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Trapdoors for Lattices: Simpler, Tighter, Faster, Smaller

  • Daniele Micciancio
  • Chris Peikert
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7237)

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.

Keywords

Inversion Algorithm Homomorphic Encryption Defense Advance Research Project Agency Gaussian Parameter Trapdoor Function 
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

© 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

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