Cryptology ePrint Archive: Report 2009/233

A strategy for recovering roots of bivariate polynomials modulo a prime

Paula Bustillo and Domingo Gomez and Jaime Gutierrez and Alvar Ibeas

Abstract: Let $p$ be a prime and $\F_p$ the finite field with $p$ elements. We show how, when given an irreducible bivariate polynomial $f \in \F_p[X,Y]$ and approximations to $(v_0,v_1) \in \F_p^2$ such that $f(v_0,v_1)=0 $, one can recover $(v_0,v_1)$ efficiently, if the approximations are good enough. This result has been motivated by the predictability problem for non-linear pseudorandom number generators and, other potential applications to cryptography.

Category / Keywords: applications / number theory, lattices and crypto

Date: received 25 May 2009

Contact author: jaime gutierrez at unican es

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Version: 20090530:051102 (All versions of this report)

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