Description
The main focus of this PhD thesis lies on the computational problem Learning With Errors (LWE). It is a core building block of lattice-based cryptography, which itself is among the most promising candidates to replace current cryptographic protocols once large-scale quantum computers may be available. The contributions of the present work are separated into two different parts. First, we study the hardness of structured variants of LWE. To this end, we show that under suitable parameter choices the Module Learning With Errors (M-LWE) problem doesn't become significantly easier to solve even if the underlying secret is replaced by a binary vector. Furthermore, we provide a classical hardness reduction for M-LWE, which further strengthens our confidence in its suitability for cryptography. Additionally, we define a new hardness assumption, the Middle-Product Computational Learning With Rounding (MP-CLWR) problem, which inherits the advantages of two existing LWE variants. Finally, we study problems related to the partial Vandermonde matrix. This is a recent source of hardness assumptions for lattice-based cryptography and its rigorous study is important to gain trust in it. In the second part of this manuscript, we show that the new hardness assumptions we introduced before serve for the construction of efficient public-key encryption. On the one hand, we design a new encryption scheme, whose security is provably based on the MP-CLWR problem. On the other hand, we modify an existing encryption scheme, called PASS Encrypt, to provide it with a security proof based on two explicitly stated partial Vandermonde problems.<br/> lien: https://youtu.be/Bu_PWWb63iU
Prochains exposés
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Polytopes in the Fiat-Shamir with Aborts Paradigm
Orateur : Hugo Beguinet - ENS Paris / Thales
The Fiat-Shamir with Aborts paradigm (FSwA) uses rejection sampling to remove a secret’s dependency on a given source distribution. Recent results revealed that unlike the uniform distribution in the hypercube, both the continuous Gaussian and the uniform distribution within the hypersphere minimise the rejection rate and the size of the proof of knowledge. However, in practice both these[…]-
Cryptographie
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Primitive asymétrique
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Mode et protocole
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Post-quantum Group-based Cryptography
Orateur : Delaram Kahrobaei - The City University of New York