A fast Jacobian group arithmetic scheme for algebraic curve cryptography

Citation
R. Harasawi et J. Suzuki, A fast Jacobian group arithmetic scheme for algebraic curve cryptography, IEICE T FUN, E84A(1), 2001, pp. 130-139
Citations number
15
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Eletrical & Eletronics Engineeing
Journal title
IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES
ISSN journal
0916-8508 → ACNP
Volume
E84A
Issue
1
Year of publication
2001
Pages
130 - 139
Database
ISI
SICI code
0916-8508(200101)E84A:1<130:AFJGAS>2.0.ZU;2-8
Abstract
The goal of this paper is to describe a practical and efficient algorithm f or computing in the Jacobian of a large class of algebraic curves over a fi nite field. For elliptic and hyperelliptic curves, there exists an algorith m for performing Jacobian group arithmetic in O(g(2)) operations in the bas e field, where g is the genus of a curve. The main problem in this paper is whether there exists a method to perform the arithmetic in more general cu rves. Galbraith, Paulus, and Smart proposed an algorithm to complete the ar ithmetic in O(g(2)) operations in the base field for the so-called superell iptic curves. We generalize the algorithm to the class of C-ab curves, whic h includes superelliptic curves as a special case. Furthermore, in the case of C-ab curves, we show that the proposed algorithm is not just general bu t more efficient than the previous algorithm as a parameter a in C-ab curve s grows large.