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
-
Key Attack on the ACDGV Matrix Encryption Scheme
Speaker : Anmoal Porwal - Technical University of Munich
I will present our key-recovery attack on the ACDGV public-key encryption scheme proposed at ASIACRYPT 2024 by Aragon, Couvreur, Dyseryn, Gaborit, and Vinçotte. The secret key is a Gabidulin code hidden by appending random rows and columns and by left- and right-multiplication with invertible matrices. Our attack exploits the resulting algebraic structure to recover an equivalent secret key. It[…]-
Cryptography
-
Asymmetric primitive
-
-
Module Learning With Errors and Structured Extrapolated Dihedral Cosets
Speaker : Jinwei Zheng - Télécom Paris
The Module Learning With Errors (MLWE) problem is the fundamental hardness assumption underlying the key encapsulation and signature schemes ML-KEM and ML-DSA, which have been selected by NIST for post-quantum cryptography standardization. Understanding its quantum hardness is crucial for assessing the security of these standardized schemes. Inspired by the equivalence between LWE and[…]-
Cryptography
-