Algebraic properties of generalized Rijndael-like ciphers

2012/10/30 by L. Babinkostova, K. W. Bombardier, Babinkostova, L. +7
Computer Science · Mathematics · #11T71 #14G50 #20B05 #20B30 #94A60 #Combinatorics (math.CO) #Cryptography and Security (cs.CR) #D.4.6 #E.3 #FOS: Computer and information sciences #FOS: Mathematics #Group Theory (math.GR) #acm:11T71 #acm:14G50 #acm:20B05 #acm:20B30 #acm:94A60 #cs.CR #math.CO #math.GR #msc:11T71 #msc:14G50 #msc:20B05 #msc:20B30 #msc:94A60

paper · pdf · doi:10.48550/arxiv.1210.7942

22 pages; Prelim04

arxiv created 2012/12/19 · arxiv updated 2012/12/20

Abstract

We provide conditions under which the set of Rijndael functions considered as permutations of the state space and based on operations of the finite field \GF (p^k) (p≥ 2 a prime number) is not closed under functional composition. These conditions justify using a sequential multiple encryption to strengthen the AES (Rijndael block cipher with specific block sizes) in case AES became practically insecure. In Sparr and Wernsdorf (2008), R. Sparr and R. Wernsdorf provided conditions under which the group generated by the Rijndael-like round functions based on operations of the finite field \GF (2^k) is equal to the alternating group on the state space. In this paper we provide conditions under which the group generated by the Rijndael-like round functions based on operations of the finite field \GF (p^k) (p≥ 2) is equal to the symmetric group or the alternating group on the state space.

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