Sharing DSS by the Chinese Remainder Theorem

Abstract

In this paper, we propose a new threshold scheme for the Digital Signature Standard (DSS) using Asmuth–Bloom secret sharing based on the Chinese Remainder Theorem (CRT). To achieve the desired result, we first show how to realize certain other threshold primitives using Asmuth–Bloom secret sharing, such as joint random secret sharing, joint exponential random secret sharing, and joint exponential inverse random secret sharing. We prove the security of our scheme against a static adversary. To the best of our knowledge, this is the first provably secure threshold DSS scheme based on CRT.