| 摘要: |
| 4 维Gallant-Lambert-Vanstone（GLV）方法可用于加速一些定义在Fp2上椭圆曲线的标量乘法计算，如Longa-Sica型具有特殊复乘结构的GLS曲线以及Guillevic-Ionica利用Weil限制得到的椭圆曲线.推广了Longa-Sica的4维GLV分解方法，并在4次复乘域中给出显式且有效的4维分解方法，且对分解系数的界做出理论估计.结果行之有效，很好地支持了GLV方法以用于这些椭圆曲线上的快速标量乘法运算的实现. |
| 关键词: 椭圆曲线 GLV 方法 标量乘法 自同态 复乘 |
| DOI： |
| 分类号: |
| 基金项目:国家自然科学基金（61272499， 10990011）；信息保障技术重点实验室（KJ-11-02） |
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| GLV Decomposition in Quartic CM Fields |
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HU Zhi1, XU Mao-Zhi2, ZHANG Guo-Liang2
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1.Beijing International Center for Mathematical Research, Peking University, Beijing 100871, China;2.LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, China
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| Abstract: |
| Four dimensional Gallant-Lambert-Vanstone (GLV) method can be applied for faster scalar multiplication on some elliptic curves over Fp2 , such as the Longa-Sica GLS curves with special complex multiplication (CM), and the Guillevic-Ionica's curves via Weil restriction. This study generalizes Long-Sica four dimensional GLV decomposition methods, and gives explicit and efficient decompositions in quartic CM fields for such elliptic curves as well as the bound for the decomposed coefficients. The presented results well support the GLV method for faster implementations of scalar multiplications on desired curves. |
| Key words: elliptic curve GLV method scalar multiplication endomorphism complex multiplication |
