Abstract
FUTURE is a recently proposed, lightweight block cipher. It has an AES-like, SP-based, 10-round encryption function, where, unlike most other lightweight constructions, the diffusion layer is based on an MDS matrix. Despite its relative complexity, it has a remarkable hardware performance due to careful design decisions.
In this paper, we conducted a MILP-based analysis of the cipher, where we incorporated exact probabilities rather than just the number of active S-boxes into the model. Through the MILP analysis, we were able to find differential and linear distinguishers for up to 5 rounds of FUTURE, extending the known distinguishers of the cipher by one round.
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References
Abdelkhalek, A., Sasaki, Y., Todo, Y., Tolba, M., Youssef, A.M.: MILP modeling for (large) S-boxes to optimize probability of differential characteristics. IACR Trans. Symmetric Cryptol. 2017(4), 99–129 (2017)
Boura, C., Coggia, D.: Efficient MILP modelings for Sboxes and linear layers of SPN ciphers. IACR Trans. Symmetric Cryptol. 2020(3), 327–361 (2020)
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
Funabiki, Y., Todo, Y., Isobe, T., Morii, M.: Several MILP-aided attacks against SNOW 2.0. In: Camenisch, J., Papadimitratos, P. (eds.) CANS 2018. LNCS, vol. 11124, pp. 394–413. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-00434-7_20
Gupta, K.C., Pandey, S.K., Samanta, S.: FUTURE: a lightweight block cipher using an optimal diffusion matrix. In: Batina, L., Daemen, J. (eds.) AFRICACRYPT 2022. LNCS, vol. 13503, pp. 28–52. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-17433-9_2
Gurobi Optimization Inc.: Gurobi optimizer reference manual (2018). http://www.gurobi.com
Ilter, M.B., Selçuk, A.A.: A new MILP model for matrix multiplications with applications to KLEIN and PRINCE. In: SECRYPT, pp. 420–427 (2021)
Mouha, N., Wang, Q., Gu, D., Preneel, B.: Differential and linear cryptanalysis using mixed-integer linear programming. In: Wu, C.-K., Yung, M., Lin, D. (eds.) Inscrypt 2011. LNCS, vol. 7537, pp. 57–76. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-34704-7_5
Sasaki, Yu., Todo, Y.: New algorithm for modeling S-box in MILP based differential and division trail search. In: Farshim, P., Simion, E. (eds.) SecITC 2017. LNCS, vol. 10543, pp. 150–165. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-69284-5_11
Sun, L., Wang, W., Liu, R., Wang, M.: MILP-aided bit-based division property for ARX-based block cipher. Cryptology ePrint Archive (2016)
Sun, L., Wang, W., Wang, M.Q.: MILP-aided bit-based division property for primitives with non-bit-permutation linear layers. IET Inf. Secur. 14(1), 12–20 (2020)
Sun, S., Hu, L., Song, L., Xie, Y., Wang, P.: Automatic security evaluation of block ciphers with S-bP structures against related-key differential attacks. In: Lin, D., Xu, S., Yung, M. (eds.) Inscrypt 2013. LNCS, vol. 8567, pp. 39–51. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-12087-4_3
Sun, S., et al.: Towards finding the best characteristics of some bit-oriented block ciphers and automatic enumeration of (related-key) differential and linear characteristics with predefined properties. IACR Cryptology ePrint Archive 2014/747 (2014)
Sun, S., Hu, L., Wang, P., Qiao, K., Ma, X., Song, L.: Automatic security evaluation and (related-key) differential characteristic search: application to SIMON, PRESENT, LBlock, DES(L) and other bit-oriented block ciphers. In: Sarkar, P., Iwata, T. (eds.) ASIACRYPT 2014. LNCS, vol. 8873, pp. 158–178. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-662-45611-8_9
The Sage Developers: SageMath, the Sage Mathematics Software System (Version 9.2) (2020). https://www.sagemath.org
Yin, J., et al.: Improved cryptanalysis of an ISO standard lightweight block cipher with refined MILP modelling. In: Chen, X., Lin, D., Yung, M. (eds.) Inscrypt 2017. LNCS, vol. 10726, pp. 404–426. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-75160-3_24
Zhu, B., Dong, X., Yu, H.: MILP-based differential attack on round-reduced GIFT. In: Matsui, M. (ed.) CT-RSA 2019. LNCS, vol. 11405, pp. 372–390. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-12612-4_19
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Appendix
Appendix
We compare the solution times of differential and linear characteristic of FUTURE modeled with the n-XOR method and the method proposed by Ilter and Selcuk [7] in Table 7 and Table 8.
As shown in Table 7 and in Table 8, the proposed n-XOR method uses fewer constraints to model xor operation, leading to shortening solution time.
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İlter, M.B., Selçuk, A.A. (2023). MILP-Aided Cryptanalysis of the FUTURE Block Cipher. In: Bella, G., Doinea, M., Janicke, H. (eds) Innovative Security Solutions for Information Technology and Communications. SecITC 2022. Lecture Notes in Computer Science, vol 13809. Springer, Cham. https://doi.org/10.1007/978-3-031-32636-3_9
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