A simple construction of CRT-based ideal secret sharing scheme and its security extension based on common factor

摘要

Secret sharing (SS) is part of the essential techniques in cryptography but still faces many challenges in efficiency and security. Currently, SS schemes based on the Chinese Remainder Theorem (CRT) are either low in the information rate or complicated in construction. To solve the above problems, 1) a simple construction of an ideal (t, n)-SS scheme is proposed based on CRT for a polynomial ring. Compared with Ning’s scheme, it is much more efficient in generating n pairwise coprime modular polynomials during the scheme construction phase. Moreover, Shamir’s scheme is also a special case of our scheme. To further improve the security, 2) a common-factor-based (t, n)-SS scheme is proposed in which all shareholders share a common polynomial factor. It enables both the verification of received shares and the establishment of a secure channel among shareholders during the reconstruction phase. As a result, the scheme is resistant to eavesdropping and modification attacks by outside adversaries.