基于特殊线性群的自同构群的签名

doi:10.3969/j.issn.1006-2475.2017.06.020

计算机与现代化

基于特殊线性群的自同构群的签名

(陕西理工大学数学与计算机科学学院，陕西汉中 723000)

收稿日期:2016-09-11 出版日期:2017-06-23 发布日期:2017-06-23
作者简介:潘平(1975-)，女，甘肃天水人，陕西理工大学数学与计算机科学学院讲师，博士，研究方向：信息安全，密码学; 曹阳(1978-)，女，讲师，硕士，研究方向：信息安全; 和斌涛(1982-)，男，讲师，硕士，研究方向：代数学，密码学。
基金资助:
国家自然科学基金资助项目(61370194); 陕西省教育厅项目(2013JK0598); 陕西理工大学校级项目(SLGQD13-24)

Signature from Automorphism Group of Special Linear Group

(School of Mathematics and Computer Science, Shaanxi University of Technology, Hanzhong 723000, China)

Received:2016-09-11 Online:2017-06-23 Published:2017-06-23

摘要/Abstract

摘要： 基于特殊线性群的自同构群上的离散对数问题，提出一种非交换群上的签名方案；分析特殊线性群的自同构群上的离散对数问题的困难性。通过适当地选取参数，表明新签名方案的安全性高于有限域上的DSA算法，甚至等同于椭圆曲线上的DSA算法。结果表明，采用Leedham-Green算法计算矩阵的幂运算，使得新方案的运行效率得到提高。

关键词: 特殊线性群, 对角自同构, 内自同构, 离散对数, 签名

Abstract: Based on the discrete logarithm problem in the automorhoism group of special linear group, this paper proposes a signature scheme over the non-commutative group, and analyzes the difficulty ofthe discrete logarithm problem in the automorhoism group of special linear group. The paper shows that, by selecting proper parameters, the new scheme is much more secure than DSA in the finite field and is as secure as DSA over elliptic curves. The result shows the running efficiency of the new scheme is improved by adopting Leedham-Green algorithm to compute the power of matrices.

Key words: special linear group, diagonal automorphism, inner automorphism, discrete logarithm, signature

中图分类号:

TP309.7

潘平，曹阳，和斌涛. 基于特殊线性群的自同构群的签名[J]. 计算机与现代化, doi: 10.3969/j.issn.1006-2475.2017.06.020.

PAN Ping, CAO Yang, HE Bin-tao. Signature from Automorphism Group of Special Linear Group[J]. Computer and Modernization, doi: 10.3969/j.issn.1006-2475.2017.06.020.

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基于特殊线性群的自同构群的签名

Signature from Automorphism Group of Special Linear Group

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