关键词: 秘密共享, 欺骗者, 二元对称多项式, 公平性

Abstract: Based on symmetric bivariate polynomial, this paper proposes a new fair [(t,n)] threshold secret sharing scheme, which can guarantee that each participant can recover the correct secret if all participants are legal and honest; when there is a cheater, all participants are unable to recover the correct secret. In the proposed scheme, a symmetric bivariate polynomial is used to generate session key for any two participants; moreover, combined with discrete logarithm, the symmetric bivariate polynomial enables the scheme to choose a sufficiently long sequence of secrets to guarantee the fairness while each participant holds a small number of shares. Additionally, the scheme also can achieve fair secret recovery in asynchronous environment. Compared with Harn’s scheme, the proposed scheme is fairer and more flexible.

Key words: secret sharing, cheater, symmetric bivariate polynomial, fairness