SumCheck 协议SumCheck是一个 interactive proof。给定一个 v - variate polynomial g defined over a finite field F ,SumCheck的作用是,使prover可以让verifier相信如下等式成立:协议流程(先直接上例子):…
在SumCheck的第一个应用#SAT中,Verifier time和Prover time都不够快。所以我们希望设计verifier and prover time都高效的interactive proofs(doubly-efficient)。 Problem Definition 算出一个简单图中有多少个三角形。 如何对这个问题应用SumCheck协议: 将图转化为邻接矩阵 A 。当 (i,j) 是简单图的边时,Ai,j=1...
All Language in NP Have Divertible Zero-Knowledge Proofs and Arguments under Cryptographic Assumptions - Burmester, Desmedt - 1991 () Citation Context ... he has to interact with the randomizer to get it. However, we want that any part of the transcript of this interaction cannot be used as...
A note on efficient zero-knowledge proofs and arguments This work considers locally decodable codes in the computationally bounded channel model. The computationally bounded channel model, introduced by Lipton in 1994, views the channel as an adversary which is restricted to polynomial-time c... J ...
Part 5: PLONK and Custom Gates with Adrian Hamelink Part 6: Lookup Arguments for Performance Optimisation Part 7: Zero Knowledge Virtual Machines (zkVM) Part 8: Achieving Decentralised Private Computation Part 9: Introduction to zkRollups
In last years, there has been an increasing effort to leverage distributed ledger technology (DLT), including blockchain. One of the main topics of interest, given its importance, is the research and development of privacy mechanisms, as for example is the case of zero knowledge proofs (ZKP)...
Zero-knowledge shuffle arguments can have multiple use cases: Secret leader electionprotocols Message shuffling inmixnets Universally verifiableelectronic votingprotocols Documentation The user-facing documentation for this library can befound here. In this library, we provide high-level protocol documentation...
zkSNARKs essentially made it possible to efficiently scale the number of polynomials that can be gated, unlocking speed and more complex potential applications for zero-knowledge proofs. The “SNARK” part of zkSNARK stands for “Succinct Non-Interactive Arguments of Knowledge”, and the words ...
verifiers at a time efficiently. The proofs are secure against the collusion of a prover and a subset of t verifiers. We refer to such ZK proofs as multi-verifier zero-knowledge (MVZK) proofs and focus on the case that a majority of verifiers are honest (i.e., t < n=2). We co...
Proofs, Arguments, and Zero-Knowledge第三章学习笔记(1) WhateverWillBe 热爱生活 1 人赞同了该文章 Multilinear extension 第二章中有讲univariate function的low degree extension。简言之,就是将univariate function的值插值成多项式,该多项式定义在一个更大的域 F 上。