Pierre Loidreau

Institut de recherche mathématique de Rennes

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Daniel Augot

Laboratoire d'Informatique de l'École Polytechnique

Thierry Pierre Berger

Université de Limoges

Victor Cauchois

Université de Rennes

Cédric Faure

Université Paris Cité

Gwezheneg Robert

Institut de recherche mathématique de Rennes

Julian Renner

Technical University of Munich

Nicolas Sendrier

CryptoExperts (France)

Matthieu Finiasz

CryptoExperts (France)

Antonia Wachter-Zeh

Technical University of Munich

Raghav Bhaskar

Data61

Cooperative Institutions

Institut national de recherche en informatique et en automatique

Centre National de la Recherche Scientifique

State Key Laboratory of Cryptology

Université de Rennes

CryptoExperts (France)

Institut de recherche mathématique de Rennes

Technical University of Munich

Université Paris Cité

Sorbonne Université

École Polytechnique

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A New Rank Metric Codes Based Encryption Scheme

Lecture notes in computer science (2017)

Pierre Loidreau

Rank (graph theory)

10.1007/978-3-319-59879-6_1

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Citations (73)

Properties of codes in rank metric

HAL (Le Centre pour la Communication Scientifique Directe) (2008)

Pierre Loidreau

We study properties of rank metric and codes in rank metric over finite fields. We show that perfect codes do not exist. We derive an equivalent of the Varshamov-Gilbert bound in Hamming metric. We study the asymptotic behavior of the minimum rank distance of codes that are on GV. We show that the packing density of maximum rank distance codes is lower bounded by a function depending on the error-correcting capability. We show that there are asymptotically perfect codes correcting errors of rank 1 over fields of characteristic 2.

Rank (graph theory)

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Citations (20)

A Welch–Berlekamp Like Algorithm for Decoding Gabidulin Codes

Lecture notes in computer science (2006)

Pierre Loidreau

Berlekamp–Welch algorithm

List decoding

Code (set theory)

10.1007/11779360_4

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Citations (105)

Codage et cryptographie

Nicolas Sendrier Daniel Augot Christelle Guiziou-Cloitre Pascale Charpin Anne Canteaut

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Citations (1)

Generalized Gabidulin codes over fields of any characteristic

arXiv (Cornell University) (2017)

Daniel Augot Pierre Loidreau Gwezheneg Robert

We generalise Gabidulin codes to the case of infinite fields, eventually with characteristic zero. For this purpose, we consider an abstract field extension and any automorphism in the Galois group. We derive some conditions on the automorphism to be able to have a proper notion of rank metric which is in coherence with linearized polynomials. Under these conditions, we generalize Gabidulin codes and provide a decoding algorithm which decode both errors and erasures. Then, we focus on codes over integer rings and how to decode them. We are then faced with the problem of the exponential growth of intermediate values, and to circumvent the problem, it is natural to propose to do computations modulo a prime ideal. For this, we study the reduction of generalized Gabidulin codes over number ideals codes modulo a prime ideal, and show they are classical Gabidulin codes. As a consequence, knowing side information on the size of the errors or the message, we can reduce the decoding problem over the integer ring to a decoding problem over a finite field. We also give examples and timings.

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Finding good linear approximations of block ciphers and its >>> application to cryptanalysis of reduced round DES

HAL (Le Centre pour la Communication Scientifique Directe) (2009)

Rafaël Fourquet Pierre Loidreau Cédric Tavernier

Impossible differential cryptanalysis

Boomerang attack

S-box

Higher-order differential cryptanalysis

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Citations (5)

Cryptanalysis of Rank-Metric Schemes Based on Distorted Gabidulin Codes

Lecture notes in computer science (2023)

Pierre Briaud Pierre Loidreau

Rank (graph theory)

10.1007/978-3-031-40003-2_2

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Citations (2)

Designing a Rank Metric Based McEliece Cryptosystem

Lecture notes in computer science (2010)

Pierre Loidreau

McEliece Cryptosystem

Rank (graph theory)

10.1007/978-3-642-12929-2_11

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Citations (58)

Properties of codes in rank metric

arXiv (Cornell University) (2006)

Pierre Loidreau

We study properties of rank metric and codes in rank metric over finite fields. We show that in rank metric perfect codes do not exist. We derive an existence bound that is the equivalent of the Gilbert--Varshamov bound in Hamming metric. We study the asymptotic behavior of the minimum rank distance of codes satisfying GV. We derive the probability distribution of minimum rank distance for random and random $\F{q}$-linear codes. We give an asymptotic equivalent of their average minimum rank distance and show that random $\F{q}$-linear codes are on GV bound for rank metric. We show that the covering density of optimum codes whose codewords can be seen as square matrices is lower bounded by a function depending only on the error-correcting capability of the codes. We show that there are quasi-perfect codes in rank metric over fields of characteristic 2.

Rank (graph theory)

Hamming distance

Hamming bound

10.48550/arxiv.cs/0610057

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Citations (46)

Le transfert inconscient

HAL (Le Centre pour la Communication Scientifique Directe) (2002)

Pierre Loidreau

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