Integral Cryptanalysis and Impossible Differential Cryptanalysis of the <i>μ</i><sup>2</sup> Algorithm

HU Bin; ZHANG Guixian

doi:10.11999/JEIT210638

Volume 44 Issue 9

Sep. 2022

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Article Navigation > Journal of Electronics & Information Technology > 2022 > 44(9): 3335-3342

HU Bin, ZHANG Guixian. Integral Cryptanalysis and Impossible Differential Cryptanalysis of the μ2 Algorithm[J]. Journal of Electronics & Information Technology, 2022, 44(9): 3335-3342. doi: 10.11999/JEIT210638

Citation:

HU Bin, ZHANG Guixian. Integral Cryptanalysis and Impossible Differential Cryptanalysis of the μ² Algorithm[J]. Journal of Electronics & Information Technology, 2022, 44(9): 3335-3342. doi: 10.11999/JEIT210638

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Integral Cryptanalysis and Impossible Differential Cryptanalysis of the μ² Algorithm

doi: 10.11999/JEIT210638

HU Bin,
ZHANG Guixian^,

The SSF Information Engineering University, Zhengzhou 450001, China

Funds: The National Natural Science Foundation of China (61802438)

Received Date: 2021-06-28
Accepted Date: 2022-03-10
Rev Recd Date: 2022-02-26

Available Online: 2022-03-20

Publish Date: 2022-09-19

Abstract

Abstract

$ {\mu ^{\text{2}}} $ is a lightweight block cipher designed by Yeoh et al (doi: 10.1007/978-981-15-0058-9-27). The cipher has 15 rounds in total and adopts TYPE-II generalized feistel network. The ability of the $ {\mu ^{\text{2}}} $ algorithm to resist differential analysis and linear analysis is evaluated by Yeoh et al. in the design document, but the ability of $ {\mu ^{\text{2}}} $ algorithm to resist integral attack and impossible differential attack is not clear. In this paper, 8/9-round integral distinguishers and 9-round impossible difference are given. Using 8-round integral distinguishers, 9-round $ {\mu ^{\text{2}}} $ is attacked and the time complexity of the attack is ${2^{76}}$ 9-round encryptions, the data complexity is ${2^{48}}$, and the memory complexity is ${2^{48}}$. Using 9-round impossible difference, 11-round $ {\mu ^{\text{2}}} $ is attacked and the time complexity of the attack is ${2^{49}}$ 11-round encryptions, the data complexity is ${2^{64}}$ pairs of plaintexts. The results show that the 9-round $ {\mu ^{\text{2}}} $ algorithm can not resist integral attack, and the 11-round $ {\mu ^{\text{2}}} $ algorithm can not resist impossible differential analysis. In addition, the ability of $ {\mu ^{\text{2}}} $ algorithm to resist differential attack is reevaluated, and the maximum probability of differential characteristic of 4-round $ {\mu ^{\text{2}}} $ algorithm is ${{\text{2}}^{{{ - 39}}}}$, which is more compact than the probability ${2^{ - 3{\text{6}}}}$ of 4-round differential characteristic pointed out in the design report.
- $ {\mu ^{\text{2}}} $ algorithm,
- Mixed Integral Linear Programming (MILP),
- Integral attack,
- Impossible differential analysis,
- Differential analysis

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References(19)

References

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