Cryptology ePrint Archive: Report 2007/088

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

Domingo Gomez and Jaime Gutierrez and 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.

Category / Keywords: foundations / Lattices reduction, Factoring

Date: received 8 Mar 2007

Contact author: jaime gutierrez at unican es

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Version: 20070308:140404 (All versions of this report)

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