Zobrazeno 1 - 10
of 127
pro vyhledávání: '"Couvreur, Alain"'
Autor:
Couvreur, Alain, Zémor, Gilles
Freiman's $3k-4$ Theorem states that if a subset $A$ of $k$ integers has a Minkowski sum $A+A$ of size at most $3k-4$, then it must be contained in a short arithmetic progression. We prove a function field analogue that is also a generalisation: it s
Externí odkaz:
http://arxiv.org/abs/2408.00183
The McEliece scheme is a generic frame which allows to use any error correcting code of which there exists an efficient decoding algorithm to design an encryption scheme by hiding the generator matrix code. Similarly, the Niederreiter frame is the du
Externí odkaz:
http://arxiv.org/abs/2405.16539
We bring in here a novel algebraic approach for attacking the McEliece cryptosystem. It consists in introducing a subspace of matrices representing quadratic forms. Those are associated with quadratic relationships for the component-wise product in t
Externí odkaz:
http://arxiv.org/abs/2306.10294
Secure computation often benefits from the use of correlated randomness to achieve fast, non-cryptographic online protocols. A recent paradigm put forth by Boyle $\textit{et al.}$ (CCS 2018, Crypto 2019) showed how pseudorandom correlation generators
Externí odkaz:
http://arxiv.org/abs/2306.03488
Autor:
Couvreur, Alain, Zappatore, Ilaria
In this article, we discuss the decoding of Gabidulin and related codes from a cryptographic point of view, and we observe that these codes can be decoded solely from the knowledge of a generator matrix. We then extend and revisit Gibson and Overbeck
Externí odkaz:
http://arxiv.org/abs/2305.01287
Autor:
Couvreur, Alain
These lecture notes have been written for a course at the Algebraic Coding Theory (ACT) summer school 2022 that took place in the university of Zurich. The objective of the course propose an in-depth presentation of the proof of one of the most strik
Externí odkaz:
http://arxiv.org/abs/2301.03569
Autor:
Couvreur, Alain
We consider the decoding of rank metric codes assuming the error matrix is symmetric. We prove two results. First, for rates $<1/2$ there exists a broad family of rank metric codes for which any symmetric error pattern, even of maximal rank can be co
Externí odkaz:
http://arxiv.org/abs/2212.08713
Publikováno v:
ACM Communications in Computer Algebra, Volume 57, Issue 4 (December 2023), 200 - 229
In 1874 Brill and Noether designed a seminal geometric method for computing bases of Riemann-Roch spaces. From then, their method has led to several algorithms, some of them being implemented in computer algebra systems. The usual proofs often rely o
Externí odkaz:
http://arxiv.org/abs/2208.12725
It is a long standing open problem to find search to decision reductions for structured versions of the decoding problem of linear codes. Such results in the lattice-based setting have been carried out using number fields: Polynomial-LWE, Ring-LWE, M
Externí odkaz:
http://arxiv.org/abs/2202.13990
Autor:
Bombar, Maxime, Couvreur, Alain
We discuss the decoding of Gabidulin and interleaved Gabidulin codes. We give the full presentation of a decoding algorithm for Gabidulin codes, which as Loidreau's seminal algorithm consists in localizing errors in the spirit of Berlekamp-Welch algo
Externí odkaz:
http://arxiv.org/abs/2112.07322