| 一种应用于椭圆曲线暗号系的曲线高速生成法 |
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| 引用本文： | 王立志,王向辉. 一种应用于椭圆曲线暗号系的曲线高速生成法[J]. 中北大学学报(自然科学版), 2006, 27(6): 480-482 |
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| 作者姓名： | 王立志 王向辉 |
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| 作者单位： | 忻州师范学院,数学系,山西,忻州,034000;忻州师范学院,数学系,山西,忻州,034000 |
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| 摘 要： | 利用虚数乘法(Complex Multiplication,CM)生成Fp上的椭圆曲线,通常只使用虚二次域的最大整环.本文将虚二次域的部分环也用于Fp上的椭圆曲线的生成上,这样由于Pell方程u2 dv2=4p在Z/2p,Z/3p上也存在解,在同样判别式范围内可以生成更多的椭圆曲线,经Mathematica编程计算,生成的曲线数量有明显增加.
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| 关 键 词： | 椭圆曲线暗号 椭圆曲线的有理点群 阶数 虚数乘法 部分环 |
| 文章编号： | 1673-3193(2006)06-0480-03 |
| 修稿时间： | 2006-06-29 |
A Rapid Procedure of Creating Elliptic Curves Applying to Cryptography |
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| WANG Li-zhi,WANG Xiang-hui. A Rapid Procedure of Creating Elliptic Curves Applying to Cryptography[J]. Journal of North University of China, 2006, 27(6): 480-482 |
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| Authors: | WANG Li-zhi WANG Xiang-hui |
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| Abstract: | When complex multiplication(CM) is used to create elliptic curves over F_p,the ring of complex quadratic field is only used.The authors propose to use sub-ring of complex quadratic field to create elliptic curves over F_p.Since the Pell equation u~2 dv~2=4p exists root over Z/2p,Z/3p,more elliptic curves can then be created at the same range of discriminant.With the computation of Mathematica programming,the number of created curves increases significantly. |
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| Keywords: | elliptic curves in cryptography group of rational points orders complex multiplication sub-ring |
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