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 Howgrave-Graham 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 1/4 Iog 2 n bits of p. © International Association for Cryptologic Research 2004.
CITATION STYLE
Coron, J. S. (2004). Finding small roots of bivariate integer polynomial equations revisited. Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 3027, 492–505. https://doi.org/10.1007/978-3-540-24676-3_29
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