关键词: 秘密共享, 中国剩余定理, 紧耦合秘密共享, 多项式环

Abstract:

In the reconstruction of[(t,n)]secret sharing, any more than[t]participants can recover a secret. But in a real application, it only needs any[ t ]participants to recover the secret when [kt≤k≤n]participants recover the secret, even if [k-t] participants do not provide shares. In a [(t,k,n)] tightly coupled secret sharing scheme, when [k ]participants seen as a group recover the secret, each one in the group needs to participate in the reconstruction of the secret. Any[k-1] participants can not get any information about the secret. In known tightly coupled secret sharing schemes, no matter what scheme based on Chinese Remainder Theorem（CRT） or based on Lagrange interpolating polynomial, they all have efficiency problems that information ratio does not equal 1. This paper generalizes CRT to a polynomial ring over finite fields and presents an ideal tightly coupled secret sharing scheme based on CRT over a polynomial ring.

Key words: secret sharing, Chinese Remainder Theorem（CRT）, tightly coupled secret sharing scheme, polynomial ring