Abstract
SM4 is a block cipher algorithm among Chinese commercial cryptographic algorithms, which is advanced in terms of efficiency and theoretical security and has become national and international standards successively. However, existing literature shows that SM4 was not designed with an emphasis on key storage, which means that in today’s world where a single trusted hardware device with the built-in key faces challenges such as vulnerability, high cost, and unreliability, the usability of SM4 may be limited. Therefore, this paper proposes an implementation scheme for SM4 based on secure multi-party computation (MPC) technology. The scheme involves dispensing the key among multiple users’ devices in a distributed manner, and when using the SM4 algorithm for encryption, multiple users perform joint computation without opening the full key. Specifically, this paper employs the MP-SPDZ framework, which satisfies security requirements in the presence of a dishonest majority of active adversaries. In view of the fact that this framework can only perform basic linear operations such as addition and multiplication, this paper focuses on the algebraic analysis of Sbox, which is the only non-linear component in SM4, and reconstructs it using the bit decomposition method. Furthermore, this paper demonstrates the conversion between the SM4-Sbox field \(GF(2^8)\) and the SPDZ parameter field \(GF(2^{40})\) through the isomorphic mapping, making it possible to perform joint calculations throughout the entire SM4 algorithm. Complexity analysis shows that this scheme has advantages in terms of data storage and communication volume, reaching a level of usability.
Supported by the National Natural Science Foundation of China under Grant No. 61907042 and Beijing Natural Science Foundation under Grant No.4194090.
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References
Aaraj, N., Raghunathan, A., Jha, N.K.: Analysis and design of a hardware/software trusted platform module for embedded systems. ACM Trans. Embedded Comput. Syst. (TECS) 8(1), 1–31 (2009)
Ben-Or, M., Goldwasser, S., Wigderson, A.: Completeness theorems for non-cryptographic fault-tolerant distributed computation. In: Providing Sound Foundations for Cryptography: On the Work of Shafi Goldwasser and Silvio Micali, pp. 351–371 (2019)
Bogdanov, D., Laur, S., Willemson, J.: Sharemind: a framework for fast privacy-preserving computations. In: Jajodia, S., Lopez, J. (eds.) ESORICS 2008. LNCS, vol. 5283, pp. 192–206. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-88313-5_13
Chaum, D., Crépeau, C., Damgard, I.: Multiparty unconditionally secure protocols. In: Proceedings of the Twentieth Annual ACM Symposium on Theory of Computing, pp. 11–19 (1988)
Chen, J.: A note on the impossible differential attacks on block cipher SM4. In: 2016 12th International Conference on Computational Intelligence and Security (CIS), pp. 551–554. IEEE (2016)
Cramer, R., Damgård, I., Escudero, D., Scholl, P., Xing, C.: SPD\(\mathbb{Z}_{2^k}\): efficient MPC mod \(2^k\) for dishonest majority. In: Shacham, H., Boldyreva, A. (eds.) CRYPTO 2018. LNCS, vol. 10992, pp. 769–798. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-96881-0_26
Damgård, I., Keller, M., Larraia, E., Miles, C., Smart, N.P.: Implementing AES via an actively/covertly secure dishonest-majority MPC protocol. In: Visconti, I., De Prisco, R. (eds.) SCN 2012. LNCS, vol. 7485, pp. 241–263. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-32928-9_14
Damgård, I., Keller, M., Larraia, E., Pastro, V., Scholl, P., Smart, N.P.: Practical covertly secure MPC for dishonest majority – or: breaking the SPDZ limits. In: Crampton, J., Jajodia, S., Mayes, K. (eds.) ESORICS 2013. LNCS, vol. 8134, pp. 1–18. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-40203-6_1
Damgård, I., Pastro, V., Smart, N., Zakarias, S.: Multiparty computation from somewhat homomorphic encryption. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 643–662. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-32009-5_38
Durak, F.B., Guajardo, J.: Improving the efficiency of AES protocols in multi-party computation. In: Borisov, N., Diaz, C. (eds.) FC 2021. LNCS, vol. 12674, pp. 229–248. Springer, Heidelberg (2021). https://doi.org/10.1007/978-3-662-64322-8_11
Escudero, D., Xing, C., Yuan, C.: More efficient dishonest majority secure computation over \(Z_{2^k}\) via Galois rings. In: Advances in Cryptology-CRYPTO 2022: 42nd Annual International Cryptology Conference, CRYPTO 2022, Santa Barbara, CA, USA, August 15–18, 2022, Proceedings, Part I, pp. 383–412. Springer (2022). https://doi.org/10.1007/978-3-031-15802-5_14
Goldreich, O., Micali, S., Wigderson, A.: How to play any mental game, or a completeness theorem for protocols with honest majority. In: Providing Sound Foundations for Cryptography: On the Work of Shafi Goldwasser and Silvio Micali, pp. 307–328 (2019)
Keller, M.: Mp-spdz: A versatile framework for multi-party computation. In: Proceedings of the 2020 ACM SIGSAC Conference on Computer and Communications Security, pp. 1575–1590 (2020)
Keller, M., Orsini, E., Rotaru, D., Scholl, P., Soria-Vazquez, E., Vivek, S.: Faster secure multi-party computation of AES and DES using lookup tables. In: Gollmann, D., Miyaji, A., Kikuchi, H. (eds.) ACNS 2017. LNCS, vol. 10355, pp. 229–249. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-61204-1_12
Keller, M., Pastro, V., Rotaru, D.: Overdrive: making SPDZ great again. In: Nielsen, J.B., Rijmen, V. (eds.) EUROCRYPT 2018. LNCS, vol. 10822, pp. 158–189. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-78372-7_6
Kocher, P., et al.: Spectre attacks: exploiting speculative execution. Commun. ACM 63(7), 93–101 (2020)
Lidl, R., Niederreiter, H.: Finite fields. No. 20, Cambridge University Press (1997)
Liu, F., et al.: Analysis of the SMS4 block cipher. In: Pieprzyk, J., Ghodosi, H., Dawson, E. (eds.) ACISP 2007. LNCS, vol. 4586, pp. 158–170. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-73458-1_13
Liu, Y., Liang, H., Wang, W., Wang, M.: New linear cryptanalysis of Chinese commercial block cipher standard SM4. Security and Communication Networks 2017 (2017)
Miao, X., Guo, C., Wang, M., Wang, W.: How fast can SM4 be in software? In: Deng, Y., Yung, M. (eds.) Information Security and Cryptology, pp. 3–22. Springer Nature Switzerland, Cham (2023). https://doi.org/10.1007/978-3-031-26553-2_1
Micali, S., Goldreich, O., Wigderson, A.: How to play any mental game. In: Proceedings of the Nineteenth ACM Symposium on Theory of Computing, STOC. pp. 218–229. ACM New York, NY, USA (1987)
Songhori, E.M., Hussain, S.U., Sadeghi, A.R., Schneider, T., Koushanfar, F.: TinyGarble: highly compressed and scalable sequential garbled circuits. In: 2015 IEEE Symposium on Security and Privacy, pp. 411–428. IEEE (2015)
of State Commercial Cipher Administration, O.: SMS4cipher for WLAN products (2006)
Tischer, M., et al.: Users really do plug in USB drives they find. In: 2016 IEEE Symposium on Security and Privacy (SP), pp. 306–319. IEEE (2016)
Wang, R., Guo, H., Lu, J., Liu, J.: Cryptanalysis of a white-box sm4 implementation based on collision attack. IET Inf. Secur. 16(1), 18–27 (2022)
Wilkins, R., Richardson, B.: UEFI secure boot in modern computer security solutions. In: UEFI forum, pp. 1–10 (2013)
Yao, A.C.: Protocols for secure computations. In: 23rd Annual Symposium on Foundations of Computer Science (SFCS 1982), pp. 160–164. IEEE (1982)
Zhang, J., Wu, W., Zheng, Y.: Security of SM4 against (Related-Key) differential cryptanalysis. In: Bao, F., Chen, L., Deng, R.H., Wang, G. (eds.) ISPEC 2016. LNCS, vol. 10060, pp. 65–78. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-49151-6_5
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This work is supported by the National Natural Science Foundation of China under Grant No. 61907042 and Beijing Natural Science Foundation under Grant No.4194090.
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Ma, X., Wang, M., Kang, Z. (2023). Distributed Implementation of SM4 Block Cipher Algorithm Based on SPDZ Secure Multi-party Computation Protocol. In: Yu, Z., et al. Data Science. ICPCSEE 2023. Communications in Computer and Information Science, vol 1879. Springer, Singapore. https://doi.org/10.1007/978-981-99-5968-6_20
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