基于Shamir秘密共享的密钥分发与恢复算法  

Key distribution and recovery algorithm based on Shamir's secret sharing

作　　者：荣辉桂[1] 莫进侠 常炳国[1] 孙光[2] 龙飞[3] 

机构地区：[1]湖南大学信息科学与工程学院,湖南长沙410082 [2]湖南财政经济学院信息管理系,湖南长沙410205 [3]长沙大学经济管理系,湖南长沙410003

出　　处：《通信学报》2015年第3期60-69,共10页Journal on Communications

基　　金：国家自然科学基金资助项目(61304184);国家科技支撑计划基金资助项目(2013BAH45F02);科技部创新基金资助项目(13C26214304053);湖南重点建设学科基金资助项目;湖南大学"青年教师成长计划"基金资助项目(531107021115)~~

摘　　要：在经典的Shamir秘密共享方案中,秘密分发者把秘密s分为n个影子秘密并分发给持有者;其中任意不少于t个影子秘密均能恢复秘密s,少于t个影子秘密则得不到秘密s的任何信息。现实的秘密恢复过程中可能存在超过t个参与者的情形。因此,在Shamir的秘密共享方案基础上讨论此种情形下秘密共享问题,通过引入影子秘密的线性组合——拉格朗日因子来恢复秘密,并进一步将其扩展为一个多秘密共享方案。理论分析与仿真实验表明:改进算法在同样复杂度条件下既保证影子秘密的安全,又能阻止欺骗者得到秘密,提高了整体安全性。In Shamir＇s secret sharing scheme, the dealer divided the secret s into n shadows and distributed it to share- holders in such a way that any t or more than t shadows can recover this secret, while fewer than t shadows cannot obtain any in[brmation about the secret s. During the actual secret recovery process, there exist other cases with more than t par- ticipants. The case of secret sharing problem was discussed based on Shamir＇s secret sharing scheme and reconstructs the secret by introducing a linear combination of shadows--Lagrange factor. Then, the improved algorithm of key distribu- tion and recovery was proposed and extended to a multi-secret sharing scheme. Theoretical analysis and simulation show that the improved scheme improves its security under the same conditions of complexity.

关 键 词：秘密共享 密钥分发 拉格朗日因子 密钥恢复 

分 类 号：TP393[自动化与计算机技术—计算机应用技术]