Searching. Please wait…

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.

 Authorship: Gómez D., Gutierrez J.,

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

 Publisher: American Mathematical Society

 Year of publication: 2014

 No. of pages: 13

 Publication type: Article

 DOI: 10.1090/S0025-5718-2014-02808-1

 ISSN: 0025-5718,1088-6842

 Spanish project: MTM2011-24678