Construction of Secure Cab Curves Using Modular Curves

Seigo ARITA  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E84-A   No.11   pp.2930-2938
Publication Date: 2001/11/01
Online ISSN: 
DOI: 
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Information Security
Keyword: 
discrete logarithm,  modular curve,  hyperelliptic curve,  Cab curve,  

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Summary: 
This paper proposes a heuristic algorithm which, given a basis of a subspace of the space of cuspforms of weight 2 for 0(N) which is invariant for the action of the Hecke operators, tests whether the subspace corresponds to a quotient A of the jacobian of the modular curve X0(N) such that A is the jacobian of a curve C. Moreover, equations for such a curve C are computed which make the quotient suitable for applications in cryptography. One advantage of using such quotients of modular jacobians is that fast methods are known for finding their number of points over finite fields.