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.

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