Hashing to Prime in Zero-Knowledge

Gross, T

doi:10.5220/0010525400620074

Hashing to Prime in Zero-Knowledge

Lookup NU author(s): Professor Thomas Gross ORCiD

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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 p_x. 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.