| 摘要: |
| 标量乘法是传统椭圆曲线密码(ECC)的核心运算. 标量表示决定了标量乘法算法中的迭代方式, 进而直接影响算法的安全性和效率. 提出两种新的标量表示算法: 一种称为规则窗口非相邻算法(ordered window width non-adjacent form, OWNAF), 它将传统的窗口非相邻算法与随机密钥分割处理相结合, 在提升计算效率的同时可以抵抗能量分析攻击; 另一种称为窗口联合正则形式(window joint regular form, wJRF), 它由传统的联合正则形式改进而来, 适用于多标量乘算法, 与已有算法相比, 在减少基础计算量的同时有着更好的安全性. |
| 关键词: 标量乘算法 侧信道攻击 窗口非相邻形式 联合正则形式 |
| DOI：10.13328/j.cnki.jos.007301 |
| 分类号:TP301 |
| 基金项目:国家自然科学基金(61972420); 湖南省自然科学基金(2020JJ3050) |
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| Safe and Efficient Scalar Multiplication Algorithms Based on Two New Scalar Representations |
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CHENG Shi, HU Zhi, TAO Zheng
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School of Mathematics and Statistics, Central South University, Changsha 410083, China
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| Abstract: |
| Scalar multiplication is the core operation in traditional elliptic curve cryptography (ECC). Scalar representations determine the iterations in scalar multiplication algorithms, which directly affect the security and efficiency of the algorithms. This study proposes two new scalar representation algorithms. One algorithm is ordered window width non-adjacent form (OWNAF) which combines traditional window non-adjacent form with random key segmentation and can resist energy analysis attacks while yielding better efficiency. The other is called window joint regular form (wJRF), which is improved from the traditional joint regular form. The wJRF algorithm is applicable to multi-scalar multiplication algorithms, which can reduce computational costs and ensure sound security compared with the existing algorithms. |
| Key words: scalar multiplication algorithm side channel attack window non-adjacent form joint regular form |
