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| 一类Koblitz椭圆曲线的快速点乘 |
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胡磊1, 冯登国2, 文铁华3
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1.信息安全国家重点实验室,中国科学院,研究生院,北京,100039;2.中国科学院,软件研究所,北京,100080;3.中南大学,信息科学与工程学院,湖南,长沙,410083
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| 摘要: |
| 考虑一类特征3的Koblitz椭圆曲线的快速点乘算法.在这类曲线上适合建立低带宽的、可证明安全的密码体制.结果显示,利用这类曲线的复乘性质,使用模约减和Frobenius展开技巧,这类曲线上存在一种不带预计算的快速点乘算法,其运算速度是通常的重复加倍-点加算法的6倍.该算法的快速优化原理与有限域算术优化和椭圆曲线点的坐标表示的选取无关. |
| 关键词: 椭圆曲线 点乘 Frobenius展开式 模约减 快速算法 |
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| 基金项目:Supported by the National Natural Science Foundation of China under Grant No.90104034 (国家自然科学基金); the National High-Tech Research and Development Plan of China under Grant No.2002AA141020 (国家高技术研究发展计划(863)) |
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| Fast Multiplication on a Family of Koblitz Elliptic Curves |
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HU Lei,FENG Deng-Guo,WEN Tie-Hua
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| Abstract: |
| Fast point multiplication on a family of Koblitz elliptic curves in characteristic 3 is considered. Such curves are suitable for establishing provable secure cryptographic schemes with low bandwidth. By utilizing the complex multiplication property of the curves and using a modulo reduction and Frobenius expansion technique, it is shown that there is a fast point multiplication method without precomputation on the curves, which is 6 times faster than the ordinary repeated-double-add method. The idea of the fast method is independent of the optimization of finite field arithmetic and the choice of coordinate expression for points of the elliptic curves. |
| Key words: elliptic curve point multiplication Frobenius expansion modulo reduction fast algorithm |
