Computing modular polynomials modulo large primes

摘要

Systems and methods for computing modular polynomials modulo large primes are described. In one aspect, the systems and methods generate l-isogenous elliptic curves. A modular polynomial modulo a large prime p is then computed as a function of l-isogenous elliptic curves modulo p. In one aspect, the modular polynomial may be used in a cryptosystem.