Now showing items 1-13 of 13

    • A study of the separating property in Reed-Solomon codes by bounding the minimum distance 

      Fernández Muñoz, Marcel; Jiménez Urroz, Jorge (2022-02)
      Article
      Open Access
      According to their strength, the tracing properties of a code can be categorized as frameproof, separating, IPP and TA. It is known that, if the minimum distance of the code is larger than a certain threshold then the TA ...
    • ANÀLISI REAL (Examen 2n quadrim) 

      Jiménez Urroz, Jorge (Universitat Politècnica de Catalunya, 2007-05-25)
      Exam
      Restricted access to the UPC academic community
    • Cropping Euler factors of modular L-functions 

      González Rovira, Josep; Jiménez Urroz, Jorge; Lario Loyo, Joan Carles (2013-09)
      Article
      Open Access
      According to the Birch and Swinnerton-Dyer conjectures, if A/Q is an abelian variety, then its L-function must capture a substantial part of the properties of A. The smallest number field L where A has all its endomorphisms ...
    • Every integer can be written as a square plus a squarefree 

      Jiménez Urroz, Jorge (2021-12-30)
      Article
      Restricted access - publisher's policy
      In the paper we can prove that every integer can be written as the sum of two integers, one perfect square and one squarefree. We also establish the asymptotic formula for the number of representations of an integer in ...
    • 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
      Open Access
      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 ...
    • Modular forms with large coefficient fields via congruences 

      Dieulefait, Luis; Jiménez Urroz, Jorge; Ribet, Keneth (Springer, 2015-05-01)
      Article
      Open Access
      We use the theory of congruences between modular forms to prove the existence of newforms with square-free level having a fixed number of prime factors such that the degree of their coefficient fields is arbitrarily large. ...
    • 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
      Open Access
      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 ...
    • On some classes of irreducible polynomials 

      Gutiérrez Gutiérrez, Jaime; Jiménez Urroz, Jorge (2020-07)
      Article
      Restricted access - publisher's policy
      One of the fundamental tasks of Symbolic Computation is the factorization of polynomials into irreducible factors. The aim of the paper is to produce new families of irreducible polynomials, generalizing previous results ...
    • Orders of CM elliptic curves modulo p with at most two primes 

      Iwaniec, Henryk; Jiménez Urroz, Jorge (2006)
      Article
      Open Access
      We prove the analog of Koblitz conjecture when replacing primes by almost prime numbers and considering elliptic curves with complex multiplication. In other words for infinitely many primes $p$, (given in a quantitative ...
    • Orders of CM elliptic curves modulo p with at most two primes 

      Iwaniec, H.; Jiménez Urroz, Jorge (2010)
      Article
      Restricted access - publisher's policy
      Nowadays the generation of cryptosystems requires two main aspects. First the security, and then the size of the keys involved in the construction and comunication process. About the former one needs a di±cult ...
    • Primes represented by quadratic polynomials via exceptional characters 

      Chamizo Lorente, Fernando; Jiménez Urroz, Jorge (Springer Nature, 2021-08-01)
      Article
      Restricted access - publisher's policy
      We estimate the number of primes represented by a general quadratic polynomial with discriminant ¿, assuming that the corresponding real character is exceptional.
    • Small primitive roots and malleability of RSA 

      Jiménez Urroz, Jorge; Dieulefait, Luis Victor (2012)
      Conference report
      Open Access
      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 ...
    • Square-free discriminants of Frobenius rings 

      David, Chantal; Jiménez Urroz, Jorge (2010-09)
      Article
      Open Access
      Let E be an elliptic curve over Q. It is well known that the ring of endomorphisms of $E_p$, the reduction of E modulo a prime p of ordinary reduction, is an order of the quadratic imaginary field $Q(\pi_p)$ generated ...