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Lattice Reduction in Cryptology: An Update

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Algorithmic Number Theory (ANTS 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1838))

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Abstract

Lattices are regular arrangements of points in space, whose study appeared in the 19th century in both number theory and crystallography. The goal of lattice reduction is to find useful representations of lattices. A major breakthrough in that field occurred twenty years ago, with the appearance of Lovász’s reduction algorithm, also known as LLL or L3. Lattice reduction algorithms have since proved invaluable in many areas of mathematics and computer science, especially in algorithmic number theory and cryptology. In this paper, we survey some applications of lattices to cryptology. We focus on recent developments of lattice reduction both in cryptography and cryptanalysis, which followed seminal works of Ajtai and Coppersmith.

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  1. École Normale Supérieure, Département d’Informatique, 45 rue d’Ulm, 75005, Paris, France

    Phong Q. Nguyen & Jacques Stern

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  1. Mathematisch Instituut, Universiteit Nijmegen, Postbus 9010, 6500 GL, Nijmegen, The Netherlands

    Wieb Bosma

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Nguyen, P.Q., Stern, J. (2000). Lattice Reduction in Cryptology: An Update. In: Bosma, W. (eds) Algorithmic Number Theory. ANTS 2000. Lecture Notes in Computer Science, vol 1838. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10722028_4

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