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2019 | OriginalPaper | Buchkapitel

Automatic Tool for Searching for Differential Characteristics in ARX Ciphers and Applications

verfasst von : Mingjiang Huang, Liming Wang

Erschienen in: Progress in Cryptology – INDOCRYPT 2019

Verlag: Springer International Publishing

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Abstract

Motivated by the algorithm of differential probability calculation of Lipmaa and Moriai, we revisit the differential properties of modular addition. We propose an efficient approach to generate the input-output difference tuples with non-zero probabilities. A novel concept of combinational DDT and the corresponding construction algorithm are introduced to make it possible to obtain all valid output differences for fixed input differences. According to the upper bound of differential probability of modular addition, combining the optimization strategies with branch and bound search algorithm, we can reduce the search space of the first round and prune the invalid difference branches of the middle rounds. Applying this tool, the provable optimal differential trails covering more rounds for SPECK32/48/64 with tight probabilities can be found, and the differentials with larger probabilities are also obtained. In addition, the optimal differential trails cover more rounds than exisiting results for SPARX variants are obtained. A 12-round differential with a probability of \(2^{-54.83}\) for SPARX-64, and a 11-round differential trail with a probability of \(2^{-53}\) for SPARX-128 are found. For CHAM-64/128 and CHAM-128/*, the 39/63-round differential characteristics we find cover 3/18 rounds more than the known results respectively.

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Vorheriges Kapitel RC4: Non-randomness in the Index j and Some Results on Its Cycles

Nächstes Kapitel Improved Related-Tweakey Rectangle Attacks on Reduced-Round Deoxys-BC-384 and Deoxys-I-256-128

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The time cost depends on the ability of the computation environment. On a 2.5 GHz CPU, it takes about 9 s.

All experiments in this paper are carried out serially on a HPC with Intel(R) Xeon(R) CPU E5-2680 v3 @ 2.50 GHz. All differences are represented in hexadecimal.

For the 7-round optimal differential trail with probability weight of 24, we limit the first round probability weight \(w_1 \le 5\) to speed up the search process.

When the statistical condition is omitted in the last round, \(\#\)Trails will perhaps be greater than the sum of the number of trail with probability weight \(\le w_{max}\).

https://csrc.nist.gov/Projects/Lightweight-Cryptography

https://www.cryptolux.org/index.php/Sparkle

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Titel: Automatic Tool for Searching for Differential Characteristics in ARX Ciphers and Applications
verfasst von: Mingjiang Huang
Liming Wang
Verlag: Springer International Publishing
Buch: Progress in Cryptology – INDOCRYPT 2019
Print ISBN: 978-3-030-35422-0

Electronic ISBN: 978-3-030-35423-7

Copyright-Jahr: 2019
DOI: https://doi.org/10.1007/978-3-030-35423-7_6

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