Lattice-based cryptography has generated considerable interest in the last two decades due toattractive features, including conjectured security against quantum attacks, strong securityguarantees from worst-case hardness assumptions and constructions of fully homomorphicencryption schemes. On the other hand, even though it is a crucial part of many lattice-basedschemes, Gaussian sampling is still lagging and continues to limit the effectiveness of this newcryptography. The first goal of this thesis is to improve the efficiency of Gaussian sampling forlattice-based hash-and-sign signature schemes. We propose a non-centered algorithm, with aflexible time-memory tradeoff, as fast as its centered variant for practicable size of precomputedtables. We also use the Rényi divergence to bound the precision requirement to the standarddouble precision. Our second objective is to construct Falcon, a new hash-and-sign signaturescheme, based on the theoretical framework of Gentry, Peikert and Vaikuntanathan for latticebasedsignatures. We instantiate that framework over NTRU lattices with a new trapdoor sampler.
| Identifer | oai:union.ndltd.org:univ-toulouse.fr/oai:oatao.univ-toulouse.fr:23886 |
| Date | 12 November 2018 |
| Creators | Ricosset, Thomas |
| Contributors | Institut National Polytechnique de Toulouse - INPT (FRANCE), Institut de Recherche en Informatique de Toulouse - IRIT (Toulouse, France) |
| Source Sets | Université de Toulouse |
| Language | English |
| Detected Language | English |
| Type | PhD Thesis, PeerReviewed, info:eu-repo/semantics/doctoralThesis |
| Format | application/pdf |
| Rights | info:eu-repo/semantics/openAccess |
| Relation | http://oatao.univ-toulouse.fr/23886/ |
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