Now showing items 1-13 of 13

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

(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) ﻿

(Universitat Politècnica de Catalunya, 2007-05-25)
Exam
• #### Cropping Euler factors of modular L-functions ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(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 ﻿

(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 ...