global On-Net">​</a></h4>
<p>A global on-net attacker has complete overview over the whole network.
A passive global attacker can listen to traffic on all links,
while the active global attacker basically carries the traffic: it can freely drop, inject, and alter traffic at all positions in the network.
This basically corresponds to the <a href="https://en.wikipedia.org/wiki/Dolev%E2%80%93Yao_model" target="_blank" rel="noopener noreferrer">Dolev-Yao model</a>.</p>
<p>An entity with this power would, in practice, also have the power of the internal linearly scaling nodes attacker.</p>
<h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="attack-based-threat-analysis">Attack-based Threat Analysis<a href="#attack-based-threat-analysis" class="hash-link" aria-label="Direct link to Attack-based Threat Analysis" title="Direct link to Attack-based Threat Analysis">​</a></h2>
<p>The following lists various attacks including the weakest attacker model in which the attack can be successfully performed.
The respective attack can be performed in all stronger attacker models as well.</p>
<p>An attack is considered more powerful if it can be successfully performed in a weaker attacker model.</p>
<p>If not stated otherwise, we look at these attacks with respect to their capability to deanonymize the message sender.</p>
<h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="scope">Scope<a href="#scope" class="hash-link" aria-label="Direct link to Scope" title="Direct link to Scope">​</a></h3>
<p>In this post, we introduce a simple tightly scoped threat model for Waku v2 Relay, which will be extended in the course of this article series.</p>
<p>In this first post, we will look at the relay protocol in isolation.
Even though many threats arise from layers Waku relay is based on, and layers that in turn live on top of relay,
we want to first look at relay in isolation because it is at the core of Waku v2.
Addressing and trying to solve all security issues of a complex system at once is an overwhelming task, which is why we focus on the soundness of relay first.</p>
<p>This also goes well with the modular design philosophy of Waku v2, as layers of varying levels of security guarantees can be built on top of relay, all of which can relay on the guarantees that Waku provides.
Instead of looking at a multiplicative explosion of possible interactions, we look at the core in this article, and cover the most relevant combinations in future posts.</p>
<p>Further restricting the scope, we will look at the data field of a relay message as a black box.
In a second article on Waku v2 relay, we will look into the data field, which according to the <a href="https://rfc.vac.dev/waku/standards/core/11/relay#message-fields" target="_blank" rel="noopener noreferrer">specification of Waku v2 relay</a> must be a <a href="https://rfc.vac.dev/waku/standards/core/14/message" target="_blank" rel="noopener noreferrer">Waku v2 message</a>.
We only consider messages with version field <code>2</code>, which indicates that the payload has to be encoded using <a href="https://github.com/waku-org/specs/blob/master/standards/application/noise.md" target="_blank" rel="noopener noreferrer">WAKU2-NOISE</a>.</p>
<h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="prerequisite-get-a-specific-position-in-the-network">Prerequisite: Get a Specific Position in the Network<a href="#prerequisite-get-a-specific-position-in-the-network" class="hash-link" aria-label="Direct link to Prerequisite: Get a Specific Position in the Network" title="Direct link to Prerequisite: Get a Specific Position in the Network">​</a></h3>
<p>Some attacks require the attacker node(s) to be in a specific position in the network.
In most cases, this corresponds to trying to get into the mesh peer list for the desired pubsub topic of the victim node.</p>
<p>In libp2p gossipsub, and by extension Waku v2 relay, nodes can simply send a graft message for the desired topic to the victim node.
If the victim node still has open slots, the attacker gets the desired position.
This only requires the attacker to know the gossipsub multiaddress of the victim node.</p>
<p>A linearly scaling nodes attacker can leverage DHT based discovery systems to boost the probability of malicious nodes being returned, which in turn significantly increases the probability of attacker nodes ending up in the peer lists of victim nodes.
<a href="https://vac.dev/wakuv2-apd" target="_blank" rel="noopener noreferrer">Waku v2 discv5</a> will employ countermeasures that mitigate the amplifying effect this attacker type can achieve.</p>
<h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="replay-attack">Replay Attack<a href="#replay-attack" class="hash-link" aria-label="Direct link to Replay Attack" title="Direct link to Replay Attack">​</a></h3>
<p>In the scope we defined above, Waku v2 is resilient against replay attacks.
GossipSub nodes, and by extension Waku relay nodes, feature a <code>seen</code> cache, and only relay messages they have not seen before.
Further, replay attacks will be punished by <a href="https://rfc.vac.dev/waku/standards/core/17/rln-relay" target="_blank" rel="noopener noreferrer">RLN</a> and <a href="https://rfc.vac.dev/waku/deprecated/18/swap" target="_blank" rel="noopener noreferrer">SWAP</a>.</p>
<h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="neighbourhood-surveillance">Neighbourhood Surveillance<a href="#neighbourhood-surveillance" class="hash-link" aria-label="Direct link to Neighbourhood Surveillance" title="Direct link to Neighbourhood Surveillance">​</a></h3>
<p>This attack can be performed by a single node attacker that is connected to all peers of the victim node <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>v</mi></mrow><annotation encoding="application/x-tex">v</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em"></span><span class="mord mathnormal" style="margin-right:0.03588em">v</span></span></span></span> with respect to a specific topic mesh.
The attacker also has to be connected to <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>v</mi></mrow><annotation encoding="application/x-tex">v</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em"></span><span class="mord mathnormal" style="margin-right:0.03588em">v</span></span></span></span>.
In this position, the attacker will receive messages <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>m</mi><mi>v</mi></msub></mrow><annotation encoding="application/x-tex">m_v</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathnormal">m</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.03588em">v</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span> sent by <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>v</mi></mrow><annotation encoding="application/x-tex">v</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em"></span><span class="mord mathnormal" style="margin-right:0.03588em">v</span></span></span></span> both on the direct path from <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>v</mi></mrow><annotation encoding="application/x-tex">v</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em"></span><span class="mord mathnormal" style="margin-right:0.03588em">v</span></span></span></span>, and on indirect paths relayed by peers of <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>v</mi></mrow><annotation encoding="application/x-tex">v</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em"></span><span class="mord mathnormal" style="margin-right:0.03588em">v</span></span></span></span>.
It will also receive messages <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>m</mi><mi>x</mi></msub></mrow><annotation encoding="application/x-tex">m_x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathnormal">m</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">x</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span> that are not sent by <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>v</mi></mrow><annotation encoding="application/x-tex">v</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em"></span><span class="mord mathnormal" style="margin-right:0.03588em">v</span></span></span></span>. These messages <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>m</mi><mi>x</mi></msub></mrow><annotation encoding="application/x-tex">m_x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathnormal">m</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">x</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span> are relayed by both <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>v</mi></mrow><annotation encoding="application/x-tex">v</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em"></span><span class="mord mathnormal" style="margin-right:0.03588em">v</span></span></span></span> and the peers of <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>v</mi></mrow><annotation encoding="application/x-tex">v</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em"></span><span class="mord mathnormal" style="margin-right:0.03588em">v</span></span></span></span>.
Messages that are received (significantly) faster from <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>v</mi></mrow><annotation encoding="application/x-tex">v</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em"></span><span class="mord mathnormal" style="margin-right:0.03588em">v</span></span></span></span> than from any other of <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>v</mi></mrow><annotation encoding="application/x-tex">v</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em"></span><span class="mord mathnormal" style="margin-right:0.03588em">v</span></span></span></span>&#x27;s peers are very likely messages that <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>v</mi></mrow><annotation encoding="application/x-tex">v</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em"></span><span class="mord mathnormal" style="margin-right:0.03588em">v</span></span></span></span> sent,
because for these messages the attacker is one hop closer to the source.</p>
<p>The attacker can (periodically) measure latency between itself and <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>v</mi></mrow><annotation encoding="application/x-tex">v</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em"></span><span class="mord mathnormal" style="margin-right:0.03588em">v</span></span></span></span>, and between itself and the peers of <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>v</mi></mrow><annotation encoding="application/x-tex">v</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em"></span><span class="mord mathnormal" style="margin-right:0.03588em">v</span></span></span></span> to get more accurate estimates for the expected timings.
An AS attacker (and if the topology allows, even a local attacker) could also learn the latency between <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>v</mi></mrow><annotation encoding="application/x-tex">v</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em"></span><span class="mord mathnormal" style="margin-right:0.03588em">v</span></span></span></span> and its well-behaving peers.
An active AS attacker could also increase the latency between <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>v</mi></mrow><annotation encoding="application/x-tex">v</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em"></span><span class="mord mathnormal" style="margin-right:0.03588em">v</span></span></span></span> and its peers to make the timing differences more prominent.
This, however, might lead to <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>v</mi></mrow><annotation encoding="application/x-tex">v</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em"></span><span class="mord mathnormal" style="margin-right:0.03588em">v</span></span></span></span> switching to other peers.</p>
<p>This attack cannot (reliably) distinguish messages <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>m</mi><mi>v</mi></msub></mrow><annotation encoding="application/x-tex">m_v</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathnormal">m</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.03588em">v</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span> sent by <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>v</mi></mrow><annotation encoding="application/x-tex">v</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em"></span><span class="mord mathnormal" style="margin-right:0.03588em">v</span></span></span></span> from messages <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>m</mi><mi>y</mi></msub></mrow><annotation encoding="application/x-tex">m_y</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7167em;vertical-align:-0.2861em"></span><span class="mord"><span class="mord mathnormal">m</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.03588em">y</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em"><span></span></span></span></span></span></span></span></span></span> relayed by peers of <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>v</mi></mrow><annotation encoding="application/x-tex">v</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em"></span><span class="mord mathnormal" style="margin-right:0.03588em">v</span></span></span></span> the attacker is not connected to.
Still, there are hop-count variations that might be leveraged.
Messages <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>m</mi><mi>v</mi></msub></mrow><annotation encoding="application/x-tex">m_v</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathnormal">m</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.03588em">v</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span> always have a hop-count of 1 on the path from <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>v</mi></mrow><annotation encoding="application/x-tex">v</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em"></span><span class="mord mathnormal" style="margin-right:0.03588em">v</span></span></span></span> to the attacker, while all other paths are longer.
Messages <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>m</mi><mi>y</mi></msub></mrow><annotation encoding="application/x-tex">m_y</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7167em;vertical-align:-0.2861em"></span><span class="mord"><span class="mord mathnormal">m</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.03588em">y</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em"><span></span></span></span></span></span></span></span></span></span> might have the same hop-count on the path from <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>v</mi></mrow><annotation encoding="application/x-tex">v</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em"></span><span class="mord mathnormal" style="margin-right:0.03588em">v</span></span></span></span> as well as on other paths.</p>
<h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="controlled-neighbourhood">Controlled Neighbourhood<a href="#controlled-neighbourhood" class="hash-link" aria-label="Direct link to Controlled Neighbourhood" title="Direct link to Controlled Neighbourhood">​</a></h3>
<p>If a multi node attacker manages to control all peers of the victim node, it can trivially tell which messages originated from <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>v</mi></mrow><annotation encoding="application/x-tex">v</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em"></span><span class="mord mathnormal" style="margin-right:0.03588em">v</span></span></span></span>.</p>
<h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="observing-messages">Observing Messages<a href="#observing-messages" class="hash-link" aria-label="Direct link to Observing Messages" title="Direct link to Observing Messages">​</a></h3>
<p>If Waku relay was not protected with Noise, the AS attacker could simply check for messages leaving <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>v</mi></mrow><annotation encoding="application/x-tex">v</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em"></span><span class="mord mathnormal" style="margin-right:0.03588em">v</span></span></span></span> which have not been relayed to <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>v</mi></mrow><annotation encoding="application/x-tex">v</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em"></span><span class="mord mathnormal" style="margin-right:0.03588em">v</span></span></span></span>.
These are the messages sent by <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>v</mi></mrow><annotation encoding="application/x-tex">v</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em"></span><span class="mord mathnormal" style="margin-right:0.03588em">v</span></span></span></span>.
Waku relay protects against this attack by employing secure channels setup using Noise.</p>
<h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="correlation">Correlation<a href="#correlation" class="hash-link" aria-label="Direct link to Correlation" title="Direct link to Correlation">​</a></h3>
<p>Monitoring all traffic (in an AS or globally), allows the attacker to identify traffic correlated with messages originating from <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>v</mi></mrow><annotation encoding="application/x-tex">v</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em"></span><span class="mord mathnormal" style="margin-right:0.03588em">v</span></span></span></span>.
This (alone) does not allow an external attacker to learn which message <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>v</mi></mrow><annotation encoding="application/x-tex">v</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em"></span><span class="mord mathnormal" style="margin-right:0.03588em">v</span></span></span></span> sent, but it allows identifying the respective traffic propagating through the network.
The more traffic in the network, the lower the success rate of this attack.</p>
<p>Combined with just a few nodes controlled by the attacker, the actual message associated with the correlated traffic can eventually be identified.</p>
<h3 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="dos">DoS<a href="#dos" class="hash-link" aria-label="Direct link to DoS" title="Direct link to DoS">​</a></h3>
<p>An active single node attacker could run a disruption attack by</p>
<ul>
<li>(1) dropping messages that should be relayed</li>
<li>(2) flooding neighbours with bogus messages</li>
</ul>
<p>While (1) has a negative effect on availability, the impact is not significant.
A linearly scaling botnet attacker, however, could significantly disrupt the network with such an attack.
(2) is thwarted by <a href="https://rfc.vac.dev/waku/standards/core/17/rln-relay" target="_blank" rel="noopener noreferrer">RLN</a>.
Also <a href="https://rfc.vac.dev/waku/deprecated/18/swap" target="_blank" rel="noopener noreferrer">SWAP</a> helps mitigating DoS attacks.</p>
<p>A local attacker can DoS Waku by dropping all Waku traffic within its controlled network segment.
An AS attacker can DoS Waku within its authority, while a global attacker can DoS the whole network.
A countermeasure are censorship resistance techniques like <a href="https://www.pluggabletransports.info/about/" target="_blank" rel="noopener noreferrer">Pluggable Transports</a>.</p>
<h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="summary-and-future-work">Summary and Future Work<a href="#summary-and-future-work" class="hash-link" aria-label="Direct link to Summary and Future Work" title="Direct link to Summary and Future Work">​</a></h2>
<p>Currently, Waku v2 relay offers k-anonymity with respect to receiver anonymity.
This also includes k-anonymity towards legitimate members of the same topic.</p>
<p>Waku v2 relay offers sender anonymity in the single node attacker model with its <a href="https://rfc.vac.dev/waku/standards/core/11/relay/#signature-policy" target="_blank" rel="noopener noreferrer">strict no sign policy</a>.
Currently, Waku v2 does not guarantee sender anonymity in the multi node and stronger attacker models.
However, we are working on modular anonymity-preserving protocols and building blocks as part of our privacy/anonymity roadmap.
The goal is to allow tunable anonymity with respect to trade offs between <em>strong anonymity</em>, <em>low bandwidth</em>, and <em>low latency</em>.
All of these cannot be fully guaranteed as the <a href="https://freedom.cs.purdue.edu/projects/trilemma.html" target="_blank" rel="noopener noreferrer">the anonymity trilemma</a> states.
Some applications have specific requirements, e.g. low latency, which require a compromise on anonymity.
Anonymity-preserving mechanisms we plan to investigate and eventually specify as pluggable anonymity protocols for Waku comprise</p>
<ul>
<li><a href="https://arxiv.org/abs/1805.11060" target="_blank" rel="noopener noreferrer">Dandelion++</a> for lightweight anonymity;</li>
<li><a href="https://en.wikipedia.org/wiki/Onion_routing" target="_blank" rel="noopener noreferrer">onion routing</a> as a building block adding a low latency anonymization layer;</li>
<li><a href="https://en.wikipedia.org/wiki/Mix_network" target="_blank" rel="noopener noreferrer">a mix network</a> for providing strong anonymity (on top of onion routing) even in the strongest attacker model at the cost of higher latency.</li>
</ul>
<p>These pluggable anonymity-preserving protocols will form a sub-set of the Waku v2 protocol set.
As an intermediate step, we might directly employ Tor for onion-routing, and <a href="https://nymtech.net/" target="_blank" rel="noopener noreferrer">Nym</a> as a mix-net layer.</p>
<p>In future research log posts, we will cover further Waku v2 protocols and identify anonymity problems that will be added to our roadmap.
These protocols comprise</p>
<ul>
<li><a href="https://rfc.vac.dev/waku/standards/core/13/store" target="_blank" rel="noopener noreferrer">13/WAKU2-STORE</a>, which can violate receiver anonymity as it allows filtering by content topic.
A countermeasure is using the content topic exclusively for local filters.</li>
<li><a href="https://rfc.vac.dev/waku/standards/core/12/filter" target="_blank" rel="noopener noreferrer">12/WAKU2-FILTER</a>, which discloses nodes&#x27; interest in topics;</li>
<li><a href="https://rfc.vac.dev/waku/standards/core/19/lightpush" target="_blank" rel="noopener noreferrer">19/WAKU2-LIGHTPUSH</a>, which also discloses nodes&#x27; interest in topics and links the lightpush client as the sender of a message to the lightpush service node;</li>
<li><a href="https://rfc.vac.dev/waku/standards/application/21/fault-tolerant-store" target="_blank" rel="noopener noreferrer">21/WAKU2-FTSTORE</a>, which discloses nodes&#x27; interest in specific time ranges allowing to infer information like online times.</li>
</ul>
<p>While these protocols are not necessary for the operation of Waku v2, and can be seen as pluggable features,
we aim to provide alternatives without the cost of lowering the anonymity level.</p>
<h2 class="anchor anchorWithHideOnScrollNavbar_WYt5" id="references">References<a href="#references" class="hash-link" aria-label="Direct link to References" title="Direct link to References">​</a></h2>
<ul>
<li><a href="https://rfc.vac.dev/waku/standards/core/10/waku2" target="_blank" rel="noopener noreferrer">10/WAKU2</a></li>
<li><a href="https://rfc.vac.dev/waku/standards/core/11/relay" target="_blank" rel="noopener noreferrer">11/WAKU2-RELAY</a></li>
<li><a href="https://github.com/libp2p/specs/blob/master/pubsub/gossipsub/README.md" target="_blank" rel="noopener noreferrer">libp2p GossipSub</a></li>
<li><a href="https://en.wikipedia.org/wiki/Information_security" target="_blank" rel="noopener noreferrer">Security</a></li>
<li><a href="https://en.wikipedia.org/wiki/Authentication" target="_blank" rel="noopener noreferrer">Authentication</a></li>
<li><a href="https://en.wikipedia.org/wiki/Non-repudiation" target="_blank" rel="noopener noreferrer">Non-repudiation</a></li>
<li><a href="https://noiseprotocol.org/" target="_blank" rel="noopener noreferrer">Noise Protocol Framework</a></li>
<li><a href="https://en.wikipedia.org/wiki/Plausible_deniability#Use_in_cryptography" target="_blank" rel="noopener noreferrer">plausible deniability</a></li>
<li><a href="https://rfc.vac.dev/waku/standards/core/14/message" target="_blank" rel="noopener noreferrer">Waku v2 message</a></li>
<li>[partitioned topics](<a href="https://rfc.vac.dev/status/deprecated/10/waku-usage" target="_blank" rel="noopener noreferrer">https://rfc.vac.dev/status/deprecated/10/waku-usage</a>
#partitioned-topic)</li>
<li><a href="https://en.wikipedia.org/wiki/Sybil_attack" target="_blank" rel="noopener noreferrer">Sybil attack</a></li>
<li><a href="https://en.wikipedia.org/wiki/Dolev%E2%80%93Yao_model" target="_blank" rel="noopener noreferrer">Dolev-Yao model</a></li>
<li><a href="https://github.com/waku-org/specs/blob/master/standards/application/noise.md" target="_blank" rel="noopener noreferrer">WAKU2-NOISE</a></li>
<li><a href="https://vac.dev/wakuv2-apd" target="_blank" rel="noopener noreferrer">33/WAKU2-DISCV5</a></li>
<li><a href="https://github.com/ethereum/consensus-specs/blob/dev/specs/phase0/p2p-interface.md#why-are-we-using-the-strictnosign-signature-policy" target="_blank" rel="noopener noreferrer">strict no sign policy</a></li>
<li><a href="https://rfc.vac.dev/waku/standards/core/11/relay#signature-policy" target="_blank" rel="noopener noreferrer">Waku v2 strict no sign policy</a></li>
<li><a href="https://rfc.vac.dev/waku/standards/core/17/rln-relay" target="_blank" rel="noopener noreferrer">17/WAKU-RLN-RELAY</a></li>
<li><a href="https://freedom.cs.purdue.edu/projects/trilemma.html" target="_blank" rel="noopener noreferrer">anonymity trilemma</a></li>
<li><a href="https://rfc.vac.dev/waku/deprecated/18/swap" target="_blank" rel="noopener noreferrer">18/WAKU2-SWAP</a></li>
<li><a href="https://www.pluggabletransports.info/about/" target="_blank" rel="noopener noreferrer">Pluggable Transports</a></li>
<li><a href="https://nymtech.net/" target="_blank" rel="noopener noreferrer">Nym</a></li>
<li><a href="https://arxiv.org/abs/1805.11060" target="_blank" rel="noopener noreferrer">Dandelion++</a></li>
<li><a href="https://rfc.vac.dev/waku/standards/core/13/store" target="_blank" rel="noopener noreferrer">13/WAKU2-STORE</a></li>
<li><a href="https://rfc.vac.dev/waku/standards/core/12/filter" target="_blank" rel="noopener noreferrer">12/WAKU2-FILTER</a></li>
<li><a href="https://rfc.vac.dev/waku/standards/core/19/lightpush" target="_blank" rel="noopener noreferrer">19/WAKU2-LIGHTPUSH</a></li>
<li><a href="https://rfc.vac.dev/waku/standards/application/21/fault-tolerant-store" target="_blank" rel="noopener noreferrer">21/WAKU2-FTSTORE</a></li>
</ul></div></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="Blog post page navigation"><a class="pagination-nav__link pagination-nav__link--prev" href="/rlog/building-privacy-protecting-infrastructure"><div class="icon_S7Kx m_thRi"><svg xmlns="http://www.w3.org/2000/svg" width="14" height="14" fill="none" viewBox="0 0 14 14"><path fill="#fff" d="M11.667 6.417h-7.1L7.83 3.156 7 2.333 2.334 7 7 11.667l.823-.823-3.255-3.26h7.099z"></path></svg></div><span class="lsd-typography lsd-typography--body2 pagination-nav__label">Building Privacy-Protecting Infrastructure</span></a><a class="pagination-nav__link pagination-nav__link--next" href="/rlog/wakuv2-noise"><span class="lsd-typography lsd-typography--body2 pagination-nav__label">Noise handshakes as key-exchange mechanism for Waku</span><div class="icon_S7Kx m_thRi"><svg xmlns="http://www.w3.org/2000/svg" width="14" height="14" fill="none" viewBox="0 0 14 14"><path fill="#fff" d="m7 2.334-.823.822 3.255 3.26H2.333v1.167h7.1l-3.256 3.261.823.823L11.667 7z"></path></svg></div></a></nav></main><div class="col col--2"><div class="tableOfContents_bqdL thin-scrollbar"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#informal-definitions-security-privacy-and-anonymity" class="table-of-contents__link toc-highlight">Informal Definitions: Security, Privacy, and Anonymity</a><ul><li><a href="#security" class="table-of-contents__link toc-highlight">Security</a></li><li><a href="#privacy" class="table-of-contents__link toc-highlight">Privacy</a></li><li><a href="#anonymity" class="table-of-contents__link toc-highlight">Anonymity</a><ul><li><a href="#receiver-anonymity" class="table-of-contents__link toc-highlight">Receiver Anonymity</a></li><li><a href="#sender-anonymity" class="table-of-contents__link toc-highlight">Sender Anonymity</a></li></ul></li><li><a href="#anonymity-trilemma" class="table-of-contents__link toc-highlight">Anonymity Trilemma</a></li><li><a href="#censorship-resistance" class="table-of-contents__link toc-highlight">Censorship Resistance</a></li></ul></li><li><a href="#attacker-types" class="table-of-contents__link toc-highlight">Attacker Types</a><ul><li><a href="#internal" class="table-of-contents__link toc-highlight">Internal</a><ul><li><a href="#single-node" class="table-of-contents__link toc-highlight">Single Node</a></li><li><a href="#multi-node" class="table-of-contents__link toc-highlight">Multi Node</a></li><li><a href="#linearly-scaling-nodes" class="table-of-contents__link toc-highlight">Linearly Scaling Nodes</a></li></ul></li><li><a href="#external" class="table-of-contents__link toc-highlight">External</a><ul><li><a href="#local" class="table-of-contents__link toc-highlight">Local</a></li><li><a href="#as" class="table-of-contents__link toc-highlight">AS</a></li><li><a href="#global-on-net" class="table-of-contents__link toc-highlight">Global On-Net</a></li></ul></li></ul></li><li><a href="#attack-based-threat-analysis" class="table-of-contents__link toc-highlight">Attack-based Threat Analysis</a><ul><li><a href="#scope" class="table-of-contents__link toc-highlight">Scope</a></li><li><a href="#prerequisite-get-a-specific-position-in-the-network" class="table-of-contents__link toc-highlight">Prerequisite: Get a Specific Position in the Network</a></li><li><a href="#replay-attack" class="table-of-contents__link toc-highlight">Replay Attack</a></li><li><a href="#neighbourhood-surveillance" class="table-of-contents__link toc-highlight">Neighbourhood Surveillance</a></li><li><a href="#controlled-neighbourhood" class="table-of-contents__link toc-highlight">Controlled Neighbourhood</a></li><li><a href="#observing-messages" class="table-of-contents__link toc-highlight">Observing Messages</a></li><li><a href="#correlation" class="table-of-contents__link toc-highlight">Correlation</a></li><li><a href="#dos" class="table-of-contents__link toc-highlight">DoS</a></li></ul></li><li><a href="#summary-and-future-work" class="table-of-contents__link toc-highlight">Summary and Future Work</a></li><li><a href="#references" class="table-of-contents__link toc-highlight">References</a></li></ul></div></div></div></div></div><footer class="footer"><div class="container container-fluid firstRow_ar1q"><div class="footer__bottom text--center"><div class="margin-bottom--sm"><a class="footerLogoLink_BH7S" href="/"><img src="/theme/image/logo.svg" alt="Vac Research" class="themedImage_kfRS themedImage--light_BL8e footer__logo" width="22"><img src="/theme/image/logo.svg" alt="Vac Research" class="themedImage_kfRS themedImage--dark_OvIx footer__logo" width="22"></a></div><div class="footer__copyright">Vac Research © 2026<br>All rights reserved.</div></div><div class="row footer__links"><div class="col footer__col"><div class="footer__title"></div><ul class="footer__items clean-list"><li class="footer__item"><a 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