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In this paper we address two different problems related with thefactorization of an RSA module N. First we can show that factoring isequivalent in deterministic polynomial time to counting points on a pair oftwisted Elliptic curves modulo N. Also we settle the malleability of factoringan RSA module, as described in [9], using the number of points of a singleelliptic curve modulo N, and Coppersmith's algorithm.

Factorization and malleability of RSA modules, and counting points on elliptic curves modulo N