基于大数分解的门限秘密共享方案

Secret sharing scheme based on large numbers factorization

秘密共享在密钥管理的方法上是一个很重要的课题.提出秘密共享体制设计的一种新思路,首先根据大数分解的困难性设立不可逆的主密钥幂,然后通过不定方程整数解的存在性计算出结构方程特解的同组组合,再利用主密钥幂和同组组合的元素构建出恢复主密钥的子密钥,设计一个完备的(t,n)门限秘密共享方案,并对该门限方案进行安全性分析,结果显示该门限方案是无条件安全的.

Secret sharing is a very important question on key management method.In this paper,a new idea about the design of secret sharing scheme was proposed.Firstly the irreversibility master key power was introduced on the basis of the difficulty of large numbers factorization.Then the same class combinations for the particular solutions of the structure equations were calculated through the existence of integer solution of indeterminate equation.Furthermore,the subkeys which would be used to restore the master key,were constructed by means of the master key power and the element of the same class combinations.At last,aperfect（t,n）-threshold secret sharing scheme had been established and the security analysis for this threshold scheme was given.The results showed that this threshold scheme was unconditionally secure.