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The Shortest Vector Problem in Lattices with Many Cycles

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Cryptography and Lattices (CaLC 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2146))

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Abstract

In this paper we investigate how the complexity of the shortest vector problem in a lattice A depends on the cycle structure of the additive group ℤn/A. We give a proof that the shortest vector problem is NP-complete in the max-norm for n-dimensional lattices A where ℤn/A has n — 1 cycles. We also give experimental data that show that the LLL algorithm does not perform significantly better on lattices with a high number of cycles.

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© 2001 Springer-Verlag Berlin Heidelberg

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Trolin, M. (2001). The Shortest Vector Problem in Lattices with Many Cycles. In: Silverman, J.H. (eds) Cryptography and Lattices. CaLC 2001. Lecture Notes in Computer Science, vol 2146. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44670-2_14

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  • DOI: https://doi.org/10.1007/3-540-44670-2_14

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42488-8

  • Online ISBN: 978-3-540-44670-5

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