• Congruences between modular forms and lowering the level mod l^n 

      Dieulefait, Luis Victor; Taixes Ventosa, Xavier (2009)
      Article
      Accés obert
      In this article we study the behavior of inertia groups for modular Galois mod ℓn representations and in some cases we give a generalization of Ribet’s lowering the level result.
    • Factorization and Malleability of RSA Moduli, and Counting Points on Elliptic Curves Modulo N 

      Dieulefait, Luis Victor; Jiménez Urroz, Jorge (Multidisciplinary Digital Publishing Institute (MDPI), 2020-11-27)
      Article
      Accés obert
      In this paper we address two different problems related with the factorization of an RSA (Rivest–Shamir–Adleman cryptosystem) modulus N. First we show that factoring is equivalent, in deterministic polynomial time, to ...
    • On fields of definition of torsion points of elliptic curves with complex multiplication 

      Dieulefait, Luis Victor; Gonzalez Jimenez, Enrique; Jiménez Urroz, Jorge (2011-06)
      Article
      Accés obert
      For any elliptic curve E defined over the rationals with complex multiplication (CM) and for every prime p, we describe the image of the mod p Galois representation attached to E. We deduce information about the field of ...
    • Small primitive roots and malleability of RSA 

      Jiménez Urroz, Jorge; Dieulefait, Luis Victor (2012)
      Text en actes de congrés
      Accés obert
      In their paper [9], P. Paillier and J. Villar make a conjectur e about the malleability of an RSA modulus. In this paper we present an ex plicit algo- rithm refuting the conjecture. Concretely we can factorize an RSA ...