Bijective S-boxes of different sizes obtained from quasi-cyclic codes

S-Boxes from Binary Quasi-Cyclic Codes

S - boxes from binary quasi - cyclic codes 1

In this paper we present a construction for S-boxes using quasi-cyclic codes. We obtain S-boxes with good nonlinearity.

Good Quasi-Cyclic Codes Derived From Irreducible Cyclic Codes

As a generalization of cyclic codes, quasi-cyclic codes contain many good linear codes. Extensive search is made and lots of good quasi-cyclic codes are obtained from irreducible cyclic codes. A new binary [95, 13, 40] code which improves the lower bound on the minimum distance, is also constructed. Index Term — Codes and coding, linear codes, cyclic codes, idempotent, irreducible codes, quasi-...

Quasi-cyclic LDPC codes from difference families

We consider in this paper regular and nearly regular quasi-cyclic low-density paritycheck (LDPC) codes, derived from families of difference sets. The codes have girth at least 6, and sparse parity-check matrices. They are designed to perform well when iteratively decoded with the sum-product decoding algorithm and to allow low complexity encoding.

Efficient Encryption from Random Quasi-Cyclic Codes

We propose a framework for constructing efficient code-based encryption schemes from codes that do not hide any structure in their public matrix. The framework is in the spirit of the schemes first proposed by Alekhnovich in 2003 and based on the difficulty of decoding random linear codes from random errors of low weight. We depart somewhat from Aleknovich’s approach and propose an encryption s...