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

Pašalić, Enes

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Naslov:	On cryptographically significant mappings over GF(2 [sup] n)
Avtorji:	ID Pašalić, Enes (Avtor)
Datoteke:	http://dx.doi.org/10.1007/978-3-540-69499-1_16
Jezik:	Angleški jezik
Vrsta gradiva:	Delo ni kategorizirano
Tipologija:	1.08 - Objavljeni znanstveni prispevek na konferenci
Organizacija:	FAMNIT - Fakulteta za matematiko, naravoslovje in informacijske tehnologije
Opis:	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.
Ključne besede:	cryptoanalysis, cryptography, permutation polynomials, power mappings, APN functions, S-box, CCZ-equivalence, algebraic properties
Leto izida:	2008
Št. strani:	Str. 189-204
PID:	20.500.12556/RUP-3586
UDK:	512.624.95
COBISS.SI-ID:	15119193
Datum objave v RUP:	15.10.2013
Število ogledov:	4311
Število prenosov:	76
Metapodatki:
:	PAŠALIĆ, Enes, 2008, On cryptographically significant mappings over GF(2 [sup] n). V : [na spletu]. Objavljeni znanstveni prispevek na konferenci. 2008. p. 189–204. [Dostopano 21 april 2025]. Pridobljeno s: http://dx.doi.org/10.1007/978-3-540-69499-1_16 Kopiraj citat