基于一般访问结构的多重秘密共享方案

A Multi-Secret Sharing Scheme Based on the General Access Structure

基于Shamir的门限方案和RSA密码体制,提出一个一般访问结构上的秘密共享方案·参与者的秘密份额是由各参与者自己选择,秘密分发者不需要向各参与者传送任何秘密信息·当秘密更新、访问结构改变或参与者加入/退出系统时,各参与者的份额不需要更新·秘密份额的长度小于或等于秘密的长度·每个参与者只需维护一个秘密份额就可以实现对多个秘密的共享·在秘密恢复过程中,每个参与者能够验证其他参与者是否进行了欺骗·方案的安全性是基于Shamir的门限方案和RSA密码体制的安全性·

Based on Shamir＇s threshold scheme and the RSA cryptosystem, a new secret sharing scheme for the general access structure is proposed in this paper. In this scheme, each participant＇s secret shadow is selected by the participant himself and the dealer need not deliver any secret information to each participant, and thus a secure channel between them is unnecessary. The shadows do not need to be changed when the shared secret is renewed, the access structure is altered, or old participants are deleted/ new participants are added. All these shadows are shorter than or as short as the shared secret. Each participant shares many secrets with other participants by holding only one shadow, and in the recovery phase each participant is allowed to check whether another participant provides the true information or not. The security of this scheme is the same as that of Shamir＇s threshold scheme and the RSA cryptosystem. Analyses show that this scheme is a computationally secure and efficient scheme.