辫子群上的公钥加密算法  

A Public Key Encryption Algorithm on Braid Groups

作　　者：汤学明[1] 洪帆[1] 崔国华[1] 

机构地区：[1]华中科技大学计算机科学与技术学院信息安全系,湖北武汉430074

出　　处：《软件学报》2007年第3期722-729,共8页Journal of Software

基　　金：Supported by the National Natural Science Foundation of China under Grant No.60403027(国家自然科学基金)

摘　　要：辫子群是一种新兴的适用于量子计算机时代的公钥密码平台,辫子群上已知的用于公钥密码系统的一些难解问题和基于这些难解问题的公钥加密算法都受到不同程度的攻击.辫子群上公钥密码系统的安全性不能仅仅依靠共轭问题的难解性.结合辫子群上非共轭变换和多变量方程组的特点所构造的难解问题,通过增加变量数量来增加问题的难解程度.新的公钥加密算法的安全性建立在新的难解问题之上,随后对其正确性、安全性、效率以及参数选择进行了分析.辫子群上新的公钥加密算法可以抵抗已知的各种攻击,将简单问题复合成多变量难解问题的思路,对公钥密码算法的设计起到一定的启发作用.Braid group is a new considerable public key cryptography platform for the quantum computer ages, but almost all current intractable braid problems used for public key cryptosystems are flawy. The security of a braid public key cryptosystem can＇t depend only on the hardness of conjugacy problems. By taking advantage of the non-conjugate transformation and multiple variant equations on braid groups, two intractable problems are proposed, and the hardness of these problems comes from the enlarged amount of variants. A new related public key algorithm and the analysis of its correctness, security, efficiency and parameter choice are subsequently presented. The new algorithm can resist current known attacks, and the ideal to combine some simple problems to a multiple variant difficult one is constructive for designing new public key algorithms.

关 键 词：公钥加密 辫子群 共轭 多变量方程组 Burau表示 

分 类 号：TP309[自动化与计算机技术—计算机系统结构]