On cryptographically significant mappings over GF(2 [sup] n)

Abstract

In this paper we investigate the algebraic properties of important cryptographic primitives called substitution boxes (S-boxes). An S-box is a mapping that takes ▫$n$▫ binary inputs whose image is a binary ▫$m$▫-tuple; therefore it is represented as ▫$F:\text{GF}(2)^n \rightarrow \text{GF}(2)^m$▫. One of the most important cryptographic applications is the case ▫$n = m$▫, thus the S-box may be viewed as a function over ▫$\text{GF}(2^n)$▫. We show that certain classes of functions over ▫$\text{GF}(2^n)$▫ do not possess a cryptographic property known as APN (AlmostPerfect Nonlinear) permutations. On the other hand, when ▫$n$▫ is odd, an infinite class of APN permutations may be derived in a recursive manner, that is starting with a specific APN permutation on ▫$\text{GF}(2^k), k$▫ odd, APN permutations are derived over ▫$\text{GF}(2^{k+2i})$▫ for any ▫$i \geq 1$▫. Some theoretical results related to permutation polynomials and algebraic properties of the functions in the ring ▫$\text{GF}(q)[x,y]$▫ are also presented. For sparse polynomials over the field ▫$\text{GF}(2^n)$▫, an efficient algorithm for finding low degree I/O equations is proposed.

Keywords

kriptoanaliza;kriptografija;algebraične lastnosti;cryptoanalysis;cryptography;permutation polynomials;power mappings;APN functions;S-box;CCZ-equivalence;algebraic properties;

Data

Language:	English
Year of publishing:	2008
Typology:	1.08 - Published Scientific Conference Contribution
Organization:	UP - University of Primorska
UDC:	512.624.95
COBISS:	15119193
Views:	3037
Downloads:	74
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary keywords:	kriptoanaliza;kriptografija;algebraične lastnosti;
Type (COBISS):	Not categorized
Pages:	Str. 189-204
ID:	1474222