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Zero-knowledge (ZK) circuits enable privacy-preserving computations and are central to many cryptographic protocols. Systems like Circom simplify ZK development by combining witness computation and circuit constraints in one program.…

Cryptography and Security · Computer Science 2026-05-26 Hideaki Takahashi , Jihwan Kim , Suman Jana , Junfeng Yang

Zero-Knowledge (ZK) proof systems are cryptographic protocols that can (with overwhelming probability) demonstrate that the pair $(X, W)$ is in a relation $R$ without revealing information about the private input $W$. This membership…

Cryptography and Security · Computer Science 2026-01-15 Pedro Antonino , Namrata Jain

Zero-knowledge (ZK) protocols have recently found numerous practical applications, such as in authentication, online-voting, and blockchain systems. These protocols are powered by highly complex pipelines that process deterministic…

Software Engineering · Computer Science 2024-11-05 Christoph Hochrainer , Anastasia Isychev , Valentin Wüstholz , Maria Christakis

We present ZK-SecreC, a domain-specific language for zero-knowledge proofs. We present the rationale for its design, its syntax and semantics, and demonstrate its usefulness on the basis of a number of non-trivial examples. The design…

Zero-knowledge proofs (ZKPs) have evolved from a theoretical cryptographic concept into a powerful tool for implementing privacy-preserving and verifiable applications without requiring trust assumptions. Despite significant progress in the…

Cryptography and Security · Computer Science 2025-05-01 Stefanos Chaliasos , Imam Al-Fath , Alastair Donaldson

Zero-knowledge circuits are sets of equality constraints over arithmetic expressions interpreted in a prime field; they are used to encode computations in cryptographic zero-knowledge proofs. We make the following contributions to the…

Logic in Computer Science · Computer Science 2023-11-16 Alessandro Coglio , Eric McCarthy , Eric W. Smith

Zero-knowledge proofs (ZKPs) are increasingly deployed in domains such as privacy-preserving authentication, verifiable computation, and secure finance. However, authoring ZK programs remains challenging: unlike conventional software…

Software Engineering · Computer Science 2026-02-03 Zhantong Xue , Pingchuan Ma , Zhaoyu Wang , Yuguang Zhou , Xiaoqin Zhang , Shuai Wang , Juergen Rahmel

Zero-knowledge proof (ZKP) systems have surged attention and held a fundamental role in contemporary cryptography. Zero-knowledge succinct non-interactive argument of knowledge (zk-SNARK) protocols dominate the ZKP usage, implemented…

Software Engineering · Computer Science 2025-12-23 Qizhe Yang , Boxuan Liang , Hao Chen , Guoqiang Li

This paper studies the complexity classes QZK and HVQZK of problems having a quantum computational zero-knowledge proof system and an honest-verifier quantum computational zero-knowledge proof system, respectively. The results proved in…

Quantum Physics · Physics 2007-05-23 Hirotada Kobayashi

The modern integrated circuit ecosystem is increasingly reliant on third-party intellectual property integration, which introduces security risks, including hardware Trojans and security vulnerabilities. Addressing the resulting trust…

Cryptography and Security · Computer Science 2026-04-13 Sirui Shen , Zunchen Huang , Chenglu Jin

Zero-knowledge (ZK) protocols enable software developers to provide proofs of their programs' correctness to other parties without revealing the programs themselves. Regular expressions are pervasive in real-world software, and…

Cryptography and Security · Computer Science 2025-04-03 John Kolesar , Shan Ali , Timos Antonopoulos , Ruzica Piskac

Zero-knowledge proofs are an essential building block in many privacy-preserving systems. However, implementing these proofs is tedious and error-prone. In this paper, we present zksk, a well-documented Python library for defining and…

Cryptography and Security · Computer Science 2019-11-12 Wouter Lueks , Bogdan Kulynych , Jules Fasquelle , Simon Le Bail-Collet , Carmela Troncoso

Zero-Knowledge Proofs (ZKPs) are a cryptographic primitive that allows a prover to demonstrate knowledge of a secret value to a verifier without revealing anything about the secret itself. ZKPs have shown to be an extremely powerful tool,…

Cryptography and Security · Computer Science 2025-04-29 Nojan Sheybani , Anees Ahmed , Michel Kinsy , Farinaz Koushanfar

We present the first constructions of single-prover proof systems that achieve perfect zero knowledge (PZK) for languages beyond NP, under no intractability assumptions: 1. The complexity class #P has PZK proofs in the model of Interactive…

Computational Complexity · Computer Science 2016-10-13 Eli Ben-Sasson , Alessandro Chiesa , Michael A. Forbes , Ariel Gabizon , Michael Riabzev , Nicholas Spooner

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…

Cryptography and Security · Computer Science 2024-01-08 Armando Cruz

We propose a new library to model and verify hardware circuits in the Coq proof assistant. This library allows one to easily build circuits by following the usual pen-and-paper diagrams. We define a deep-embedding: we use a (dependently…

Logic in Computer Science · Computer Science 2011-08-23 Thomas Braibant

Zero-knowledge proofs (ZKPs) have emerged as a promising solution to address the scalability challenges in modern blockchain systems. This study proposes a methodology for generating and verifying ZKPs to ensure the computational integrity…

Cryptography and Security · Computer Science 2026-04-13 Oleksandr Kuznetsov , Anton Yezhov , Vladyslav Yusiuk , Kateryna Kuznetsova

Machine learning is increasingly deployed through outsourced and cloud-based pipelines, which improve accessibility but also raise concerns about computational integrity, data privacy, and model confidentiality. Zero-knowledge proofs (ZKPs)…

Cryptography and Security · Computer Science 2026-03-31 Zhizhi Peng , Chonghe Zhao , Taotao Wang , Guofu Liao , Zibin Lin , Yifeng Liu , Bin Cao , Long Shi , Qing Yang , Shengli Zhang

We introduce a technology to formally verify that a software system satisfies a temporal specification of functional correctness, without revealing the system itself. Our method combines a deductive approach to model checking to obtain a…

Cryptography and Security · Computer Science 2026-05-04 Pascal Berrang , Mirco Giacobbe , Jacob Swales , Xiao Yang

Zero-Knowledge (ZK) protocols have been intensely studied due to their fundamental importance and versatility. However, quantum information's inherent differences significantly alter the landscape, necessitating a re-examination of ZK…

Quantum Physics · Physics 2025-04-08 Nai-Hui Chia , Kai-Min Chung , Xiao Liang , Jiahui Liu
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