摘要： 多秘密共享就是在一次秘密共享过程中共享多个秘密，已有的多秘密共享方案都是利用Lagrange插值多项式来共享秘密。针对上述情况，基于RSA密码系统中大数分解问题，利用简单的异或运算“ ”设计一个多秘密共享方案，该方案的特点是运算简单、计算量小，参与者的子秘密可以重复使用，能够防止秘密分发者和参与者的欺诈，且在整个方案中不需要安全信道。

关键词: 秘密共享, 多秘密共享, 访问结构, 欺诈

Abstract: In the multi-secret sharing scheme, several secrets can be shared during one secret sharing process simultaneously. The previous multi-secret sharing schemes are based on the Lagrange interpolating polynomial. In this paper, using the “ ” operation in arithmetic, a simple multi-secret sharing scheme based on the difficulty of factoring the RSA modulus is proposed. The features of the scheme are that the computation is fast and the operation is simple. The participants can share many secrets one time and each one of them only holds one shadows which can be reused after the shared secrets have been recovered. The dealer and the participants’ cheating are resisted. The secret channel is not provided in this scheme.

Key words: secret sharing, multi-secret sharing, access structure, cheating

中图分类号: 

• TP309