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中文摘要：
介绍了有限域上的一般线性群的基本性质和群中元素的阶的求法,由此提出了有限域上一般线性群的ElGamal公钥密码体制,并基于新体制,提出了一般线性群的ElGamal签名方案,这两种体制大大提高了加密和签名的效率,其安全性都是基于离散对数问题的难解性。
英文摘要：
Some basic properties of the general linear groups and the solution of the order of their elements are introduced,and the ElGamal public-key cryptosystem based on general linear groups is proposed.Furthermore,based on this new cryptosystem,a general linear groups ElGamal digital signature is presented.This two systems have improved efficiency largely in encrypting and signature,and the security of them is mainly based on the intractability of discrete logarithm problem.
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