Information-theoretic secure verifiable secret sharing over RSA modulus

Abstract

The well-known non-interactive and information-theoretic secure verifiable secret sharing scheme presented by Pedersen is over a large prime. In this paper, we construct a novel non-interactive and information-theoretic verifiable secret sharing over RSA (Rivest, Shamir, Adleman) modulus and give the rigorous security proof. It is shown how to distribute a secret among a group such that any set ofk parties get no information about the secret. The presented scheme is generally applied to constructions of secure distributed multiplication and threshold or forward-secure signature protocols.