An  Algorithm for Finding  Small Roots of Multivariate Polynomials over the Integers

Domingo Gomez; Jaime Gutierrez; Alvar Ibeas

Paper 2007/088 Original: eprint.iacr.org/2007/088 ↗

An Algorithm for Finding Small Roots of Multivariate Polynomials over the Integers

Domingo Gomez

Jaime Gutierrez

Alvar Ibeas

Abstract

In this paper we present a new algorithm for finding small roots of a system of multivariate polynomials over the integers based on lattice reduction techniques. Our simpler heuristic method is inspired in algorithms for predicting pseudorandom numbers, and it can be considered as another variant of Coppersmith's method for finding small solutions of integer bivariate polynomials. We also apply the method to the well known problem of factoring an integer when we know the high-order bits of one of the factors.

Metadata

Available format(s): PDF
Category: Foundations
Publication info: Preprint.
History: 2007-03-08: last updated; 2007-03-08: published
Short URL: https://ia.cr/2007/088
License: https://creativecommons.org/licenses/by/4.0/

BibTeX

@misc{cryptoeprint:2007/088,
      author = {Domingo Gomez and Jaime Gutierrez and Alvar Ibeas},
      title = {An  Algorithm for Finding  Small Roots of Multivariate Polynomials over the Integers},
      howpublished = {Cryptology {ePrint} Archive, Paper 2007/088},
      year = {2007},
      url = {https://eprint.iacr.org/2007/088}
}