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Finding Small Roots of Bivariate Integer Polynomial Equations Revisited
 PROC. ADVANCES IN CRYPTOLOGY EUROCRYPT’04, LNCS 3027
, 2004
"... At Eurocrypt ’96, Coppersmith proposed an algorithm for finding small roots of bivariate integer polynomial equations, based on lattice reduction techniques. But the approach is difficult to understand. In this paper, we present a much simpler algorithm for solving the same problem. Our simplificati ..."
Abstract

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At Eurocrypt ’96, Coppersmith proposed an algorithm for finding small roots of bivariate integer polynomial equations, based on lattice reduction techniques. But the approach is difficult to understand. In this paper, we present a much simpler algorithm for solving the same problem. Our simplification is analogous to the simplification brought by HowgraveGraham to Coppersmith’s algorithm for finding small roots of univariate modular polynomial equations. As an application, we illustrate the new algorithm with the problem of finding the factors of n = pq if we are given the high order 1/4log 2 n bits of p.