一种防欺骗的广义多秘密分享方案

A Generalized Multi-secret Sharing Scheme to Identify Cheaters

秘密分享是信息安全和密码学的重要研究课题,对通信密钥管理和计算机网络安全具有重要意义。本文针对现有的多秘密分享方案不能有效地防止分发者和分享者的欺骗,以及子秘密恢复时计算复杂量大等问题,在基于离散对数与因式分解难题上,提出一种具有广义接入结构的高效的多秘密分享方案。该方案具有如下特点:可高效地检测秘密管理者与分享者的欺诈行为;秘密管理者只需公开少量数据就可动态地增加一个新子秘密;采用并行算法恢复子秘密;可高效地增加或删除成员,无需重新计算其他成员的秘密份额。该方案可在分布式会议秘密分配、安全分布式计算、电子商务等领域应用。

Secret sharing is an important research area in information security and cryptography, which is significant to managing communication keys and ensuring the safety of computer networks. Most previous multi-secret sharing schemes have problems in efficiently detecting the cheating of either the dealer or shadowholders and in carrying out complex and large-amount computation for secret recovery. The authors have designed an efficient multi-secret sharing scheme with a generalized access structure on the basis of dealing with the difficul- ty of computing the discrete logarithm modulo for a composite number and the factorization problem of a large integer. The proposed scheme has the following properties： （1）Cheating of the dealer or any participant can be detected efficiently; （2）a new secret can be added on the bulletin by the dealer at any time on condition that small-amount of data are made public; （3） the participants can reconstruct a secret with the parallel procedure in a secret recovery phase; （4）the shadows of the participants will not change when the system accepts a new participant or fires an old participant. This scheme will find wide applications in conferences distributed secretly, securely-distributed computation and electronic commerce.