Paper 2009/233 Original: eprint.iacr.org/2009/233 ↗
A strategy for recovering roots of bivariate polynomials modulo a prime
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
- Preprint.
- History
- 2009-05-30: last updated
- 2009-05-30: published
- Short URL
- https://ia.cr/2009/233
- License
- https://creativecommons.org/licenses/by/4.0/
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}
}