Exhaustive search for small dimension recursive MDS diffusion layers for block ciphers and hash functions

Author

Augot, Daniel ; Finiasz, Matthieu

Author_Institution

LIX, Ecole Polytech., Palaiseau, France

fYear

2013

fDate

7-12 July 2013

Firstpage

1551

Lastpage

1555

Abstract

This article presents a new algorithm to find MDS matrices that are well suited for use as a diffusion layer in lightweight block ciphers. Using an recursive construction, it is possible to obtain matrices with a very compact description. Classical field multiplications can also be replaced by simple F₂-linear transformations (combinations of XORs and shifts) which are much lighter. Using this algorithm, it was possible to design a 16×16 matrix on a 5-bit alphabet, yielding an efficient 80-bit diffusion layer with maximal branch number.

Keywords

block codes; cryptography; file organisation; matrix algebra; MDS matrix algorithm; exhaustive search; hash function; lightweight block matrix; maximal branch number; maximum distance separable code; simple F₂- linear transformation; small dimension recursive MDS diffusion layer; word length 5 bit; word length 80 bit; Ciphers; Computer science; Information theory; Matrices; Polynomials; Symmetric matrices; Block ciphers; Branch number; Companion matrices; Generalised Feistel; MDS codes; MDS conjecture; Singleton bound;

fLanguage

English

Publisher

ieee

Conference_Titel

Information Theory Proceedings (ISIT), 2013 IEEE International Symposium on

Conference_Location

Istanbul

ISSN

2157-8095

Type

conf

DOI

10.1109/ISIT.2013.6620487

Filename

6620487