自同构群在公钥密码学中的应用

摘要

This paper surveys the applications and new developments of automorphism groups in the public-key cryptography later years .MOR cryptosystem is a simple generalization of the ElGamal cryptosystem to non-commutative group .Through several kinds of non-commutative groups ( such as unitriangular matrix group, special linear group, nilpotent group and finite p-group etc.), MOR cryptosystem and the key ex-change protocol based on automorphism groups of non-commutative groups are described .Finally, some future problems concerning secur and efficient MOR cryptosystem are put forward .%综述了近年来自同构群在公钥密码学中的应用及其最新进展。 MOR密码系统是ElGamal密码系统在非交换群上的推广，更具有一般性。以几类经典的非交换群（如单位三角矩阵群、特殊线性群、幂零群、有限p群等）为主线，介绍了MOR密码系统在这些非交换群的自同构群下的研究成果及自同构群的一个应用：密钥交换协议。为了实现安全、高效的MOR密码系统，最后给出了仍需深入研究的一些问题。