52 citations · 134 across the 30 of their papers we have counts for
37 papers
An extension of Overbeck's attack with an application to cryptanalysis of Twisted Gabidulin-based schemes
Alain Couvreur, Ilaria Zappatore
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…
Correlated Pseudorandomness from the Hardness of Quasi-Abelian Decoding
Maxime Bombar, Geoffroy Couteau, Alain Couvreur +1
Secure computation often benefits from the use of correlated randomness to achieve fast, non-cryptographic online protocols. A recent paradigm put forth by Boyle …
A new approach based on quadratic forms to attack the McEliece cryptosystem
Alain Couvreur, Rocco Mora, Jean-Pierre Tillich
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 assoc…
Improved decoding of symmetric rank metric errors
Alain Couvreur
We consider the decoding of rank metric codes assuming the error matrix is symmetric. We prove two results. First, for rates there exists a broad family of rank metric codes…
A proof of the Brill-Noether method from scratch
Elena Berardini, Alain Couvreur, Grégoire Lecerf
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…
On Codes and Learning With Errors over Function Fields
Maxime Bombar, Alain Couvreur, Thomas Debris-Alazard
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…
Right-hand side decoding of Gabidulin code and applications
Maxime Bombar, Alain Couvreur
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 algorit…
How arithmetic and geometry make error correcting codes better
Alain Couvreur
This note completes a talk given at the conference Curves over Finite Fields: past, present and future celebrating the publication the book {\em Rational Points on Curves over Fini…
Decoding supercodes of Gabidulin codes and applications to cryptanalysis
Maxime Bombar, Alain Couvreur
This article discusses the decoding of Gabidulin codes and shows how to extend the usual decoder to any supercode of a Gabidulin code at the cost of a significant decrease of the d…
Recovering or Testing Extended-Affine Equivalence
Anne Canteaut, Alain Couvreur, Léo Perrin
Extended Affine (EA) equivalence is the equivalence relation between two vectorial Boolean functions and such that there exist two affine permutations , , and an affi…
On the hardness of code equivalence problems in rank metric
Alain Couvreur, Thomas Debris-Alazard, Philippe Gaborit
In the recent years, the notion of rank metric in the context of coding theory has known many interesting developments in terms of applications such as space time coding, network c…
Algebraic geometry codes and some applications
Alain Couvreur, Hugues Randriambololona
This article surveys the development of the theory of algebraic geometry codes since their discovery in the late 70's. We summarize the major results on various problems such as: a…
On the security of subspace subcodes of Reed-Solomon codes for public key encryption
Alain Couvreur, Matthieu Lequesne
This article discusses the security of McEliece-like encryption schemes using subspace subcodes of Reed-Solomon codes, i.e. subcodes of Reed-Solomon codes over w…
Rank-metric codes over arbitrary Galois extensions and rank analogues of Reed-Muller codes
Daniel Augot, Alain Couvreur, Julien Lavauzelle +1
This paper extends the study of rank-metric codes in extension fields equipped with an arbitrary Galois group . We propose a f…
Toward good families of codes from towers of surfaces
Alain Couvreur, Philippe Lebacque, Marc Perret
We introduce in this article a new method to estimate the minimum distance of codes from algebraic surfaces. This lower bound is generic, i.e. can be applied to any surface, and tu…
Power Error Locating Pairs
Alain Couvreur, Isabella Panaccione
We present a new decoding algorithm based on error locating pairs and correcting an amount of errors exceeding half the minimum distance. When applied to Reed--Solomon or algebraic…
Practical Algebraic Attack on DAGS
Magali Bardet, Manon Bertin, Alain Couvreur +1
DAGS scheme is a key encapsulation mechanism (KEM) based on quasi-dyadic alternant codes that was submitted to NIST standardization process for a quantum resistant public key algor…
Anticanonical codes from del Pezzo surfaces with Picard rank one
Régis Blache, Alain Couvreur, Emmanuel Hallouin +4
We construct algebraic geometric codes from del Pezzo surfaces and focus on the ones having Picard rank one and the codes associated to the anticanonical class. We give explicit co…
On the security of a Loidreau's rank metric code based encryption scheme
Daniel Coggia, Alain Couvreur
We present a polynomial time attack of a rank metric code based encryption scheme due to Loidreau for some parameters.
Recovering short secret keys of RLCE in polynomial time
Alain Couvreur, Matthieu Lequesne, Jean-Pierre Tillich
We present a key recovery attack against Y. Wang's Random Linear Code Encryption (RLCE) scheme recently submitted to the NIST call for post-quantum cryptography. This attack recove…
An efficient structural attack on NIST submission DAGS
Elise Barelli, Alain Couvreur
We present an efficient key recovery attack on code based encryption schemes using some quasi-dyadic alternant codes with extension degree 2. This attack permits to break the propo…
Towards a function field version of Freiman's Theorem
Christine Bachoc, Alain Couvreur, Gilles Zémor
We discuss a multiplicative counterpart of Freiman's theorem in the context of a function field over an algebraically closed field . Such a theorem would give a preci…
On tensor products of CSS Codes
Benjamin Audoux, Alain Couvreur
CSS codes are in one-to-one correspondance with length 3 chain complexes. The latter are naturally endowed with a tensor product which induces a similar operation on the…
A Polynomial-Time Attack on the BBCRS Scheme
Alain Couvreur, Ayoub Otmani, Jean-Pierre Tillich +1
The BBCRS scheme is a variant of the McEliece public-key encryption scheme where the hiding phase is performed by taking the inverse of a matrix which is of the form $\mathbf{T} +\…