一种改进的椭圆曲线离散对数快速冗余算法

A New Redundant Binary Algorithm for the Elliptic Curves Cryptosystems

提高点倍乘的运算效率是椭圆曲线密码体制得以广泛应用的基础 在大数的二进制序列中引入 - 1,构成等价的二进制冗余序列 ,可使序列中 0的个数增加 ,从而使得大数倍乘中加法运算减少 提出了一种新的椭圆曲线离散对数快速冗余算法 算法针对大数的二进制冗余序列 ,给出了新的合理构建 ,消除序列转换中不必要的步骤 分析表明 ,新算法显著减少了倍乘的运算 。

To improve the rate for the numerical multiplication of the points is the foundation to apply the elliptic curve cryptosystems. When the binary representation is changed into the binary redundant representations by introducing -1 in binary representation for number, the addition computing steps for the numerical multiplication of the points are decreased. In this paper a new fast redundant binary algorithm for the elliptic curves discrete logarithm problem is presented. A new binary redundant representation, which is a necessity to transformation for a very large integer, is defined, and this algorithm facilitates the speed improvement for decreasing those operations.