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Hashing to Prime in Zero-Knowledge

Lookup NU author(s): Professor Thomas Gross

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This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND).


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, signature and attribute-based credential schemes 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, with applications to setting up secure special RSA moduli.


Publication metadata

Author(s): Gross T

Editor(s): Sabrina De Capitani di Vimercati and Pierangela Samarati

Publication type: Conference Proceedings (inc. Abstract)

Publication status: Published

Conference Name: Proceedings of the 18th International Conference on Security and Cryptography - SECRYPT

Year of Conference: 2021

Pages: 62-74

Print publication date: 01/10/2021

Online publication date: 01/10/2021

Acceptance date: 16/04/2021

Date deposited: 28/06/2022

Publisher: SciTePress

URL: https://doi.org/10.5220/0010525400620074

DOI: 10.5220/0010525400620074

Library holdings: Search Newcastle University Library for this item

ISBN: 9789897585241


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