Abstract
The search for differential characteristics on block ciphers is a difficult combinatorial problem. In this paper, we investigate the performances of an AI-originated technique, Single Player Monte-Carlo Tree Search (SP-MCTS), in finding good differential characteristics on ARX ciphers, with an application to the block cipher SPECK. In order to make this approach competitive, we include several heuristics, such as the combination of forward and backward searches, and achieve significantly faster results than state-of-the-art works that are not based on automatic solvers. We reach 9, 11, 13, 13 and 15 rounds for SPECK32, SPECK48, SPECK64, SPECK96 and SPECK128 respectively. In order to build our algorithm, we revisit Lipmaa and Moriai’s algorithm for listing all optimal differential transitions through modular addition, and propose a variant to enumerate all transitions with probability close (up to a fixed threshold) to the optimal, while fixing a minor bug in the original algorithm.
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References
Abramson, B.D.: The expected-outcome model of two-player games. Ph.D. thesis, Columbia University, USA (1987). AAI8827528
Biryukov, A., Roy, A., Velichkov, V.: Differential analysis of block ciphers SIMON and SPECK. In: Cid, C., Rechberger, C. (eds.) FSE 2014. LNCS, vol. 8540, pp. 546–570. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46706-0_28
Biham, E., Shamir, A.: Differential cryptanalysis of des-like cryptosystems. J. Cryptol. 4, 3–72 (1991)
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, DAC 2015. Association for Computing Machinery, New York (2015)
Biryukov, A., Velichkov, V.: Automatic search for differential trails in ARX ciphers (extended version). IACR Cryptology ePrint Archive 2013:853 (2013)
Biryukov, A., Velichkov, V.: Automatic search for differential trails in ARX ciphers. In: Benaloh, J. (ed.) CT-RSA 2014. LNCS, vol. 8366, pp. 227–250. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-04852-9_12
Biryukov, A., Velichkov, V., Le Corre, Y.: Automatic search for the best trails in ARX: application to block cipher Speck. In: Peyrin, T. (ed.) FSE 2016. LNCS, vol. 9783, pp. 289–310. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-52993-5_15
Burmeister, J., Wiles, J.: The challenge of go as a domain for AI research: a comparison between go and chess. In: Proceedings of Third Australian and New Zealand Conference on Intelligent Information Systems. ANZIIS-95, pp. 181–186 (1995)
Chaslot, G., Bakkes, S., Szitai, I., Spronck, P.: Monte-Carlo tree search: a new framework for game AI1. In: Belgian/Netherlands Artificial Intelligence Conference, pp. 389–390 (2008)
Coulom, R.: Efficient selectivity and backup operators in Monte-Carlo tree search. In: van den Herik, H.J., Ciancarini, P., Donkers, H.H.L.M.J. (eds.) CG 2006. LNCS, vol. 4630, pp. 72–83. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-75538-8_7
Dinur, I.: Improved differential cryptanalysis of round-reduced speck. In: Joux, A., Youssef, A. (eds.) SAC 2014. LNCS, vol. 8781, pp. 147–164. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-13051-4_9
Dwivedi, A.D., Morawiecki, P., Srivastava, G.: Differential cryptanalysis of round-reduced speck suitable for internet of things devices. IEEE Access 7, 16476–16486 (2019)
Ashutosh Dhar Dwivedi and Gautam Srivastava: Differential cryptanalysis of round-reduced lea. IEEE Access 6, 79105–79113 (2018)
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
Hart, P.E., Nilsson, N.J., Raphael, B.: A formal basis for the heuristic determination of minimum cost paths. IEEE Trans. Syst. Sci. Cybern. 4(2), 100–107 (1968)
Helmbold, D., Parker-Wood, A.: All-moves-as-first heuristics in Monte-Carlo go. In: Proceedings of the 2009 International Conference on Artificial Intelligence, ICAI 2009, vol. 2, pp. 605–610, January 2009
Huang, M., Wang, L.: Automatic tool for searching for differential characteristics in ARX ciphers and applications. In: Hao, F., Ruj, S., Sen Gupta, S. (eds.) INDOCRYPT 2019. LNCS, vol. 11898, pp. 115–138. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-35423-7_6
Korf, R.E.: Depth-first iterative-deepening: an optimal admissible tree search. Artif. Intell. 27(1), 97–109 (1985)
Kozen, D.C.: Depth-first and breadth-first search. In: Kozen, D.C. (ed.) The Design and Analysis of Algorithms. Texts and Monographs in Computer Science, pp. 19–24. Springer, New York (1992). https://doi.org/10.1007/978-1-4612-4400-4_4
Kocsis, L., Szepesvári, C.: Bandit based Monte-Carlo planning. In: Fürnkranz, J., Scheffer, T., Spiliopoulou, M. (eds.) ECML 2006. LNCS (LNAI), vol. 4212, pp. 282–293. Springer, Heidelberg (2006). https://doi.org/10.1007/11871842_29
Liu, Z., Li, Y., Jiao, L., Wang, M.: A new method for searching optimal differential and linear trails in ARX ciphers. IEEE Trans. Inf. Theory 67(2), 1054–1068 (2021)
Lipmaa, H., Moriai, S.: Efficient algorithms for computing differential properties of addition. In: Matsui, M. (ed.) FSE 2001. LNCS, vol. 2355, pp. 336–350. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-45473-X_28
Lai, X., Massey, J.L., Murphy, S.: Markov ciphers and differential cryptanalysis. In: Davies, D.W. (ed.) EUROCRYPT 1991. LNCS, vol. 547, pp. 17–38. Springer, Heidelberg (1991). https://doi.org/10.1007/3-540-46416-6_2
Matsui, M.: On correlation between the order of S-boxes and the strength of DES. In: De Santis, A. (ed.) EUROCRYPT 1994. LNCS, vol. 950, pp. 366–375. Springer, Heidelberg (1995). https://doi.org/10.1007/BFb0053451
Song, L., Huang, Z., Yang, Q.: Automatic differential analysis of ARX block ciphers with application to SPECK and LEA. In: Liu, J.K., Steinfeld, R. (eds.) ACISP 2016. LNCS, vol. 9723, pp. 379–394. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-40367-0_24
Schadd, M.P.D., Winands, M.H.M., van den Herik, H.J., Chaslot, G.M.J.-B., Uiterwijk, J.W.H.M.: Single-player Monte-Carlo tree search. In: van den Herik, H.J., Xu, X., Ma, Z., Winands, M.H.M. (eds.) CG 2008. LNCS, vol. 5131, pp. 1–12. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-87608-3_1
Sun, L., Wang, W., Wang, M.: Accelerating the search of differential and linear characteristics with the sat method. IACR Trans. Symmetric Cryptol. 269–315 (2021)
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Appendices
Appendix a All Optimal Characteristics on SPECK32
See Table 2.
Appendix B Best Characteristics Found with Our Method
See Table 3.
Appendix C Pseudocode for the Search Algorithm
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Bellini, E., Gerault, D., Protopapa, M., Rossi, M. (2022). Monte Carlo Tree Search for Automatic Differential Characteristics Search: Application to SPECK. In: Isobe, T., Sarkar, S. (eds) Progress in Cryptology – INDOCRYPT 2022. INDOCRYPT 2022. Lecture Notes in Computer Science, vol 13774. Springer, Cham. https://doi.org/10.1007/978-3-031-22912-1_17
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