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Finding small roots of univariate modular equations revisited

Part of the Lecture Notes in Computer Science book series (LNCS,volume 1355)

Abstract

An alternative technique for finding small roots of univariate modular equations is described. This approach is then compared with that taken in (Coppersmith, 1996), which links the concept of the dual lattice (see (Cassels, 1971)) to the LLL algorithm (see (Lenstra et al., 1982)). Timing results comparing both algorithms are given, and practical considerations are discussed. This work has direct applications to several low exponent attacks on the RSA cryptographic scheme (see (Coppersmith, 1996)).

Keywords

  • Dual Basis
  • Small Root
  • Lattice Reduction
  • Dual Lattice
  • Relevant Matrice

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  • Cassels, J. W. S. 1971. An introduction to the geometry of numbers. Springer.

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  • Cohen, H. 1991. A Course in Computational Algebraic Number Theory. Springer-Verlag.

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  • Coppersmith, D. 1996. Finding a small root of a univariate modular equation. In: Proceedings of Eurocrypt 96.

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  • Lenstra, A. K., Lenstra, H. W., & Lovasz, L. 1982. Factoring polynomials with integer coefficients. Mathematische Annalen, 261, 513–534.

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© 1997 Springer-Verlag Berlin Heidelberg

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Howgrave-Graham, N. (1997). Finding small roots of univariate modular equations revisited. In: Darnell, M. (eds) Crytography and Coding. Cryptography and Coding 1997. Lecture Notes in Computer Science, vol 1355. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0024458

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  • DOI: https://doi.org/10.1007/BFb0024458

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63927-5

  • Online ISBN: 978-3-540-69668-1

  • eBook Packages: Springer Book Archive