arXiv subjects

Jorge Urroz

Publications and source records attributed to Jorge Urroz.

4 recordsLinked to original sources

arXiv2026

A new attack to RSA with small private exponent and partial information

We give a new algorithm to attack RSA with small private exponent, when some partial information of $p+q$ is given.The algorithm is a very simple modification of original Wiener's attack with continued fractions, and allows to factor $n$ whenever $d<n^{(1+\delta)/4}$ if we know a $\delta$-fraction of the most significant bits of $p+q$. The algorithm is unconditional, which is not the case in previous improvements that use Coppersmith method. As an example, ouir algorithm can be applied to break any criptosystem with modulus of $512$ bits and $d<n^{0.3}$, giving an improvement in the original attack of Wiener.

math.NT↗

arXiv2021

A Study of the Separating Property in Reed-Solomon Codes by Bounding the Minimum Distance

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 property implies the rest. Silverberg et al. ask if there is some kind of tracing capability left when the minimum distance falls below the threshold. Under different assumptions, several papers have given a negative answer to the question. In this paper further progress is made. We establish values of the minimum distance for which Reed-Solomon codes do not posses the separating property.

cs.IT↗

arXiv2020

Every integer can be written as a square plus a squarefree

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 asympotic formula for the number of representations of an integer in this form. The result is deeply related with the divisor function. In the course of our study we get an independent result about it. Concretely we are able to deduce a new upper bound for the divisor function valid for any integer and fully explicit.

math.NT↗

arXiv2019

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

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

math.NT↗