Abstract
Grover’s algorithm provides a quantum attack against block ciphers by searching for a k-bit key using \(O(\sqrt{2^k})\) calls to the cipher, when given a small number of plaintext-ciphertext pairs. Recent works by Grassl et al. in PQCrypto’16 and Almazrooie et al. in QIP’18 have estimated the cost of this attack against AES by analyzing the quantum circuits of the cipher.
We present a quantum reversible circuit of ARIA, a Korean standardized block cipher that is widely deployed in government-to-public services. Firstly, we design quantum circuits for the main components of ARIA, and then combine them to construct the complete circuit of ARIA. We implement Grover’s algorithm-based exhaustive key-search attack on ARIA. For all three variants of ARIA-{128, 192, 256}, we establish precise bounds for the number of qubits and the number of Clifford\(+T\) gates that are required to implement Grover’s algorithm.
We also estimate the G-cost as the total number of gates, and DW-cost as the product of circuit depth and width. To find the circuit depth of various circuits such as squaring, multiplier, and permutation layer, we implement them in an open-source quantum computing platform QISKIT developed by IBM.
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
Almazrooie, M., Samsudin, A., Abdullah, R., Mutter, K.N.: Quantum reversible circuit of AES-128. Quantum Inf. Process. 17(5), 1–30 (2018). https://doi.org/10.1007/s11128-018-1864-3
Amy, M., Maslov, D., Mosca, M., Roetteler, M.: A meet-in-the-middle algorithm for fast synthesis of depth-optimal quantum circuits. IEEE Trans. Comput.-Aided Design Integr. Circu. Syst. 32(6), 818-830 (2013)
Amy, M., Di Matteo, O., Gheorghiu, V., Mosca, M., Parent, A., Schanck, J.: Estimating the cost of generic quantum pre-image attacks on SHA-2 and SHA-3. In: Avanzi, R., Heys, H. (eds.) SAC 2016. LNCS, vol. 10532, pp. 317–337. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-69453-5_18
Banegas, G., Bernstein, D.J.: Low-communication parallel quantum multi-target preimage search. In: Adams, C., Camenisch, J. (eds.) SAC 2017. LNCS, vol. 10719, pp. 325–335. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-72565-9_16
Bonnetain, X., Naya-Plasencia, M., Schrottenloher, A.: Quantum security analysis of AES. IACR Trans. Symmetric Cryptol. 2, 2019 (2019)
Boyar, J., Peralta, R.: A small depth-16 circuit for the AES S-Box. In: Gritzalis, D., Furnell, S., Theoharidou, M. (eds.) SEC 2012. IAICT, vol. 376, pp. 287–298. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-30436-1_24
Boyer, M., Brassard, G., Hoeyer, P., Tapp, A.: Tight bounds on quantum searching (1996). arXiv:quant-ph/9605034
Cheung, D., Maslov, D., Mathew, J., Pradhan, D.K.: On the design and optimization of a quantum polynomial-time attack on elliptic curve cryptography. In: Kawano, Y., Mosca, M. (eds.) TQC 2008. LNCS, vol. 5106, pp. 96–104. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-89304-2_9
Abraham, H., et al.: Qiskit: An open-source framework for quantum computing (2019. https://qiskit.org
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
Grover, L.K.: A fast quantum mechanical algorithm for database search. In: ACM Symposium on the Theory of Computing (1996)
Guajardo, J., Paar, C.: Itoh-Tsujii inversion in standard basis and its application in cryptography and codes. Design Codes Cryptogr. 25(2), 207–216 (2002). https://doi.org/10.1023/A:1013860532636
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
Jaques, S., Schanck, J.M.: Quantum cryptanalysis in the RAM Model: claw-finding attacks on SIKE. In: Boldyreva, A., Micciancio, D. (eds.) CRYPTO 2019. LNCS, vol. 11692, pp. 32–61. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-26948-7_2
Kim, P., Han, D., Jeong, K.C.: Time–space complexity of quantum search algorithms in symmetric cryptanalysis: applying to AES and SHA-2. Quantum Inf. Process. 17(12), 1–39 (2018). https://doi.org/10.1007/s11128-018-2107-3
Kwon, D., et al.: New block cipher ARIA. In: Information Security and Cryptology - ICISC (2003)
Langenberg, B., Pham, H., Steinwandt, R.: Reducing the cost of implementing the advanced encryption standard as a quantum circuit. IEEE Trans. Quantum Eng. 1, 1–12 (2020)
Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. 10th, Anniversary edn. Cambridge Univ, Press (2011)
NIST. Submission requirements and evaluation criteria for the post-quantum cryptography standardization process (2017). https://csrc.nist.gov/CSRC/media/Projects/Post-Quantum-Cryptography/documents/call-for-proposals-final-dec-2016.pdf/
Ramos-Calderer, S., Bellini, E., Latorre, J.I., Manzano, M., Mateu, V.: Quantum search for scaled hash function preimages. IACR Cryptol. ePrint Arch. 1062 (2020). https://eprint.iacr.org/2020/1062
Selinger, P.: Quantum circuits of \(T\)-depth one. Phys. Rev. A 87, 042302 (2013)
Shor, P.W.: Polynomial time algorithms for discrete logarithms and factoring on a quantum computer. In: Adleman, L.M., Huang, M.-D. (eds.) ANTS 1994. LNCS, vol. 877, pp. 289–289. Springer, Heidelberg (1994). https://doi.org/10.1007/3-540-58691-1_68
Wiebe, N., Roetteler, M.: Quantum arithmetic and numerical analysis using repeat-until-success circuits. Quantum Inf. Comput. 16(1&2) (2016)
William, S., et al.: Sagemath, the Sage Mathematics Software System Version 8.1 (2017). https://www.sagemath.org
Acknowledgment
We would like to thank the anonymous reviewers of SPACE 2020 for their insightful comments and suggestions, which has significantly improved the presentation and technical quality of this work. The second author would also like to thank MATRICS grant 2019/1514 by the Science and Engineering Research Board (SERB), Dept. of Science and Technology, Govt. of India for supporting the research carried out in this work. We would also like to thank Dr. Kai-Min Chung for initial discussions on quantum computing.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Chauhan, A.K., Sanadhya, S.K. (2020). Quantum Resource Estimates of Grover’s Key Search on ARIA. In: Batina, L., Picek, S., Mondal, M. (eds) Security, Privacy, and Applied Cryptography Engineering. SPACE 2020. Lecture Notes in Computer Science(), vol 12586. Springer, Cham. https://doi.org/10.1007/978-3-030-66626-2_13
Download citation
DOI: https://doi.org/10.1007/978-3-030-66626-2_13
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-66625-5
Online ISBN: 978-3-030-66626-2
eBook Packages: Computer ScienceComputer Science (R0)