Research on public-key cryptosystems from hyperelliptic-curves

基于超椭圆​​曲线的公钥密码系统研究

• 批准号: 11558033
• 负责人: SAKURAI Kouichi
• 金额: $ 3.97万
• 依托单位: Kyushu University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 1999
• 资助国家: 日本
• 起止时间: 1999 至 2001
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-11558033/
• 关键词: cryptography; information security; hyperelliptic curve; public-key encryption; algorithm; cryptanalysis; elliptic curve; fast computation; モンゴメリー型; 梗塞演算

We have designed hyperelliptic curve cryptosystems with considering security and efficiency.We have implemented our designed hyperelliptic curve cryptosystems both over software and over hardware, and confirm their practical performance.We consider the performance of hyperelliptic curve cryptosystems over GF(p) vs. over GF(2^n).We analyze the complexity of the group law of Jacobians and make comparison of their performance between over over GF(p) vs. over GF(2^n). with considering the effectiveness of the word size (32-bit or 64-bit) of the applied CPU (Alpha and Pentium) on the arithmetic on the definition field.We also develop efficient algorithms for the jacobian of the hyperelliptic curve defined by the equation $y^2 = x^p-x+1$ over a finite field GF(p^n) of odd characteristic p. We first determine the zeta function of the curve which yields the order of the jacobian. And we investigate the Frobenius operator and use it to show that, for field extensions GF(p^n) of degree n prime to p, the jacobian has a cyclic group structure. We furthermore propose a method for faster scalar multiplication in the jacobian by using efficient operators other than the Frobenius that have smaller eigenvalues.

我们已经通过考虑安全性和效率设计了高椭圆曲线密码系统。我们已经在软件和硬件上实施了设计的超椭圆曲线密码系统，并确认它们的实际性能。我们考虑到高纤维化曲线加密系统的性能，而不是GF（P）与GF（2^n）的效果（2^n）。 GF（P）与GF（2^n）。考虑到定义字段算术上所应用的CPU（Alpha和Pentium）单词大小（32位或64位）的有效性。我们还为公式$ y^2 = x^p-x+1 $ 1 $ over a Over a Over a Over a Primite p^p^p^p^p^p^p^p^p^p^p^p^p^p^p^p^p^p^p^p^n offecobian jacobian jacobian jacobian的高效算法。我们首先确定曲线的ZETA函数，该曲线产生了Jacobian的顺序。我们研究了Frobenius操作员，并使用它来表明，对于n prime到p的场扩展GF（p^n），雅各布式具有循环组结构。我们此外，通过使用具有较小特征值的Frobenius以外的有效运算符，提出了一种在Jacobian中更快的标量乘法的方法。

项目成果

Okeya, K., Sakurai, K.: "Efficient elliptic curve cryptosystems from a scalar multiplication algorithm with recovery of the y-coordinate on a Montgomery-form elliptic curve"Proc. Workshop on Cryptographic Hardware and Embedded Systems 2001 (May 2001, Pari

Okeya, K.、Sakurai, K.：“基于标量乘法算法的高效椭圆曲线密码系统，可恢复蒙哥马利型椭圆曲线上的 y 坐标”Proc。

酒井康行,櫻井幸一: "有限体F_<2^n>上の超楕円曲線暗号のソフトウエア実装"電子情報通信学会論文誌. J82-A,No.8. 1305-1306 (1999)

Yasuyuki Sakai、Koichi Sakurai：“有限域 F_<2^n> 上超椭圆曲线密码学的软件实现”，电子、信息和通信工程师学会汇刊 J82-A，第 8 期。1305-1306 (1999)。

Masato YAMAMICHI, Masahiro MAMBO, Hiroki SHIZUYA: "On the Complexity of Constructing an Elliptic Curve of a Given Order"Ieice Trans.. E84-A・No.1. 140-145 (2001)

Masato YAMAMICHI、Masahiro MAMBO、Hiroki SHIZUYA：“论构造给定阶数的椭圆曲线的复杂性”Ieice Trans.. E84-A·No.1 (2001)。

CHIDA,OHMORI,and SHIZUYA: "A Way of Making Trapdoor One-Way Functions Trapdoor No-Way"IEICE Trans.Fundamentals. E84-A,1. 151-156 (2001)

CHIDA、OHMORI 和 SHIZUYA：“一种制作活板门单向函数活板门无路的方法”IEICE Trans.Fundamentals。

Y. Sakai and K. Sakurai: "Over F_p vs.F_<2^n> over and on Pentium vs. Alpha in Software Implementation of Hyperelliptic Curve"PreProc, 1999 International Conference on Information Security and Cryptology December 9-10,1999 Korea University,Seoul,Korea. 67

Y. Sakai 和 K. Sakurai：“Over F_p vs.F_<2^n> over and on Pentium v​​s. Alpha in Software Implementing of Hyperelliptic Curve”PreProc，1999 年信息安全与密码学国际会议，1999 年 12 月 9-10 日，韩国