Towards a zk-SNARK compiler for Wolfram language

Zero-knowledge proofs (zk-Proofs) are communication protocols by which a prover can demonstrate to a verifier that it possesses a solution to a given public problem without revealing the content of the solution. Arbitrary computations can be transformed into an interactive zk-Proof so anyone is convinced that it was executed correctly without knowing what was executed on, having huge implications for digital currency. Despite this, interactive proofs are not suited for blockchain applications but novel protocols such as zk-SNARKs have made zero-knowledge ledgers like Zcash possible. This project builds upon Wolfram's ZeroKnowledgeProofs paclet and implements a zk-SNARK compiler based on Pinocchio protocol

Secure formation of public parameters and elimination of vulnerabilities of zero-knowledge succint non-interactive arguments of knowledge

Рассматриваются известные методы устранения уязвимостей кратких неинтерактивнвгх аргументов с нулевым разглашением на основе корректировки уравнений верификации доказателвств, значений публичных параметров в виде главных ссылочных строк и ключей формирования доказателвств. Описаны способы защищённого формирования главных ссылочных строк с исполвзованием доверенной третьей стороны и многостороннего взаимодействия

A Fully Anonymous e-Voting Protocol Employing Universal zk-SNARKs and Smart Contracts

The idea of smart contracts has been around for a long time. The introduction of Ethereum has taken the concept of smart contracts to new heights because of its integration with Blockchain technology. As a result, the applications of smart contracts have also surged in areas such as e-Voting, Insurance, Crowdfunding, etc. In this paper, we aim to present the construction of a “Fully Anonymous e-Voting” protocol using the concepts of zkHawk and Zcash. zkHawk is a novel smart contract protocol designed during this Ph.D. that improves upon the Hawk protocol by solving the underlying anonymity problem of a trusted manager. We will leverage the concept of zk-SNARKs in Zcash to carry out the voting phase of the election and the zkHawk smart contract protocol to tally the results of the election. The voting phase employing Zcash will be initially designed with Non-Universal zk-SNARKs and improved upon with Universal zk-SNARKs

A Note On Groth-Ostrovsky-Sahai Non-Interactive Zero-Knowledge Proof System

In 2006, Groth, Ostrovsky and Sahai designed one non-interactive zero-knowledge (NIZK) proof system [new version, J. ACM, 59(3), 1-35, 2012] for plaintext being zero or one using bilinear groups with composite order. Based on the system, they presented the first perfect NIZK argument system for any NP language and the first universal composability secure NIZK argument for any NP language in the presence of a dynamic/adaptive adversary. This resolves a central open problem concerning NIZK protocols. In this note, we remark that in their proof system the prover has not to invoke the trapdoor key to generate witnesses. The mechanism was dramatically different from the previous works, such as Blum-Feldman-Micali proof system and Blum-Santis-Micali-Persiano proof system. We would like to stress that the prover can cheat the verifier to accept a false claim if the trapdoor key is available to him

Ways to improve the performance of zero-knowledge succinct non-interactivearguments of knowledge and the analysis of the rusults achieved

Рассматриваются способы повышения производительности кратких неинтерактивных аргументов с нулевым разглашением на основе полиномиальных наборов с использованием различных вычислительных методов. Проводится сравнительный анализ протоколов по размерам главных ссылочных строк и доказательств достоверности вычислений, затратам формирования доказательств и их верификации

Making Sigma-Protocols Non-interactive Without Random Oracles

Damg˚ard, Fazio and Nicolosi (TCC 2006) gave a transformation of Sigma-protocols, 3-move honest verifier zero-knowledge proofs, into efficient non-interactive zero-knowledge arguments for a designated verifier. Their transformation uses additively homomorphic encryption to encrypt the verifier’s challenge, which the prover uses to compute an encrypted answer. The transformation does not rely on the random oracle model but proving soundness requires a complexity leveraging assumption. We propose an alternative instantiation of their transformation and show that it achieves culpable soundness without complexity leveraging. This improves upon an earlier result by Ventre and Visconti (Africacrypt 2009), who used a different construction which achieved weak culpable soundness. We demonstrate how our construction can be used to prove validity of encrypted votes in a referendum. This yields a voting system with homomorphic tallying that does not rely on the Fiat-Shamir heuristic