## 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

**Available format(s): **PDF | BibTeX Citation

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

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