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Erschienen in:
2012 | OriginalPaper | Buchkapitel
Trapdoors for Lattices: Simpler, Tighter, Faster, Smaller
verfasst von : Daniele Micciancio, Chris Peikert
Erschienen in: Advances in Cryptology – EUROCRYPT 2012
Verlag: Springer Berlin Heidelberg
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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.