Combined Algebraic and Truncated Differential Cryptanalysis on Reduced-round Simon

Nicolas Courtois, Theodosis Mourouzis, Guangyan Song, Pouyan Sepehrdad, Petr Susil

2014

Abstract

Recently, two families of ultra-lightweight block ciphers were proposed, SIMON and SPECK, which come in a variety of block and key sizes (Beaulieu et al., 2013). They are designed to offer excellent performance for hardware and software implementations (Beaulieu et al., 2013; Aysu et al., 2014). In this paper, we study the resistance of SIMON-64/128 with respect to algebraic attacks. Its round function has very low Multiplicative Complexity (MC) (Boyar et al., 2000; Boyar and Peralta, 2010) and very low non-linearity (Boyar et al., 2013; Courtois et al., 2011) since the only non-linear component is the bitwise multiplication operation. Such ciphers are expected to be very good candidates to be broken by algebraic attacks and combinations with truncated differentials (additional work by the same authors). We algebraically encode the cipher and then using guess-then-determine techniques, we try to solve the underlying system using either a SAT solver (Bard et al., 2007) or by ElimLin algorithm (Courtois et al., 2012b). We consider several settings where P-C pairs that satisfy certain properties are available, such as low Hamming distance or follow a strong truncated differential property (Knudsen, 1995). We manage to break faster than brute force up to 10(/44) rounds for most cases we have tried. Surprisingly, no key guessing is required if pairs which satisfy a strong truncated differential property are available. This reflects the power of combining truncated differentials with algebraic attacks in ciphers of low non-linearity and shows that such ciphers require a large number of rounds to be secure.

Paper Citation

in Harvard Style

Courtois N., Mourouzis T., Song G., Sepehrdad P. and Susil P. (2014). Combined Algebraic and Truncated Differential Cryptanalysis on Reduced-round Simon . In Proceedings of the 11th International Conference on Security and Cryptography - Volume 1: SECRYPT, (ICETE 2014) ISBN 978-989-758-045-1, pages 399-404. DOI: 10.5220/0005064903990404

in Bibtex Style

@conference{secrypt14,
author={Nicolas Courtois and Theodosis Mourouzis and Guangyan Song and Pouyan Sepehrdad and Petr Susil},
title={Combined Algebraic and Truncated Differential Cryptanalysis on Reduced-round Simon},
booktitle={Proceedings of the 11th International Conference on Security and Cryptography - Volume 1: SECRYPT, (ICETE 2014)},
year={2014},
pages={399-404},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0005064903990404},
isbn={978-989-758-045-1},
}

in EndNote Style

TY - CONF
JO - Proceedings of the 11th International Conference on Security and Cryptography - Volume 1: SECRYPT, (ICETE 2014)
TI - Combined Algebraic and Truncated Differential Cryptanalysis on Reduced-round Simon
SN - 978-989-758-045-1
AU - Courtois N.
AU - Mourouzis T.
AU - Song G.
AU - Sepehrdad P.
AU - Susil P.
PY - 2014
SP - 399
EP - 404
DO - 10.5220/0005064903990404