We cryptanalyse here two variants of the McEliece cryptosystem based on quasi-cyclic codes. Both aim at reducing the key size by restricting the public and secret generator matrices to be in quasi-cyclic form. The first variant considers subcodes of a primitive BCH code. The aforementioned constraint on the public and secret keys implies to choose very structured permutations. We prove that thi...

We propose the study of quasi-cryptographic primitives and protocols. These are relaxed versions of standard cryptographic primitives and protocols where the adversary may be given more resources than some of the honest parties. The purpose of this study is to obtain a better understanding of some of the obstacles in basing cryptography on NP-hardness, as well as the relations between various c...

Dans une permutation, un record est maximum ou minimum, en partant de la droite gauche. Les éléments d’une permutation peuvent être classés deux types : les records (dits points extérieurs) et autres intérieurs). permutations sans point intérieur ont été étudiées sous le nom carrées. Ici, nous explorons ayant nombre fini intérieurs, dites quasi-carrées. Contrairement aux carrées, l’énumération ...

In this paper, we present a fully pipelined LDPC decoder for 802.11n standard that supports variable block sizes and multiple code rates. The proposed architecture utilizes features of Quasi-Cyclic LDPC codes and layered decoding to reduce memory bits and interconnection complexity through efficient utilization of permutation network for forward and backward interconnection routing. Permutation...

Repeat-Accumulate (RA) codes, consisting of a simple binary repetition followed by a permutation and an accumulator, are converting into quasi-cyclic codes with multiple cross-linked cycles. The algebraic heuristics are used to design codes with an explicit algebraic permutation yielding desirable graph properties. Recursive graph constructions techniques are given for the construction of very ...

We give conditions under which a quasi-isometric map between direct products of hyperbolic spaces splits as a direct product up to bounded distance and permutation of factors. This is a variation on a result due to Kapovich, Kleiner and Leeb.

We present a simple proof of the balancedness of permutation games. In the proof we use the existence of envy-free allocations in economies with indivisible objects, quasi-linear utility functions, and an amount of money.  2000 Elsevier Science S.A. All rights reserved.

1.1. Aschbacher-Scott Program. Primitive permutation groups have been studied since Galois and Jordan and have applications in many different areas. If Γ is a transitive permutation group with a point stabilizer M then Γ is primitive if and only if M < Γ is a maximal subgroup. So studying primitive permutation groups is equivalent to studying maximal subgroups. In most problems involving a fini...