中文摘要：

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。

英文摘要：

Based on the discrete logarithm problem in the automorhoism group of special linear group, this paper proposes a sig- nature scheme over the non-commutative group, and analyzes the difficulty of the 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.