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Lattice-based digital signature and discrete gaussian sampling

Ricosset, Thomas. Lattice-based digital signature and discrete gaussian sampling. PhD, Réseaux, Télécommunications, Systèmes et Architecture, Institut National Polytechnique de Toulouse, 2018

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Abstract

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.

Item Type:PhD Thesis
Uncontrolled Keywords:
Institution:Université de Toulouse > Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE)
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Research Director:
Aguilar Melchor, Carlos
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Deposited On:23 May 2019 09:07

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