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@@ -46,7 +46,7 @@ When utilizing the non-interactive variant of the folding method for relaxed R1C
the verifier’s expenses remain consistent, leading to a verifier circuit of constant size, primarily influenced by two group scalar multiplications.
The work required by the prover at each juncture is majorly defined by two multiexponentiations, roughly mirroring the magnitude of the incremental computation |F|.
Nova’s methodology paves the way for executing IVC with a concise verifier circuit and streamlined prover calculations.
Nova’s methodology paves the way for executing IVC with a concise verifier circuit and streamlined prover calculations.
It sidesteps the need for FFTs and can be effectively set up using any elliptic curve cycles where the Discrete Logarithm Problem (DLOG) poses challenges.
Furthermore, Nova integrates a proficient zero-knowledge succinct non-interactive argument (zkSNARK) to succinctly and confidentially validate the possession of legitimate IVC proofs.
This ensures a brief, confidential validation of a genuine IVC demonstration.
@@ -56,33 +56,33 @@ The work required by the prover at each juncture is majorly defined by two multi
Computation (NIVC) approach, improving the folding scheme implementations significantly. The integration of the SuperNova protocol into Arecibo, is a significant leap in cryptographic
proofs and folding schemes.
Several optimizations were implemented to enhance the efficiency of the Arecibo implementation. Specifically, the number of variables and constraints in the recursive
Several optimizations were implemented to enhance the efficiency of the Arecibo implementation. Specifically, the number of variables and constraints in the recursive
verification circuit were significantly reduced and the accuracy of the recursive SNARK verification was improved. This allows for the verification of the folding logic
without the need to generate a full compressed SNARK.
To avoid a malicious prover from generating a valid proof for any public input, Arecibo builds on the Bounded Witness Sumcheck which presents an effective solution
To avoid a malicious prover from generating a valid proof for any public input, Arecibo builds on the Bounded Witness Sumcheck which presents an effective solution
in both individual and batched settings, maintaining uniformity and enhancing security. Moreover, an optimized SNARK tailored for SuperNova's folded proofs was developed.
Nova currently utilizes an adapted Spartan SNARK protocol for compressing relaxed R1CS instances at the final stage. With the advancement to SuperNova, a batched version
of the Spartan protocol was introduced. This version can verify several relaxed R1CS instances simultaneously within a single SNARK proof, significantly improving the efficiency of the verification process.
To address the issue of the costs for both the prover and the verifier when compressing SuperNova proofs (which requires the prover to supply a distinct SNARK proof for every circuit), Arecibo implemented solution that consolidates multiple Spartan proofs into a single batch for combined proof and verification. This innovative method substantially reduces the complexity for the verifier, equating it to the challenge of verifying a single Spartan proof, or two in the case of cycle of curves scenarios. This batching approach not only streamlines the verification process but also significantly cuts down on the resources and time required for both parties involved.
To address the issue of the costs for both the prover and the verifier when compressing SuperNova proofs (which requires the prover to supply a distinct SNARK proof for every circuit), Arecibo implemented solution that consolidates multiple Spartan proofs into a single batch for combined proof and verification. This innovative method substantially reduces the complexity for the verifier, equating it to the challenge of verifying a single Spartan proof, or two in the case of cycle of curves scenarios. This batching approach not only streamlines the verification process but also significantly cuts down on the resources and time required for both parties involved.
* _Halo2 (GWC)_: Halo2 emerges as a pioneering zk-SNARK framework, enabling recursive proof composition without a trusted setup, marking a significant advancement in cryptographic protocols. It operates based on the discrete log assumption, utilizing standard cycles of elliptic curves to verify complex computational tasks incrementally. A notable innovation within Halo2 is the introduction of a unique pair of elliptic curves, Tweedledum and Tweedledee, forming a 2-cycle that plays a critical role in its operations.
Incorporating UltraPLONK's advancements, Halo2 extends its capabilities with PLONKish circuits, which are designed with a focus on efficiency and flexibility. These circuits are organized in a matrix format, with components categorized into fixed, advice, and instance columns, supporting a variety of polynomial and lookup arguments. This structure is underpinned by a finite field \(F\), with configurations that include limits on constraint degrees and specific columns for equality constraints.
Incorporating UltraPLONK's advancements, Halo2 extends its capabilities with PLONKish circuits, which are designed with a focus on efficiency and flexibility. These circuits are organized in a matrix format, with components categorized into fixed, advice, and instance columns, supporting a variety of polynomial and lookup arguments. This structure is underpinned by a finite field \(F\), with configurations that include limits on constraint degrees and specific columns for equality constraints.
One of the keys to Halo2's efficiency is its utilization of specific endomorphisms, significantly reducing the size of the verification circuit. This ensures that both the proof size and the verification time remain manageable, regardless of the recursion levels involved. The protocol's design emphasizes minimizing resource requirements while maximizing performance, making it stand out in terms of proof size, recursion capability, and proving speed when compared to other zk-SNARK constructions.
One of the keys to Halo2's efficiency is its utilization of specific endomorphisms, significantly reducing the size of the verification circuit. This ensures that both the proof size and the verification time remain manageable, regardless of the recursion levels involved. The protocol's design emphasizes minimizing resource requirements while maximizing performance, making it stand out in terms of proof size, recursion capability, and proving speed when compared to other zk-SNARK constructions.
By integrating PLONKish circuit designs, Halo2 leverages the strengths of UltraPLONK, including custom gates and enhanced lookup arguments, to support its innovative recursive proof system. This synergy between Halo2's foundational elliptic curve operations and the PLONKish circuit framework establishes a robust and efficient platform for secure, scalable, and trustless verification of computational tasks.
By integrating PLONKish circuit designs, Halo2 leverages the strengths of UltraPLONK, including custom gates and enhanced lookup arguments, to support its innovative recursive proof system. This synergy between Halo2's foundational elliptic curve operations and the PLONKish circuit framework establishes a robust and efficient platform for secure, scalable, and trustless verification of computational tasks.
* _Halo2 (SHPlonk)_: SHPlonk is a significant advancement over the PLONK protocol, representing a more efficient solution compared to PLONK. Its implementation in Halo2 underscores its potential to build more scalable and secure blockchains.
The key differentiator of SHPlonk lies in its utilization of a multi-poly commitment scheme, wherein the prover commits to multiple polynomials instead of just one. This approach adds an extra layer of security, as the verifier would need to guess the values of all committed polynomials to successfully refute the proof, thus reducing the likelihood of cheating.
The key differentiator of SHPlonk lies in its utilization of a multi-poly commitment scheme, wherein the prover commits to multiple polynomials instead of just one. This approach adds an extra layer of security, as the verifier would need to guess the values of all committed polynomials to successfully refute the proof, thus reducing the likelihood of cheating.
Furthermore, SHPlonk optimizes the polynomial commitment layer, offering advantages such as reducing the workload of the prover and enabling multiple polynomial openings. These benefits include a more effective commitment scheme compared to the KZG10 commitment, support for multi-polynomial and multi-openings, and a reduction in the number of elliptic curve operations required by the verifier.
By streamlining the verification process and reducing gas consumption, SHPlonk paves the way for the development of more efficient and scalable cryptographic protocols, making it a valuable tool for enhancing blockchain security and privacy.
By streamlining the verification process and reducing gas consumption, SHPlonk paves the way for the development of more efficient and scalable cryptographic protocols, making it a valuable tool for enhancing blockchain security and privacy.
* _Plonky2_: Plonky2 represents a cryptographic argument system designed for rapid recursive composition. While it’s grounded in the TurboPLONK arithmetization framework,
it diverges by integrating the FRI (Fast Reed- Solomon Interactive Oracle Proof) into its polynomial testing approach.