基于ElGamal体制的门限秘密共享方案

基于Shamir 的门限方案和ElGamal密码体制，采用Lagrange插值法进行秘密拆分和恢复，提出一个动态多重秘密共享方案。参与者的秘密份额由各参与者自己选择，在参与者间不需要维护一条安全信道，并且一次可以共享多个秘密。当秘密更新、参与者加入或退出系统时，各参与者的份额不需要更新。在秘密重构过程中，合法的参与者或攻击者试图出示假的子秘密来欺骗秘密生成者是不可行的。该方案实现了动态 门限秘密共享时不需要重新构造多项式，使计算量开销更小。

Threshold Secret Sharing Scheme Based on ElGamal Cryptosystem

Based on Shamir’s threshold scheme and ElGamal cryptosystem,by using Lagrange interpolation method and the restoration of secret splitting,this paper proposes a dynamic multi-secret sharing scheme.Participants share the secret of their choice by the participants,among the participants do not need to maintain a safe channel,and a number of secrets can be shared.When the secrets update,and the participants join or exit the system,each participant’s share does not require updates.In the secret reconstruction process,the legitimate participants or the attacker try to produce a false sub-secret secret to deceive the generator,which is not feasible.The program does not require re-constructing polynomial when it implements the dynamic threshold secret sharing,and its computation overhead is even smaller.