A Tool Kit for Finding Small Roots of Bivariate Polynomials over the Integers

A Tool Kit for Finding Small Roots of Bivariate Polynomials over the Integers (2005)

by Johannes Blömer , Alexander May

Venue:	PROCEEDINGS OF EUROCRYPT 2005, LNCS 3494
Citations:	7 - 1 self

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Datum	Value	Source
TITLE	A Tool Kit for Finding Small Roots of Bivariate Polynomials over the Integers	user correction - Legacy Corrections
AUTHOR NAME	Johannes Blömer	user correction
AUTHOR AFFIL	Faculty of Computer Science, Electrical Engineering and Mathematics; University of Paderborn	user correction
AUTHOR ADDR	33102 Paderborn, Germany	user correction
AUTHOR NAME	Alexander May	user correction
AUTHOR AFFIL	Faculty of Computer Science, Electrical Engineering and Mathematics; University of Paderborn	user correction
AUTHOR ADDR	33102 Paderborn, Germany	user correction
ABSTRACT	We present a new and flexible formulation of Coppersmith's method for finding small solutions of bivariate polynomials p(x, y) over the integers. Our approach allows to maximize the bound on the solutions of p(x, y) in a purely combinatorial way. We give various construction rules for di#erent shapes of p(x, y)'s Newton polygon. Our method has several applications. Most interestingly, we reduce the case of solving univariate polynomials f(x) modulo some composite number N of unknown factorization to the case of solving bivariate polynomials over the integers. Hence, our approach unifies both methods given by Coppersmith at Eurocrypt 1996.	user correction - Legacy Corrections
YEAR	2005	INFERENCE
VENUE	PROCEEDINGS OF EUROCRYPT 2005, LNCS 3494	user correction
VENUE TYPE	CONFERENCE	INFERENCE
PAGES	251--267	INFERENCE
VOLUME	3494	INFERENCE
CITATIONS	14 found	ParsCit 1.0