Parallelisable variants of Camellia and SMS4 block cipher: p-Camellia and p-SMS4 (Q381127)

Summary: We propose two parallelisable variants of Camellia and SMS4 block ciphers based on the \(n\)-cell GF-NLFSR. The \(n\)-cell generalised Feistel-non-linear feedback shift register (GF-NLFSR) structure [\textit{J. Choy} et al., ACISP 2009, Lect. Notes Comput. Sci. 5594, 73--89 (2009; Zbl 1307.94048); Cryptogr. Commun. 3, No. 3, 141--164 (2011; Zbl 1235.94046)] is a generalised unbalanced Feistel network that can be considered as a generalisation of the outer function \(FO\) of the KASUMI block cipher. An advantage of this cipher over other \(n\)-cell generalised Feistel networks, e.g., SMS4 [\textit{W. Diffe} and \textit{G. Ledin}, ``SMS4 encryption algorithm for wireless networks'', Cryptology ePrint Archive: Report 2008/329] and Camellia [\textit{K. Aoki} et al., SAC 2000, Lect. Notes Comput. Sci. 2012, 39--56 (2001; Zbl 1037.94540)], is that it is parallelisable for up to \(n\) rounds. In hardware implementations, the benefits translate to speeding up encryption by up to n times while consuming similar area and significantly less power. At the same time, \(n\)-cell GF-NLFSR structures offer similar proofs of security against differential cryptanalysis as conventional \(n\)-cell Feistel structures. In this paper, we prove security against differential, linear and boomerang attacks. We also show that the selected number of rounds are conservative enough to provide high security margin against other known attacks such as integral, impossible differential, higher order differential, interpolation, slide, XSL and related-key differential attacks.