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Erschienen in:
2007 | OriginalPaper | Buchkapitel
Toward a Rigorous Variation of Coppersmith’s Algorithm on Three Variables
verfasst von : Aurélie Bauer, Antoine Joux
Erschienen in: Advances in Cryptology - EUROCRYPT 2007
Verlag: Springer Berlin Heidelberg
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In 1996, Coppersmith introduced two lattice reduction based techniques to find small roots in polynomial equations. One technique works for modular univariate polynomials, the other for bivariate polynomials over the integers. Since then, these methods have been used in a huge variety of cryptanalytic applications. Some applications also use extensions of Coppersmith’s techniques on more variables. However, these extensions are heuristic methods. In the present paper, we present and analyze a new variation of Coppersmith’s algorithm on three variables over the integers. We also study the applicability of our method to short RSA exponents attacks. In addition to lattice reduction techniques, our method also uses Gröbner bases computations. Moreover, at least in principle, it can be generalized to four or more variables.