Paper 2021/052

Elementary Attestation of Cryptographically Useful Composite Moduli

Rémi Géraud-Stewart and David Naccache

Abstract

This paper describes a non-interactive process allowing a prover to convince a verifier that a modulus $n$ is the product of two primes ($p,q$) of about the same size. A further heuristic argument conjectures that $p-1$ and $q-1$ have sufficiently large prime factors for cryptographic applications. The new protocol relies upon elementary number-theoretic properties and can be implemented efficiently using very few operations. This contrasts with state-of-the-art zero-knowledge protocols for RSA modulus proper generation assessment. The heuristic argument at the end of our construction calls for further cryptanalysis by the community and is, as such, an interesting research question in its own right.