Hashing to Prime in Zero-Knowledge

Thomas Groß

2021

Abstract

We establish a set of zero-knowledge arguments that allow for the hashing of a committed secret a-bit input x to a committed secret (k +1)-bit prime number px. The zero-knowledge arguments can convince a verifier that a commitment indeed is the correctly generated prime number derived from x with a soundness error probability of at most 2−k + 2−t dependent on the number of zero-knowledge argument rounds k and the number of primality bases t to establish primality. Our constructions offer a range of contributions including enabling dynamic encodings for prime-based accumulator (Barić and Pfitzmann, 1997; Camenisch and Lysyanskaya, 2002), signature (Groß, 2015) and attribute-based credential schemes (Camenisch and Groß, 2008) allowing to reduce these schemes’ public key size and setup requirements considerably and rendering them extensible. While our new primality zero-knowledge arguments are of independent interest, we also show improvements on proving that a secret number is the product of two secret safe primes significantly more efficient than previously known results (Camenisch and Michels, 1999), with applications to setting up secure special RSA moduli.

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Paper Citation


in Harvard Style

Groß T. (2021). Hashing to Prime in Zero-Knowledge. In Proceedings of the 18th International Conference on Security and Cryptography - Volume 1: SECRYPT, ISBN 978-989-758-524-1, pages 62-74. DOI: 10.5220/0010525400620074


in Bibtex Style

@conference{secrypt21,
author={Thomas Groß},
title={Hashing to Prime in Zero-Knowledge},
booktitle={Proceedings of the 18th International Conference on Security and Cryptography - Volume 1: SECRYPT,},
year={2021},
pages={62-74},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0010525400620074},
isbn={978-989-758-524-1},
}


in EndNote Style

TY - CONF

JO - Proceedings of the 18th International Conference on Security and Cryptography - Volume 1: SECRYPT,
TI - Hashing to Prime in Zero-Knowledge
SN - 978-989-758-524-1
AU - Groß T.
PY - 2021
SP - 62
EP - 74
DO - 10.5220/0010525400620074