A strategy for recovering  roots of  bivariate polynomials modulo a prime

Paula Bustillo; Domingo Gomez; Jaime Gutierrez; Alvar Ibeas

Paper 2009/233

A strategy for recovering roots of bivariate polynomials modulo a prime

Paula Bustillo, Domingo Gomez, 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.

Metadata

Available format(s): PDF
Category: Applications
Publication info: Published elsewhere. Unknown where it was published
Keywords: number theory lattices and crypto
Contact author(s): jaime gutierrez @ unican es
History: 2009-05-30: received
Short URL: https://ia.cr/2009/233
License: CC BY

BibTeX

@misc{cryptoeprint:2009/233,
      author = {Paula Bustillo and Domingo Gomez and Jaime Gutierrez and Alvar Ibeas},
      title = {A strategy for recovering  roots of  bivariate polynomials modulo a prime},
      howpublished = {Cryptology {ePrint} Archive, Paper 2009/233},
      year = {2009},
      url = {https://eprint.iacr.org/2009/233}
}