New lattice based cryptographic constructions

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We introduce the use of Fourier analysis on lattices as an integral part of a lattice based construction. The tools we develop provide an elegant description of certain Gaussian distributions around lattice points. Our results include two cryptographic constructions which are based on the worst-case hardness of the unique shortest vector problem. The main result is a new public key cryptosystem whose security guarantee is considerably stronger than previous results (O(n1.5) instead of O(n7)). This provides the first alternative to Ajtai and Dwork's original 1996 cryptosystem. Our second result is a collision resistant hash function which, apart from improving the security in terms of the unique shortest vector problem, is also the first example of an analysis which is not based on Ajtai's iterative step. Surprisingly, the two results are derived from the same tool which presents two indistinguishable distributions on the segment [0,1). It seems that this tool can have further applications and as an example we mention how it can be used to solve an open problem related to quantum computation.

Original languageEnglish (US)
Title of host publicationConference Proceedings of the Annual ACM Symposium on Theory of Computing
Pages407-416
Number of pages10
StatePublished - 2003
Event35th Annual ACM Symposium on Theory of Computing - San Diego, CA, United States
Duration: Jun 9 2003Jun 11 2003

Other

Other35th Annual ACM Symposium on Theory of Computing
CountryUnited States
CitySan Diego, CA
Period6/9/036/11/03

Keywords

  • Average-case hardness
  • Cryptography
  • Lattices
  • Public key encryption
  • Quantum computing

ASJC Scopus subject areas

  • Software

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