基于扭共轭搜索问题的有偏比特承诺

Biased bit commitment based on the twisted conjugacy search problem

提出了基于扭共轭搜索问题的有偏比特承诺方案.(双)扭共轭搜索问题是指:已知G上的一对自同态(?),ψ及G中两元素w,t,找出s∈G,使得:t=ψ(s^(-1))w(?)(s).(假设至少存在一个这样的s.)给出了方案的正确性,安全性的证明,并且在一个具体的平台上讨论了密钥空间,参数设置,并且给出了安全性分析.

The paper is a contribution to the study of biased bit commitment based on thetwisted conjugacy search problem.The twisted conjugacy search problem is:given a pair of endomorphisms (?),ψof a group G and a pair of elementsω,t of G,find an element s(?)G,such that t=ψ(s^(-1))ω(?)(s) provided at least one such s exists.The presented scheme is proved to be correct and secure.We also sketch out the key space,parameters and the cryptanalysis on a specific platform.