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The Two Faces of Lattices in Cryptology

  • Phong Q. Nguyen
  • Jacques Stern
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2146)

Abstract

Lattices are regular arrangements of points in n-dimensional space, whose study appeared in the 19th century in both number theory and crystallography. Since the appearance of the celebrated Lenstra-Lenstra-Lovász lattice basis reduction algorithm twenty years ago, lattices have had surprising applications in cryptology. Until recently, the applications of lattices to cryptology were only negative, as lattices were used to break various cryptographic schemes. Paradoxically, several positive cryptographic applications of lattices have emerged in the past five years: there now exist public-key cryptosystems based on the hardness of lattice problems, and lattices play a crucial rôle in a few security proofs. We survey the main examples of the two faces of lattices in cryptology.

Keywords

Knapsack Problem Lattice Reduction Modular Equation Digital Signature Algorithm Hermite Normal Form 
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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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Phong Q. Nguyen
    • 1
  • Jacques Stern
    • 1
  1. 1.Département d’InformatiqueÉcole Normale SupérieureParisFrance

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