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 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 factorization to the case of solving bivariate polynomials over the integers. Hence, our approach unifies both methods given by Coppersmith at Eurocrypt 1996.
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Blömer, J., May, A. (2005). A Tool Kit for Finding Small Roots of Bivariate Polynomials over the Integers. In: Cramer, R. (eds) Advances in Cryptology – EUROCRYPT 2005. EUROCRYPT 2005. Lecture Notes in Computer Science, vol 3494. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11426639_15
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DOI: https://doi.org/10.1007/11426639_15
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