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**2009/233**

**Title:**

A strategy for recovering roots of bivariate polynomials modulo a prime

**Authors:**
Paula Bustillo, Domingo Gomez, Jaime Gutierrez, 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.

**ePrint:**
https://eprint.iacr.org/2009/233

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