Abstract
In a differential cryptanalysis attack, the attacker tries to observe a block cipher’s behavior under an input difference: if the system’s resulting output differences show any non-random behavior, a differential distinguisher is obtained. While differential cryptanlysis has been known for several decades, Gohr was the first to propose in 2019 the use of machine learning (ML) to build a distinguisher.
In this paper, we present the first Partial Differential (PD) ML distinguisher, and demonstrate its effectiveness on cipher SPECK32/64. As a PD-ML-distinguisher is based on a selection of bits rather than all bits in a block, we also study if different selections of bits have different impact in the accuracy of the distinguisher, and we find that to be the case. More importantly, we also establish that certain bits have reliably higher effectiveness than others, through a series of independent experiments on different datasets, and we propose an algorithm for assigning an effectiveness score to each bit in the block. By selecting the highest scoring bits, we are able to train a partial ML-distinguisher over 8-bits that is almost as accurate as an equivalent ML-distinguisher over the entire 32 bits (68.8% against 72%), for six rounds of SPECK32/64. Furthermore, we demonstrate that our obtained machine can reduce the time complexity of the key-averaging algorithm for training a 7-round distinguisher by a factor of \(2^5\) at a cost of only 3% in the resulting machine’s accuracy. These results may therefore open the way to the application of (partial) ML-based distinguishers to ciphers whose block size has so far been considered too large.
This publication has emanated from research supported in part by a Grant from Science Foundation Ireland under Grant number 18/CRT/6222.
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Notes
- 1.
In symmetric key algorithms, the S-box (substitution-box) is a fundamental building block that is responsible for carrying out the substitution of bits.
- 2.
Given a plaintext block and a key, the substitution-permutation network (SPN) generates the ciphertext block through a series of rounds or layers of substitution boxes (S-boxes) and permutation boxes (P-boxes).
References
Bassham, L., Çalık, Ç., McKay, K., Turan, M.S.: Submission requirements and evaluation criteria for the lightweight cryptography standardization process. US National Institute of Standards and Technology (2018)
Daemen, J., Rijmen, V.: AES proposal: Rijndael (1999)
Biham, E., Shamir, A.: Differential cryptanalysis of the full 16-round DES. In: Brickell, E.F. (ed.) CRYPTO 1992. LNCS, vol. 740, pp. 487–496. Springer, Heidelberg (1993). https://doi.org/10.1007/3-540-48071-4_34
Matsui, M.: Linear cryptanalysis method for DES cipher. In: Helleseth, T. (ed.) EUROCRYPT 1993. LNCS, vol. 765, pp. 386–397. Springer, Heidelberg (1994). https://doi.org/10.1007/3-540-48285-7_33
Fu, K., Wang, M., Guo, Y., Sun, S., Hu, L.: MILP-based automatic search algorithms for differential and linear trails for speck. In: Peyrin, T. (ed.) FSE 2016. LNCS, vol. 9783, pp. 268–288. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-52993-5_14
Mironov, I., Zhang, L.: Applications of SAT solvers to cryptanalysis of hash functions. In: Biere, A., Gomes, C.P. (eds.) SAT 2006. LNCS, vol. 4121, pp. 102–115. Springer, Heidelberg (2006). https://doi.org/10.1007/11814948_13
Gurobi Optimization, L.: Gurobi optimizer reference manual (2021). https://www.gurobi.com
Schneier, B.: Applied Cryptography: Protocols, Algorithms, and Source Code in C, 20th edn. Wiley, Hoboken (2015)
Abadi, M., Andersen, D.G.: Learning to protect communications with adversarial neural cryptography. arXiv preprint arXiv:1610.06918 (2016)
Gohr, A.: Improving attacks on round-reduced SPECK32/64 using deep learning. In: Boldyreva, A., Micciancio, D. (eds.) CRYPTO 2019. LNCS, vol. 11693, pp. 150–179. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-26951-7_6
Yadav, T., Kumar, M.: Differential-ML distinguisher: machine learning based generic extension for differential cryptanalysis. In: Longa, P., Ràfols, C. (eds.) LATINCRYPT 2021. LNCS, vol. 12912, pp. 191–212. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-88238-9_10
Baksi, A., Breier, J., Chen, Y., Dong, X.: Machine learning assisted differential distinguishers for lightweight ciphers. In: 2021 Design, Automation & Test in Europe Conference & Exhibition (DATE), pp. 176–181. IEEE (2021)
Hou, B., Li, Y., Zhao, H., Wu, B.: Linear attack on round-reduced DES using deep learning. In: Chen, L., Li, N., Liang, K., Schneider, S. (eds.) ESORICS 2020. LNCS, vol. 12309, pp. 131–145. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-59013-0_7
Zahednejad, B., Li, J.: An improved integral distinguisher scheme based on deep learning. EasyChair, Technical report (2020)
Liu, G., Lu, J., Li, H., Tang, P., Qiu, W.: Preimage attacks against lightweight scheme Xoodyak based on deep learning. In: Arai, K. (ed.) FICC 2021. AISC, vol. 1364, pp. 637–648. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-73103-8_45
Benamira, A., Gerault, D., Peyrin, T., Tan, Q.Q.: A deeper look at machine learning-based cryptanalysis. IACR Cryptol. ePrint Arch 287, 2021 (2021)
Baksi, A., Breier, J., Dasu, V.A., Hou, X.: Machine learning attacks on speck. In: Security and Implementation of Lightweight Cryptography (SILC), pp. 1–6 (2021)
Beaulieu, R., Shors, D., Smith, J., Treatman-Clark, S., Weeks, B., Wingers, L.: The SIMON and SPECK lightweight block ciphers. In: Proceedings of the 52nd Annual Design Automation Conference, pp. 1–6 (2015)
Albrecht, M.R., Leander, G.: An all-in-one approach to differential cryptanalysis for small block ciphers. In: Knudsen, L.R., Wu, H. (eds.) SAC 2012. LNCS, vol. 7707, pp. 1–15. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-35999-6_1
Bellini, E., Rossi, M.: Performance comparison between deep learning-based and conventional cryptographic distinguishers. IACR Cryptol. ePrint Arch. 2020, 953 (2020). https://eprint.iacr.org/2020/953
Kingma, D.P., Ba, J.: Adam: a method for stochastic optimization. arXiv preprint arXiv:1412.6980 (2014)
Chollet, F., et al.: Keras (2015). https://github.com/fchollet/keras
Bisong, E.: Building Machine Learning and Deep Learning Models on Google Cloud Platform: A Comprehensive Guide for Beginners. Apress (2019)
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Ebrahimi, A., Regazzoni, F., Palmieri, P. (2023). Reducing the Cost of Machine Learning Differential Attacks Using Bit Selection and a Partial ML-Distinguisher. In: Jourdan, GV., Mounier, L., Adams, C., Sèdes, F., Garcia-Alfaro, J. (eds) Foundations and Practice of Security. FPS 2022. Lecture Notes in Computer Science, vol 13877. Springer, Cham. https://doi.org/10.1007/978-3-031-30122-3_8
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