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Differential cryptanalysis of PRESENT-like cipher

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Abstract

In 2011, Borghoff et al. introduced a slender-set differential cryptanalysis on PRESENT-like ciphers with key-dependent S-boxes. Borghoff’s differential attack mainly divides into two parts: data collection phase and S-box recovery phase. In this paper, we investigate different attacks on PRESENT-like cipher with secret S-boxes and public S-boxes. For PRESENT-like cipher with secret S-boxes, we introduce two new cryptanalytic techniques, and use them to recover the secret S-boxes more efficiently. Our first new idea is that we present a new method of data collection based on the method of optimal distinguisher for collecting information efficiently. Another new technique is that we propose a method of constructing the entire correct slender-sets instead of checking the correctness of slender-sets in the S-box recovery phase. In particular, we implemented a successful attack on the cipher Maya in practice. In our experiments, the correct S-boxes can be recovered with \(2^{26}\) data complexity and \(2^{22.4}\) time complexity at a success rate of 100 % based on 200 independent trials. Furthermore, we propose a new method of recovering the secret key of PRESENT-like cipher with public S-boxes with lower data and time complexity. To the 12-round PRESENT-80, the experiments show that we can recover the entire 80-bit secret key with \(2^{34.9}\) data and \(2^{38.9}\) time complexity. To the 22-round \(\mathrm{PRINT}_\mathrm{CIPHER}\), experiments show that we can recover the entire 80-bit secret key with \(2^{37.5}\) data complexity and \(2^{41.5}\) time complexity. To the best of our knowledge, our attack is the best known differential attacks on PRESENT and \(\mathrm{PRINT}_\mathrm{CIPHER}\) in practice.

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Acknowledgments

I wish to thank the anonymous reviewers for very useful comments that help to improve the paper. This work was supported by National Natural Science Foundation of China (Grant No. 61272488).

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Authors and Affiliations

  1. Zhengzhou Information Science and Technology Institute, 450000 , Zhengzhou, China

    Guo-Qiang Liu & Chen-Hui Jin

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  1. Guo-Qiang Liu
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  2. Chen-Hui Jin
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Correspondence to Guo-Qiang Liu.

Additional information

Communicated by L. R. Knudsen.

Appendices

Appendices

Table 12 The top 32 values of \(LL\tilde{R}_{D_{\{ x,y\} }, D_1}\) in the sorted list in our data collection and in [10, 11]
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Fig. 1
figure 1

The candidate slender-set of our attack and Borghoff’s attack in data collection with \(2^{33}\) data complexity to 16 round Maya

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Fig. 2
figure 2

The candidate slender-set of our attack and \(\chi ^2 \) statistic method in data collection with \(2^{33}\) data complexity to 16 round Maya

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Table 13 The top 32 order of \(e_k\) for each \(0 \le k \le 15\) to PRESENT-80 with round key being \((0111)_2\)
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Table 14 The order of \(e_k \) for each \(k\) to \(\mathrm{PRINT}_\mathrm{CIPHER}\)-48 with round key being \((011)_2\)
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Liu, GQ., Jin, CH. Differential cryptanalysis of PRESENT-like cipher. Des. Codes Cryptogr. 76, 385–408 (2015). https://doi.org/10.1007/s10623-014-9965-1

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