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Recovering zeros of polynomials modulo a prime

Abstract: Let $ p$ be a prime and $ \mathbb{F}_p$ the finite field with $ p$ elements. We show how, when given an irreducible bivariate polynomial $ F \in \mathbb{F}_p[X,Y]$ and an approximation to a zero, one can recover the root efficiently, if the approximation is good enough. The strategy can be generalized to polynomials in the variables $ X_1,\ldots ,X_m$ over the field $ \mathbb{F}_p$. These results have been motivated by the predictability problem for nonlinear pseudorandom number generators and other potential applications to cryptography.

 Autoría: Gómez D., Gutierrez J.,

 Fuente: Mathematics of computation, 2014, 83(290), 2953-2965

 Editorial: American Mathematical Society

 Año de publicación: 2014

 Nº de páginas: 13

 Tipo de publicación: Artículo de Revista

 DOI: 10.1090/S0025-5718-2014-02808-1

 ISSN: 0025-5718,1088-6842

 Proyecto español: MTM2011-24678