将ElGamal密码体制推广到非交换群  

A Generalization of the ElGamal Cryptosystem to Non-abelian Groups

作　　者：孔晶[1] 韩广国[1] 

机构地区：[1]杭州电子科技大学数学研究所,浙江杭州310018

出　　处：《杭州电子科技大学学报（自然科学版）》2012年第1期76-78,共3页Journal of Hangzhou Dianzi University：Natural Sciences

基　　金：国家自然科学基金资助项目(11071081);浙江省自然科学基金杰出青年团队资助项目(R1090138)

摘　　要：多数公钥密码体制是建立在交换群上的,基于非交换群的密码体制也得到了快速发展。MOR密码体制是ElGamal密码体制的推广。该文提出了一种新的建立在非交换群上的MOR密码体制,利用半直积构造出非交换群Sz(q)×θZp,自同构取内自同构。并且从内自同构群上的离散对数问题,矩阵的运算两方面来分析这类MOR密码体制是安全的。Most public key cryptosystems have been constructed based on abelian groups,the cryptosystems based on non-abelian groups also have been developed quickly.MOR cryptosystem is the generalization of the ElGamal cryptosystem.This paper proposes a new MOR cryptosystem based on the non-abelian groups,using the semi-direct product constructs a non-abelian group Sz（q）×θZp,and chooses the inner automorphism as the automorphism.Through the analysis of the discrete logarithm problem of the inner automorphism groups and the operation of the matrix,this paper shows that the MOR cryptosystem is secure.

关 键 词：密码体制 非交换群 半直积 内自同构 

分 类 号：O152.8[理学—数学]