Construction of secure C-ab curves using modular curves

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.