Description
This talk focuses on a new variant of the Learning With Errors (LWE) problem, a fundamental computational problem used in lattice-based cryptography.<br/> At Crypto17, Roşca et al. introduced the Middle-Product LWE problem (MP-LWE), whose hardness is based on the hardness of the Polynomial LWE (P-LWE) problem parameterized by a large set of polynomials, making it more secure against the possible weakness of a single defining polynomial. As a cryptographic application, they also provided an encryption scheme based on the MP-LWE problem. In this talk, I present a deterministic variant of their encryption scheme, which does not need Gaussian sampling and is thus simpler than the original one. Still, it has the same quasi-optimal asymptotic key and ciphertext sizes. The hardness of the scheme is based on a new assumption called Middle-Product Computational Learning With Rounding. We prove that this new assumption is as hard as the decisional version of MP-LWE and thus benefits from worst-case to average-case hardness guarantees.<br/> lien: http://e-learning.sviesolutions.com/4bl7vxoqql0b
Next sessions
-
Efficient zero-knowledge proofs and arguments in the CL framework
Speaker : Agathe Beaugrand - Institut de Mathématiques de Bordeaux
The CL encryption scheme, proposed in 2015 by Castagnos and Laguillaumie, is a linearly homomorphic encryption scheme, based on class groups of imaginary quadratic fields. The specificity of these groups is that their order is hard to compute, which means it can be considered unknown. This particularity, while being key in the security of the scheme, brings technical challenges in working with CL,[…] -
Constant-time lattice reduction for SQIsign
Speaker : Sina Schaeffler - IBM Research
SQIsign is an isogeny-based signature scheme which has recently advanced to round 2 of NIST's call for additional post-quantum signatures. A central operation in SQIsign is lattice reduction of special full-rank lattices in dimension 4. As these input lattices are secret, this computation must be protected against side-channel attacks. However, known lattice reduction algorithms like the famous[…] -
Circuit optimisation problems in the context of homomorphic encryption
Speaker : Sergiu Carpov - Arcium
Fully homomorphic encryption (FHE) is an encryption scheme that enables the direct execution of arbitrary computations on encrypted data. The first generation of FHE schemes began with Gentry's groundbreaking work in 2019. It relies on a technique called bootstrapping, which reduces noise in FHE ciphertexts. This construction theoretically enables the execution of any arithmetic circuit, but[…] -
Cycles of pairing-friendly abelian varieties
Speaker : Maria Corte-Real Santos - ENS Lyon
A promising avenue for realising scalable proof systems relies on the existence of 2-cycles of pairing-friendly elliptic curves. More specifically, such a cycle consists of two elliptic curves E/Fp and E’/Fq that both have a low embedding degree and also satisfy q = #E(Fp) and p = #E’(Fq). These constraints turn out to be rather restrictive; in the decade that has passed since 2-cycles were first[…]-
Cryptography
-