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

@inproceedings{Blmer2005ATK, title={A Tool Kit for Finding Small Roots of Bivariate Polynomials over the Integers}, author={Johannes Bl{\"o}mer and Alexander May}, booktitle={EUROCRYPT}, year={2005} }

- Published 2005 in EUROCRYPT
DOI:10.1007/11426639_15

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 different 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… CONTINUE READING