Algebraic properties of generalized Rijndael-like ciphers

Abstract

Abstract. We provide conditions under which the set of Rijndael-like functions considered as permutations of the state space and based on operations of the finite field GF(p k ) (p ≥ 2) is not closed under functional composition. These conditions justify using a sequential multiple encryption to strengthen generalized Rijndael like ciphers. In [39], 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.

On the group generated by the round functions of translation based ciphers over arbitrary finite fields

“…In [17] Patel, Ramzan and Sundaram showed that Luby-Rackoff ciphers are secure against adaptive chosen plaintext and ciphertext attacks, and have better time/space complexity if considered over the prime field F p for p > 2. Some results in this direction are also contained in [2]. This paper is organised as follows.…”