arXiv subjects
Publications and source records attributed to Gérard Cohen.
Two Hamilton paths in $K_n$ are separated by a cycle of length $k$ if their union contains such a cycle. For small fixed values of $k$ we bound the asymptotics of the maximum cardinality of a family of Hamilton paths in $K_n$ such that any pair of paths in the family is separated by a cycle of length $k.$
We begin a systematic study of the problem of the zero--error capacity of noisy binary channels with memory and solve some of the non--trivial cases.
We introduce a new protocol for secure two-party computation of linear functions in the semi-honest model, based on coding techniques. We first establish a parallel between the second version of the wire-tap channel model and secure two-party computation. This leads us to our protocol, that combines linear coset coding and oblivious transfer techniques. Our construction requires the use of binary intersecting codes or $q$-ary minimal codes, which are also studied in this paper.
Recently, Dziembowski et al. introduced the notion of non-malleable codes (NMC), inspired from the notion of non-malleability in cryptography and the work of Gennaro et al. in 2004 on tamper proof security. Informally, when using NMC, if an attacker modifies a codeword, decoding this modified codeword will return either the original message or a completely unrelated value. The definition of NMC is related to a family of modifications authorized to the attacker. In their paper, Dziembowski et al. propose a construction valid for the family of all bit-wise independent functions. In this article, we study the link between the second version of the Wire-Tap (WT) Channel, introduced by Ozarow and Wyner in 1984, and NMC. Using coset-coding, we describe a new construction for NMC w.r.t. a subset of the family of bit-wise independent functions. Our scheme is easier to build and more efficient than the one proposed by Dziembowski et al.
We present a method to strengthen a very low cost solution for key agreement with a RFID device. Starting from a work which exploits the inherent noise on the communication link to establish a key by public discussion, we show how to protect this agreement against active adversaries. For that purpose, we unravel integrity $(I)$-codes suggested by Cagalj et al. No preliminary key distribution is required.
Starting from a practical use of Reed-Solomon codes in a cryptographic scheme published in Indocrypt'09, this paper deals with the threshold of linear $q$-ary error-correcting codes. The security of this scheme is based on the intractability of polynomial reconstruction when there is too much noise in the vector. Our approach switches from this paradigm to an Information Theoretical point of view: is there a class of elements that are so far away from the code that the list size is always superpolynomial? Or, dually speaking, is Maximum-Likelihood decoding almost surely impossible? We relate this issue to the decoding threshold of a code, and show that when the minimal distance of the code is high enough, the threshold effect is very sharp. In a second part, we explicit lower-bounds on the threshold of Maximum-Distance Separable codes such as Reed-Solomon codes, and compute the threshold for the toy example that motivates this study.
We investigate the packing and covering densities of linear and nonlinear binary codes, and establish a number of duality relationships between the packing and covering problems. Specifically, we prove that if almost all codes (in the class of linear or nonlinear codes) are good packings, then only a vanishing fraction of codes are good coverings, and vice versa: if almost all codes are good coverings, then at most a vanishing fraction of codes are good packings. We also show that any specific maximal binary code is either a good packing or a good covering, in a certain well-defined sense.
Using the notion of generalized weight we improve estimates on the parameters of quantum codes obtained by Steane's construction from binary codes. This yields several new families of quantum codes.