Generating secure genus two hyperelliptic curves using Elkies' point counting algorithm

被引：0

作者：

Kanayama, N

Nagao, K

Uchiyama, S

机构：

[1] Waseda Univ, Sch Sci & Engn, Dept Math Sci, Tokyo 1698555, Japan

[2] Kanto Gakuin Univ, Fac Engn, Yokohama, Kanagawa 2368501, Japan

[3] NTT Corp, Informat Sharing Platform Labs, Yokosuka, Kanagawa 2390847, Japan

来源：

IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES | 2003年 / E86A卷 / 04期

关键词：

hyperelliptic curve; BSGS; point counting;

D O I：

暂无

中图分类号：

TP3 [计算技术、计算机技术];

学科分类号：

0812 ;

摘要：

This paper proposes an improvement of Elkies' point counting algorithm for the Jacobian of a genus 2 hyperelliptic curve defined over a finite field in a practical sense and introduces experimental results. Our experimental results show that we can generate a cryptographic secure genus 2 hyperelliptic curve, where the order of its Jacobian is a 160-bit prime number in about 8.1 minutes on average, on a 700 MHz PentiumIII level PC. We improve Elkies' algorithm by proposing some complementary techniques for speeding up the baby-step giant-step.

引用

页码：919 / 927

页数：9

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