Skip to main content
SpringerLink
Log in

A quantum circuit design of AES requiring fewer quantum qubits and gate operations

  • Research Article
  • Published:
Frontiers of Physics Aims and scope Submit manuscript

Abstract

Advanced Encryption Standard (AES) is one of the most widely used block ciphers nowadays, and has been established as an encryption standard in 2001. Here we design AES-128 and the sample-AES (S-AES) quantum circuits for deciphering. In the quantum circuit of AES-128, we perform an affine transformation for the SubBytes part to solve the problem that the initial state of the output qubits in SubBytes is not the ∣0⟩⊗8 state. After that, we are able to encode the new round sub-key on the qubits encoding the previous round sub-key, and this improvement reduces the number of qubits used by 224 compared with Langenberg et al.’s implementation. For S-AES, a complete quantum circuit is presented with only 48 qubits, which is already within the reach of existing noisy intermediate-scale quantum computers.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. M. Bellare and P. Rogaway, Introduction to modern cryptography, Ucsd Cse 207, 207 (2005)

    Google Scholar 

  2. R. L. Rivest, A. Shamir, and L. Adleman, A method for obtaining digital signatures and public key cryptosystems, Comm. ACM 21(2), 120 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  3. P. W. Shor, Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer, SIAM J. Comput. 26(5), 1484 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  4. D. Joan and R. Vincent, The design of rijndael: AES — The advanced encryption standard, Inf. Secur. Cryptogr (2002)

  5. L. K. Grover, A fast quantum mechanical algorithm for database search, in: Proceedings of the Twenty-eighth Annual ACM Symposium on Theory of Computing, 1996, pp 212–219

  6. G. L. Long, Grover algorithm with zero theoretical failure rate, Phys. Rev. A 64(2), 022307 (2001)

    Article  ADS  Google Scholar 

  7. A. Yamamura and H. Ishizuka, Quantum cryptanalysis of block ciphers (Algebraic Systems, Formal Languages and Computations), RIMS Kokyuroku 1166, 235 (2000)

    MATH  Google Scholar 

  8. M. Kaplan, Quantum attacks against iterated block ciphers, arXiv: 1410.1434 (2014)

  9. R. J. Li and C. H. Jin, Meet-in-the-middle attacks on 10-round AES-256, Des. Codes Cryptogr. 80(3), 459 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  10. A. Ambainis, Quantum walk algorithm for element distinctness, SIAM J. Comput. 37(1), 210 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  11. M. Roetteler and R. Steinwandt, A note on quantum related-key attacks, Inf. Process. Lett. 115(1), 40 (2015)

    Article  MATH  Google Scholar 

  12. D. R. Simon, On the power of quantum computation, in: Proceedings of the 35th Annual Symposium on Foundations of Computer Science, 1994, pp 116–123

  13. M. Grassl, B. Langenberg, M. Roetteler, and R. Steinwandt, Applying Grover’s algorithm to AES: Quantum resource estimates, in: Post-Quantum Cryptography, Springer, 2016, pp 29–43

  14. P. Kim, D. Han, and K. C. Jeong, Time-space complexity of quantum search algorithms in symmetric cryptanalysis: Applying to AES and SHA-2, Quantum Inform. Process. 17(12), 339 (2018)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  15. M. Almazrooie, R. Abdullah, A. Samsudin, and K. N. Mutter, Quantum Grover attack on the simplified-AES, in: Proceedings of the 7th International Conference on Software and Computer Applications, 2018, pp 204–211

  16. F. Arute, K. Arya, R. Babbush, D. Bacon, J. C. Bardin, et al., Quantum supremacy using a programmable superconducting processor, Nature 574(7779), 505 (2019)

    Article  ADS  Google Scholar 

  17. J. Xu, S. Li, T. Chen, and Z. Y. Xue, Nonadiabatic geometric quantum computation with optimal control on superconducting circuits, Front. Phys. 15(4), 41503 (2020)

    Article  ADS  Google Scholar 

  18. B. Langenberg, H. Pham, and R. Steinwandt, Reducing the cost of implementing the advanced encryption standard as a quantum circuit, IEEE Trans. Quantum Eng. 1, 1 (2020)

    Article  Google Scholar 

  19. J. Boyar and R. Peralta, A new combinational logic minimization technique with applications to cryptology, in: International Symposium on Experimental Algorithms, Springer, 2010, pp 178–189

  20. J. Zou, Z. H. Wei, S. W. Sun, X. M. Liu, and W. L. Wu, Quantum circuit implementations of AES with fewer qubits, in: International Conference on the Theory and Application of Cryptology and Information Security, Springer, 2020, pp 697–726

Download references

Acknowledgements

We gratefully acknowledges support from the National Natural Science Foundation of China under Grant Nos. 11974205 and 11774197, the National Key Research and Development Program of China (No. 2017YFA0303700), the Key Research and Development Program of Guangdong province (No. 2018B030325002), and Beijing Advanced Innovation Center for Future Chip (ICFC). S.W. also acknowledges the China Postdoctoral Science Foundation (No. 2020M670172) and the National Natural Science Foundation of China under Grant No. 12005015.

Author information

Authors and Affiliations

  1. State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing, 100084, China

    Ze-Guo Wang, Shi-Jie Wei & Gui-Lu Long

  2. Beijing Academy of Quantum Information Sciences, Beijing, 100193, China

    Shi-Jie Wei & Gui-Lu Long

  3. Beijing National Research Center for Information Science and Technology and School of Information Tsinghua University, Beijing, 100084, China

    Gui-Lu Long

  4. Frontier Science Center for Quantum Information, Beijing, 100084, China

    Gui-Lu Long

Authors
  1. Ze-Guo Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shi-Jie Wei
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Gui-Lu Long
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Shi-Jie Wei or Gui-Lu Long.

Additional information

This article can also be found at http://journal.hep.com.cn/fop/EN/10.1007/s11467-021-1141-2.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, ZG., Wei, SJ. & Long, GL. A quantum circuit design of AES requiring fewer quantum qubits and gate operations. Front. Phys. 17, 41501 (2022). https://doi.org/10.1007/s11467-021-1141-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11467-021-1141-2

Keywords

Search

Navigation