| 摘要: |
| 标量乘和多标量乘是实现椭圆曲线密码体制的核心运算,其运算速度从整体上决定了椭圆曲线密码体制的实现效率.提出了一种多标量乘算法,该算法的基本思想是,将标量用带符号的整数阶乘展开式表示,并结合固定基窗口标量乘算法,使得实现多标量乘算法只需做点加运算即可.这不仅突破了传统求多标量乘算法的模式,而且提高了多标量乘的计算速度.同时,还对算法正确性和复杂度进行了分析.由实验结果可知,在m=2 的情况下,该算法在计算效率上比已有的多标量乘算法提高了约47.8%~56.5%. |
| 关键词: 点乘 多标量乘 阶乘展开式 T-形多标量乘 固定基窗口算法 |
| DOI：10.3724/SP.J.1001.2011.03730 |
| 分类号: |
| 基金项目:国家自然科学基金(90704003); 国家高技术研究发展计划(863)(863-317-01-04-99, 2007AA01Z431); 河南省重大科技攻关项目(092101210502) |
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| A Multiple Scalar Multiplications Algorithm in the Elliptic Curve Cryptosystem |
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CHEN Hou-You, MA Chuan-Gui
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Institute of Information Engineering, Information Engineering University, Zhengzhou 450002, China
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| Abstract: |
| The main operations of elliptic curve cryptosystems (ECCs) are scalar multiplications and multi-scalar multiplications, which heavily determined the overall implementation of the efficiency of ECC. This algorithm extends the fixed-base window method by using the signed integer factorial expansions of scalar. The main characteristic of this method is that only a point addition computation is required, and it greatly improves the computational performance of a multi-scalar. Furthermore, the correctness proof and complexity analysis of the new algorithm are presented. At last, experimental results show that the computational efficiency increases about 47.8% to 56.5% when compared with other existing methods in the case m=2. |
| Key words: point multiplication multi-scalar multiplication factorial expansion T-multi-scalar multiplication fixed-base window method |
