Annual International Conference on the Theory and Applications of Cryptographic Techniques

EUROCRYPT 2012: Advances in Cryptology – EUROCRYPT 2012 pp 700-718

Trapdoors for Lattices: Simpler, Tighter, Faster, Smaller

  • Daniele Micciancio
  • Chris Peikert
Conference paper

DOI: 10.1007/978-3-642-29011-4_41

Volume 7237 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Micciancio D., Peikert C. (2012) Trapdoors for Lattices: Simpler, Tighter, Faster, Smaller. In: Pointcheval D., Johansson T. (eds) Advances in Cryptology – EUROCRYPT 2012. EUROCRYPT 2012. Lecture Notes in Computer Science, vol 7237. Springer, Berlin, Heidelberg

Abstract

We give new methods for generating and using “strong trapdoors” in cryptographic lattices, which are simultaneously simple, efficient, easy to implement (even in parallel), and asymptotically optimal with very small hidden constants. Our methods involve a new kind of trapdoor, and include specialized algorithms for inverting LWE, randomly sampling SIS preimages, and securely delegating trapdoors. These tasks were previously the main bottleneck for a wide range of cryptographic schemes, and our techniques substantially improve upon the prior ones, both in terms of practical performance and quality of the produced outputs. Moreover, the simple structure of the new trapdoor and associated algorithms can be exposed in applications, leading to further simplifications and efficiency improvements. We exemplify the applicability of our methods with new digital signature schemes and CCA-secure encryption schemes, which have better efficiency and security than the previously known lattice-based constructions.

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Copyright information

© International Association for Cryptologic Research 2012

Authors and Affiliations

  • Daniele Micciancio
    • 1
  • Chris Peikert
    • 2
  1. 1.University of CaliforniaSan DiegoUSA
  2. 2.Georgia Institute of TechnologyUSA