Name
Title | ||
|---|---|---|
Generating Secure Genus Two Hyperelliptic Curves Using Elkies' Point Counting Algorithm |
Abstract | ||
|---|---|---|
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. |
Year | Venue | Keywords |
|---|---|---|
2003 | IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES | hyperelliptic curve, BSGS, point counting |
DocType | Volume | Issue |
Journal | E86A | 4 |
ISSN | Citations | PageRank |
0916-8508 | 1 | 0.38 |
References | Authors | |
0 | 3 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Naoki Kanayama | 1 | 139 | 19.29 |
| Koh-Ichi Nagao | 2 | 36 | 6.17 |
| Shigenori Uchiyama | 3 | 371 | 40.90 |