Construction of secure C-ab curves using modular curves

Authors
Citation
S. Arita, Construction of secure C-ab curves using modular curves, IEICE T FUN, E84A(11), 2001, pp. 2930-2938
Citations number
16
Categorie Soggetti
Eletrical & Eletronics Engineeing
Journal title
IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES
ISSN journal
09168508 → ACNP
Volume
E84A
Issue
11
Year of publication
2001
Pages
2930 - 2938
Database
ISI
SICI code
0916-8508(200111)E84A:11<2930:COSCCU>2.0.ZU;2-S
Abstract
This paper proposes a heuristic algorithm which, given a basis of a subspac e of the space of cuspforms of weight 2 for Gamma (0)(N) which is invariant for the action of the Hecke operators, tests whether the subspace correspo nds to a quotient A of the jacobian of the modular curve Xo (N) such that A is the jacobian of a curve C. Moreover, equations for such a curve C are c omputed which make the quotient suitable for applications in cryptography. One advantage of using such quotients of modular jacobians is that fast met hods are known for finding their number of points over finite fields.