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
Next sessions
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Lie algebras and the security of cryptosystems based on classical varieties in disguise
Speaker : Mingjie Chen - KU Leuven
In 2006, de Graaf et al. proposed a strategy based on Lie algebras for finding a linear transformation in the projective linear group that connects two linearly equivalent projective varieties defined over the rational numbers. Their method succeeds for several families of “classical” varieties, such as Veronese varieties, which are known to have large automorphism groups. In this talk, we[…]-
Cryptography
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Some applications of linear programming to Dilithium
Speaker : Paco AZEVEDO OLIVEIRA - Thales & UVSQ
Dilithium is a signature algorithm, considered post-quantum, and recently standardized under the name ML-DSA by NIST. Due to its security and performance, it is recommended in most use cases. During this presentation, I will outline the main ideas behind two studies, conducted in collaboration with Andersson Calle-Vierra, Benoît Cogliati, and Louis Goubin, which provide a better understanding of[…] -
Wagner’s Algorithm Provably Runs in Subexponential Time for SIS^∞
Speaker : Johanna Loyer - Inria Saclay
At CRYPTO 2015, Kirchner and Fouque claimed that a carefully tuned variant of the Blum-Kalai-Wasserman (BKW) algorithm (JACM 2003) should solve the Learning with Errors problem (LWE) in slightly subexponential time for modulus q = poly(n) and narrow error distribution, when given enough LWE samples. Taking a modular view, one may regard BKW as a combination of Wagner’s algorithm (CRYPTO 2002), run[…]-
Cryptography
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CryptoVerif: a computationally-sound security protocol verifier
Speaker : Bruno Blanchet - Inria
CryptoVerif is a security protocol verifier sound in the computational model of cryptography. It produces proofs by sequences of games, like those done manually by cryptographers. It has an automatic proof strategy and can also be guided by the user. It provides a generic method for specifying security assumptions on many cryptographic primitives, and can prove secrecy, authentication, and[…]-
Cryptography
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Structured-Seed Local Pseudorandom Generators and their Applications
Speaker : Nikolas Melissaris - IRIF
We introduce structured‑seed local pseudorandom generators (SSL-PRGs), pseudorandom generators whose seed is drawn from an efficiently sampleable, structured distribution rather than uniformly. This seemingly modest relaxation turns out to capture many known applications of local PRGs, yet it can be realized from a broader family of hardness assumptions. Our main technical contribution is a[…]-
Cryptography
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