Abstract
Grover’s search algorithm accelerates the key search on the symmetric key cipher and the pre-image attack on the hash function. To perform Grover’s search algorithm, the target algorithm should be implemented in a quantum circuit. For this reason, we propose an optimal SM3 hash function (Chinese standard) in a quantum circuit. We focused on minimizing the use of qubits and reducing the use of quantum gates. To do this, the on-the-fly approach is utilized for message expansion and compression functions. In particular, the previous value is restored and used without allocating new qubits in the permutation operation. Finally, we estimate the quantum resources required for the quantum pre-image attack based on the proposed SM3 hash function implementation in the quantum circuit.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comput. 26, 1484–1509 (1997)
Grover, L.K.: A fast quantum mechanical algorithm for database search. In: Proceedings of the Twenty-Eighth Annual ACM Symposium on Theory of Computing, pp. 212–219 (1996)
Grassl, M., Langenberg, B., Roetteler, M., Steinwandt, R.: Applying Grover’s algorithm to AES: quantum resource estimates. In: Takagi, T. (ed.) PQCrypto 2016. LNCS, vol. 9606, pp. 29–43. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-29360-8_3
Langenberg, B., Pham, H., Steinwandt, R.: Reducing the cost of implementing AES as a quantum circuit. Techical report, Cryptology ePrint Archive, Report 2019/854 (2019)
Jaques, S., Naehrig, M., Roetteler, M., Virdia, F.: Implementing Grover oracles for quantum key search on AES and LowMC. In: Canteaut, A., Ishai, Y. (eds.) EUROCRYPT 2020. LNCS, vol. 12106, pp. 280–310. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-45724-2_10
Anand, R., Maitra, A., Mukhopadhyay, S.: Grover on SIMON. Quant. Inf. Process. 19(9), 1–17 (2020)
Jang, K., Choi, S., Kwon, H., Seo, H.: Grover on SPECK: quantum resource estimates. Cryptology ePrint Archive, Report 2020/640 (2020). https://eprint.iacr.org/2020/640
Jang, K., Kim, H., Eum, S., Seo, H.: Grover on GIFT. Cryptology ePrint Archive, Report 2020/1405 (2020). https://eprint.iacr.org/2020/1405
Schlieper, L.: In-place implementation of quantum-Gimli. arXiv preprint arXiv:2007.06319 (2020)
Jang, K., Choi, S., Kwon, H., Kim, H., Park, J., Seo, H.: Grover on Korean block ciphers. Appl. Sci. 10(18), 6407 (2020)
Jang, K., Song, G., Kim, H., Kwon, H., Kim, H., Seo, H.: Efficient implementation of PRESENT and GIFT on quantum computers. Appl. Sci. 11(11), 4776 (2021)
Song, G., Jang, K., Kim, H., Lee, W.-K., Seo, H.: Grover on Caesar and Vigenère ciphers. IACR Cryptol. ePrint Arch. 2021, 554 (2021)
Jang, K., et al.: Grover on PIPO. Electronics 10(10), 1194 (2021)
Amy, M., Matteo, O.D., Gheorghiu, V., Mosca, M., Parent, A., Schanck, J.: Estimating the cost of generic quantum pre-image attacks on SHA-2 and SHA-3 (2016)
Gheorghiu, V., Mosca, M.: Benchmarking the quantum cryptanalysis of symmetric, public-key and hash-based cryptographic schemes (2019)
Steiger, D.S., Häner, T., Troyer, M.: ProjectQ: an open source software framework for quantum computing. Quantum 2, 49 (2018)
Acknowledgment
This work was partly supported by Institute for Information & communications Technology Planning & Evaluation (IITP) grant funded by the Korea government(MSIT) (<Q|Crypton>, No.2019-0-00033, Study on Quantum Security Evaluation of Cryptography based on Computational Quantum Complexity, 40%) and this work was partly supported by Institute for Information & communications Technology Promotion(IITP) grant funded by the Korea government(MSIT) (No.2018-0-00264, Research on Blockchain Security Technology for IoT Services, 40%). Zhi Hu was partially supported by the National Natural Science Foundation of China (61972420, 61602526) and the Natural Science Foundation of Hunan Province (2020JJ3050, 2019JJ50827).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Song, G., Jang, K., Kim, H., Lee, WK., Hu, Z., Seo, H. (2022). Grover on SM3. In: Park, J.H., Seo, SH. (eds) Information Security and Cryptology – ICISC 2021. ICISC 2021. Lecture Notes in Computer Science, vol 13218. Springer, Cham. https://doi.org/10.1007/978-3-031-08896-4_22
Download citation
DOI: https://doi.org/10.1007/978-3-031-08896-4_22
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-08895-7
Online ISBN: 978-3-031-08896-4
eBook Packages: Computer ScienceComputer Science (R0)