Skip to main content
Springer Nature Link
Log in

Improved Quantum Analysis of SPECK and LowMC

  • Conference paper
  • First Online:
Progress in Cryptology – INDOCRYPT 2022 (INDOCRYPT 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13774))

Included in the following conference series:

  • 521 Accesses

Abstract

As the prevalence of quantum computing is growing in leaps and bounds over the past few years, there is an ever-growing need to analyze the symmetric-key ciphers against the upcoming threat. Indeed, we have seen a number of research works dedicated to this. Our work delves into this aspect of block ciphers, with respect to the SPECK family and LowMC family.

The SPECK family received two quantum analysis till date (Jang et al., Applied Sciences, 2020; Anand et al., Indocrypt, 2020). We revisit these two works, and present improved benchmarks SPECK (all 10 variants). Our implementations incur lower full depth compared to the previous works.

On the other hand, the quantum circuit of LowMC was explored earlier in Jaques et al.’s Eurocrypt 2020 paper. However, there is an already known bug in their paper, which we patch. On top of that, we present two versions of LowMC (on L1, L3 and L5 variants) in quantum, both of which incur significantly less full depth than the bug-fixed implementation.

Hyunji Kim and Hwajeong Seo were supported by the Institute for Information & Communications Technology Planning & Evaluation (IITP) grant funded by the Korean government (MSIT) (\(\langle {\text {Q}}|{\text {Crypton}}\), number 2019-0-00033, Study on Quantum Security Evaluation of Cryptography based on Computational Quantum Complexity); and Kyungbae Jang was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2022R1A6A3A13062701) of the Korean government. Anupam Chattopadhyay was partly supported by the NRF Grant Award, number NRF2021-QEP2-02-P05 by the Singaporean government. Further, we thank Da Lin (Hubei University, Wuhan, PR China) for the kind support during preparation of the manuscript.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

Notes

  1. 1.

    However the reduction of full depth is less prominent (ranging from 10% to 12% depending on the variant of SPECK), still our implementation takes less quantum resource. See Table 4 for the benchmark.

  2. 2.

    Homepage: https://projectq.ch/. Code: https://github.com/ProjectQ-Framework/ProjectQ. Documentation: https://projectq.readthedocs.io/en/latest/.

  3. 3.

    https://github.com/starj1023/SPECK_LowMC_QC.

  4. 4.

    Apart from LowMC, Picnic also uses SHA-3 in some form.

  5. 5.

    As the exact specification is generated at random, it is suggested in [8] to call LowMC as a ‘meta-cipher’ (instead of a ‘cipher’).

  6. 6.

    Key Schedule in quantum (of LowMC) denotes the product of the matrix of the round and the input key, and the product is stored in qubits for the round key. The reverse operation (i.e., uncompute) of Key Schedule is defined as Key Schedule\(^\dagger \), and cleans the qubits for the round key.

  7. 7.

    https://github.com/microsoft/grover-blocks.

  8. 8.

    https://github.com/microsoft/grover-blocks/blob/master/numbers/lowmc.csv.

References

  1. Albrecht, M.R., Rechberger, C., Schneider, T., Tiessen, T., Zohner, M.: Ciphers for MPC and FHE. In: Oswald, E., Fischlin, M. (eds.) EUROCRYPT 2015. LNCS, vol. 9056, pp. 430–454. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46800-5_17

    Chapter  Google Scholar 

  2. Almazrooie, M., Samsudin, A., Abdullah, R., Mutter, K.N.: Quantum reversible circuit of AES-128. Quant. Inf. Process. 17(5), 1–30 (2018). https://doi.org/10.1007/s11128-018-1864-3

    Article  MathSciNet  MATH  Google Scholar 

  3. 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

    Chapter  Google Scholar 

  4. Amy, M., Maslov, D., Mosca, M., Roetteler, M., Roetteler, M.: A meet-in-the-middle algorithm for fast synthesis of depth-optimal quantum circuits. IEEE Trans. Comput. Aided Des. Integr. Circuits Syst. 32(6), 818–830 (2013). https://doi.org/10.1109/tcad.2013.2244643

  5. Anand, R., Maitra, A., Maitra, S., Mukherjee, C.S., Mukhopadhyay, S.: Quantum resource estimation for FSR based symmetric ciphers and related Grover’s attacks. In: Adhikari, A., Küsters, R., Preneel, B. (eds.) INDOCRYPT 2021. LNCS, vol. 13143, pp. 179–198. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-92518-5_9

    Chapter  Google Scholar 

  6. Anand, R., Maitra, A., Mukhopadhyay, S.: Evaluation of quantum cryptanalysis on SPECK. In: Bhargavan, K., Oswald, E., Prabhakaran, M. (eds.) INDOCRYPT 2020. LNCS, vol. 12578, pp. 395–413. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-65277-7_18

    Chapter  Google Scholar 

  7. Anand, R., Maitra, A., Mukhopadhyay, S.: Grover on \(SIMON\). Quant. Inf. Process. 19(9), 1–17 (2020). https://doi.org/10.1007/s11128-020-02844-w

    Article  MathSciNet  Google Scholar 

  8. Baksi, A., Bhattacharjee, A., Breier, J., Isobe, T., Nandi, M.: Big brother is watching you: a closer look at backdoor construction. Cryptology ePrint Archive, Paper 2022/953 (2022). https://eprint.iacr.org/2022/953

  9. Baksi, A., Jang, K., Song, G., Seo, H., Xiang, Z.: Quantum implementation and resource estimates for Rectangle and Knot. Quant. Inf. Process. 20(12), 1–24 (2021). https://doi.org/10.1007/s11128-021-03307-6

    Article  MathSciNet  MATH  Google Scholar 

  10. Banegas, G., Bernstein, D.J., Van Hoof, I., Lange, T.: Concrete quantum cryptanalysis of binary elliptic curves. Cryptology ePrint Archive (2020)

    Google Scholar 

  11. Bathe, B., Anand, R., Dutta, S.: Evaluation of Grover’s algorithm toward quantum cryptanalysis on ChaCha. Quant. Inf. Process. 20(12), 1–19 (2021). https://doi.org/10.1007/s11128-021-03322-7

    Article  MathSciNet  MATH  Google Scholar 

  12. Beaulieu, R., Shors, D., Smith, J., Treatman-Clark, S., Weeks, B., Wingers, L.: The SIMON and SPECK families of lightweight block ciphers. Cryptology ePrint Archive, Report 2013/404 (2013). https://eprint.iacr.org/2013/404

  13. Bijwe, S., Chauhan, A.K., Sanadhya, S.K.: Quantum search for lightweight block ciphers: gift, skinny, saturnin. Cryptology ePrint Archive, Paper 2020/1485 (2020). https://eprint.iacr.org/2020/1485

  14. Boyer, M., Brassard, G., Høyer, P., Tapp, A.: Tight bounds on quantum searching. Fortschritte der Physik 46(4–5), 493–505 (1998). https://doi.org/10.1002/(SICI)1521-3978(199806)46:4/5<493::AID-PROP493>3.0.CO;2-P

  15. Cuccaro, S., Draper, T., Kutin, S., Moulton, D.: A new quantum ripple-carry addition circuit. arXiv (2008). https://arxiv.org/pdf/quant-ph/0410184.pdf

  16. Gidney, C.: Factoring with n+2 clean qubits and n-1 dirty qubits. arXiv preprint arXiv:1706.07884 (2017)

  17. 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

    Chapter  MATH  Google Scholar 

  18. 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)

    Google Scholar 

  19. Häner, T., Jaques, S., Naehrig, M., Roetteler, M., Soeken, M.: Improved quantum circuits for elliptic curve discrete logarithms. In: Ding, J., Tillich, J.-P. (eds.) PQCrypto 2020. LNCS, vol. 12100, pp. 425–444. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-44223-1_23

    Chapter  MATH  Google Scholar 

  20. Häner, T., Roetteler, M., Svore, K.M.: Factoring using 2n+ 2 qubits with toffoli based modular multiplication. arXiv preprint arXiv:1611.07995 (2016)

  21. He, Y., Luo, M.X., Zhang, E., Wang, H.K., Wang, X.F.: Decompositions of n-qubit toffoli gates with linear circuit complexity. Int. J. Theor. Phys. 56(7), 2350–2361 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  22. Huang, Z., Sun, S.: Synthesizing quantum circuits of AES with lower t-depth and less qubits. Cryptology ePrint Archive, Report 2022/620 (2022). https://eprint.iacr.org/2022/620

  23. Jang, K., Choi, S., Kwon, H., Kim, H., Park, J., Seo, H.: Grover on Korean block ciphers. Appl. Sci. 10(18) (2020). https://doi.org/10.3390/app10186407

  24. Jang, K., Baksi, A., Breier, J., Seo, H., Chattopadhyay, A.: Quantum implementation and analysis of default. Cryptology ePrint Archive, Paper 2022/647 (2022). https://eprint.iacr.org/2022/647

  25. Jang, K., Baksi, A., Kim, H., Seo, H., Chattopadhyay, A.: Improved quantum analysis of speck and LOWMC (full version). Cryptology ePrint Archive, Paper 2022/1427 (2022). https://eprint.iacr.org/2022/1427

  26. Jang, K., Baksi, A., Kim, H., Song, G., Seo, H., Chattopadhyay, A.: Quantum analysis of AES. Cryptology ePrint Archive, Paper 2022/683 (2022). https://eprint.iacr.org/2022/683

  27. 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

  28. 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) (2021). https://www.mdpi.com/2076-3417/11/11/4776

  29. Jang, K., Song, G., Kim, H., Kwon, H., Kim, H., Seo, H.: Parallel quantum addition for Korean block cipher. IACR Cryptology ePrint Archive, p. 1507 (2021). https://eprint.iacr.org/2021/1507

  30. Jang, K., et al.: Grover on PIPO. Electronics 10(10), 1194 (2021)

    Article  Google Scholar 

  31. 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

    Chapter  Google Scholar 

  32. Langenberg, B., Pham, H., Steinwandt, R.: Reducing the cost of implementing the advanced encryption standard as a quantum circuit. IEEE Trans. Quant. Eng. 1, 1–12 (2020). https://doi.org/10.1109/TQE.2020.2965697

  33. NIST.: Submission requirements and evaluation criteria for the post-quantum cryptography standardization process (2016). https://csrc.nist.gov/CSRC/media/Projects/Post-Quantum-Cryptography/documents/call-for-proposals-final-dec-2016.pdf

  34. Putranto, D.S.C., Wardhani, R.W., Larasati, H.T., Kim, H.: Another concrete quantum cryptanalysis of binary elliptic curves. Cryptology ePrint Archive (2022)

    Google Scholar 

  35. Rahman, M., Paul, G.: Grover on katan: quantum resource estimation. IEEE Trans. Quant. Eng. 3, 1–9 (2022)

    Article  Google Scholar 

  36. Selinger, P.: Quantum circuits of t-depth one. Phys. Rev. A 87(4), 042302 (2013)

    Article  Google Scholar 

  37. Selinger, P.: Quantum circuits of \(t\)-depth one. Phys. Rev. A 87, 042302 (2013). https://doi.org/10.1103/PhysRevA.87.042302

  38. Shor, P.W.: Algorithms for quantum computation: discrete logarithms and factoring. In: Proceedings 35th Annual Symposium on Foundations of Computer Science, pp. 124–134. IEEE (1994)

    Google Scholar 

  39. Song, G., Jang, K., Kim, H., Lee, W., Hu, Z., Seo, H.: Grover on SM3. IACR Cryptology ePrint Archive (2021). https://eprint.iacr.org/2021/668

  40. Takahashi, Y., Tani, S., Kunihiro, N.: Quantum addition circuits and unbounded fan-out (2009). https://arxiv.org/abs/0910.2530

  41. Zaverucha, G., et al.: The Picnic signature algorithm. Submission to PQC Third Round (2020). https://github.com/microsoft/Picnic/blob/master/spec/spec-v3.0.pdf

  42. Zou, J., Li, L., Wei, Z., Luo, Y., Liu, Q., Wu, W.: New quantum circuit implementations of SM4 and sm3. Quant. Inf. Process. 21(5), 1–38 (2022)

    Article  MathSciNet  MATH  Google Scholar 

  43. Zou, J., Wei, Z., Sun, S., Liu, X., Wu, W.: Quantum circuit implementations of AES with fewer qubits. In: Moriai, S., Wang, H. (eds.) ASIACRYPT 2020. LNCS, vol. 12492, pp. 697–726. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-64834-3_24

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Division of IT Convergence Engineering, Hansung University, Seoul, South Korea

    Kyungbae Jang, Hyunji Kim & Hwajeong Seo

  2. Temasek Laboratories, Nanyang Technological University, Singapore, Singapore

    Anubhab Baksi & Anupam Chattopadhyay

Authors
  1. Kyungbae Jang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Anubhab Baksi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hyunji Kim
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Hwajeong Seo
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Anupam Chattopadhyay
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Kyungbae Jang .

Editor information

Editors and Affiliations

  1. University of Hyogo, Hyogo, Japan

    Takanori Isobe

  2. Indian Institute of Technology Madras, Chennai, India

    Santanu Sarkar

Rights and permissions

Reprints and permissions

Copyright information

© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Jang, K., Baksi, A., Kim, H., Seo, H., Chattopadhyay, A. (2022). Improved Quantum Analysis of SPECK and LowMC. 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_23

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-22912-1_23

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-22911-4

  • Online ISBN: 978-3-031-22912-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics