Abstract
In CRYPTO 2019, Gohr shows that well-trained neural networks can perform cryptanalytic distinguishing tasks superior to traditional differential distinguishers. Moreover, applying an unorthodox key guessing strategy, an 11-round key-recovery attack on a modern block cipher Speck32/64 improves upon the published state-of-the-art result. This calls into the next questions. To what extent is the advantage of machine learning (ML) over traditional methods, and whether the advantage generally exists in the cryptanalysis of modern ciphers? To answer the first question, we devised ML-based key-recovery attacks on more extended round-reduced Speck32/64. We achieved an improved 12-round and the first practical 13-round attacks. The essential for the new results is enhancing a classical component in the ML-based attacks, that is, the neutral bits. To answer the second question, we produced various neural distinguishers on round-reduced Simon32/64 and provided comparisons with their pure differential-based counterparts.
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Notes
- 1.
Speck can be represented as a composition of two Feistel maps [6].
- 2.
For Speck, there is no whitening key and the first subkey is XORed after the first non-linear operation, which makes the first round free in differential attack (see the top of Fig. 3 in [5]).
- 3.
In these considered variables, \(({x_1}, {y_1}) = (\tilde{x}_1\oplus k_0, \tilde{y}_1\oplus k_0)\) is the real input to the \(\mathcal{C}\mathcal{D}\) (see Fig. 3 in [5]), where \((\tilde{x}_1, \tilde{y}_1)\) is the chosen data in the key-recovery attack (since, in the key-recovery attack, the \(\mathcal{C}\mathcal{D}\) will be freely extended one round backward).
- 4.
Since the first two 3-round \(\mathcal{C}\mathcal{D}\)s are used as paired differentials, the key bit \(k_0[5] \oplus k_0[14]\) does not need to be guessed. Besides, since the CSNBS [6, 11, 12, 18] in Table 4 is not used in the attack, the key bit \(k_0[2] \oplus k_0[11]\) does not need to be guessed. In total only 5 bits of \(k_0\) are guessed.
- 5.
Tesla V100-SXM2-32GB, computeCapability: 7.0; coreClock: 1.53 GHz; coreCount: 80; deviceMemorySize: 31.72 GB; deviceMemoryBandwidth: 836.37 GB/s).
- 6.
Under the assumption that one second equals the time of \(2^{28}\) executions of Speck32/64 on a CPU, and \(r = \log _{2}(cpu/gpu)\), where cpu is the CPU time and gpu is the GPU time running an attack. In our computing systems, \(r=2.4\).
- 7.
Equipped with a 32-core Intel Cascade-Lake Xeon(R) Platinum 9221 2.30 GHz, and with 384 GB RAM, on CentOS 7.6.
- 8.
Some \({v_2}_{\textrm{max}}\)’s corresponding to success cases are lower than cutoff \(c_2\); that is due to the final improvement.
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Acknowledgments
The authors would like to thank anonymous reviewers for their insightful and helpful comments which helped us improve the manuscript significantly. This research is partially supported by Nanyang Technological University in Singapore under Start-up Grant 04INS000397C230, and Ministry of Education in Singapore under Grants RG91/20 and MOE2019-T2-1-060; Zhenzhen Bao was supported by the Gopalakrishnan – NTU Presidential Postdoctoral Fellowship 2020; the Tsinghua University in China under Start-up Grant 533344001; the National Key R &D Program of China (Grant No. 2018YFA0704701), the Major Program of Guangdong Basic and Applied Research (Grant No. 2019B030302008), the Shandong Province Key R &D Project (Nos. 2020ZLYS09 and 2019JZZY010133). Meicheng Liu was supported by the National Natural Science Foundation of China (Grant Nos. 62122085 and 12231015), and the Youth Innovation Promotion Association of Chinese Academy of Sciences.
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Bao, Z., Guo, J., Liu, M., Ma, L., Tu, Y. (2022). Enhancing Differential-Neural Cryptanalysis. In: Agrawal, S., Lin, D. (eds) Advances in Cryptology – ASIACRYPT 2022. ASIACRYPT 2022. Lecture Notes in Computer Science, vol 13791. Springer, Cham. https://doi.org/10.1007/978-3-031-22963-3_11
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