Application of Grover's quantum search algorithm attack on S-Des cryptography
Email:
quynhln@actvn.edu.vn
Abstract
With the advent of quantum computers, many cryptographic systems in use today can be broken with fast execution speed. Cryptanalysis algorithms using quantum computing are still modest and are in the research stage. For block cipher systems, the quantum Grover search algorithm is a popular tool. Grover's algorithm has the advantage of using amplitude amplification techniques to speed up and reduce time significantly, reducing the computational complexity of the algorithm. Specifically, Grover's algorithm is a quantum algorithm used to search an unsorted database of N elements, in which the time complexity is O(√N) and uses O(log N) storage space. In Mishal Almazrooie's work, he proposed a method to prove and demonstrate the feasibility of applying Grover's search algorithm to cryptanalysis of the S-DES symmetric key cryptosystem. Based on international and domestic research, in this study, the authors implement the S-DES cryptosystem using Grover's algorithm with the aim of testing the feasibility and orienting the application of this algorithm to explore other block cipher systems in future publications.References
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[2]. I. B. Djordjevic, Quantum Information Processing, Quantum Computing, and Quantum Error Correction: An Engineering Approach, Second Edi. Elsevier, 2021.
[3]. M. Schwetz, R. M. Noack, Simon algorithm in measurement-based quantum computing, 2024. http://arxiv.org/abs/2405.18143
[4]. C. Guo, Grover’s Algorithm – Implementations and Implications, Highlights Sci. Eng. Technol., 38 (2023) 1071–1078. https://doi.org/10.54097/hset.v38i.5997
[5]. D. Camps, R. Van Beeumen, C. Yang, Quantum Fourier transform revisited, Numer. Linear Algebr. with Appl., 28 (2021). https://doi.org/10.1002/nla.2331
[6]. D. V. Denisenko, M. V. Nikitenkova, Application of Grover’s Quantum Algorithm for SDES Key Searching, J. Exp. Theor. Phys., 128 (2019) 25–44. https://doi.org/10.1134/S1063776118120142
[7]. D. V. Lữ, H. P. Anh, H. B. Nguyên, N. N. M. Trí, C. T. M. Hảo, N. T. Hồng, Nghiên cứu ứng dụng thuật toán lượng tử Grover trong giải trình tự DNA, TNU J. Sci. Technol., 229 (2024) 65–72. https://doi.org/10.34238/tnu-jst.9932
[8]. E. F. Schaefer, A Simplified Data Encryption Standard Algorithm, Cryptologia, 20 (1996) 77–84. https://doi.org/10.1080/0161-119691884799
[9]. D. R. Stinson, Cryptography, Third Edit. Chapman and Hall/CRC, 2005.
[10]. R. Awadallah, A. Samsudin, M. Almazrooie, Verifiable Homomorphic Encrypted Computations for Cloud Computing, Int. J. Adv. Comput. Sci. Appl., 12 (2021). https://doi.org/10.14569/IJACSA.2021.0121089
[11]. M. Almazrooie, A. Samsudin, R. Abdullah, K. N. Mutter, Quantum exhaustive key search with simplified-DES as a case study, Springerplus, 5 (2016) 1494. https://doi.org/10.1186/s40064-016-3159-4.
[12]. L. Nhu Quynh, L. Van Anh, Implement quantum random number generation on the IBM quantum computer platform, Transp. Commun. Sci. J., 75 (2024) 1644–1658. https://doi.org/10.47869/tcsj.75.4.14
[13]. A. Javadi-Abhari, M. Treinish, K. Krsulich, C. J. Wood, J. Lishman, J. Gacon, S. Martiel, P. D. Nation, L. S. Bishop, A. W. Cross, B. R. Johnson, J. M. Gambetta, Quantum computing with Qiskit, (2024). http://arxiv.org/abs/2405.08810
[14]. M. Fingerhuth, T. Babej, P. Wittek, Open source software in quantum computing, PLoS One, 13 (2018) e0208561. https://doi.org/10.1371/journal.pone.0208561
[15]. K.-B. Jang, G.-J. Song, H.-J. Kim, H.-J. Seo, Grover on Simplified AES, 2021 IEEE International Conference on Consumer Electronics-Asia (ICCE-Asia), 2021, IEEE, pp. 1–4. https://doi.org/10.1109/ICCE-Asia53811.2021.9642017
[16]. M. Almazrooie, R. Abdullah, A. Samsudin, K. N. Mutter, Quantum Grover Attack on the Simplified-AES, Proceedings of the 2018 7th International Conference on Software and Computer Applications, 2018, New York, USA: ACM, pp. 204–211. https://doi.org/10.1145/3185089.3185122
[17]. S. Mandal, R. Anand, M. Rahman, S. Sarkar, T. Isobe, Implementing Grover’s on AES-based AEAD schemes, Sci. Rep., 14 (2024) 21105. https://doi.org/10.1038/s41598-024-69188-8
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Received
19/01/2025
Revised
04/04/2025
Accepted
10/04/2025
Published
15/04/2025
Type
Research Article
How to Cite
Nguyễn Tất, T., Đào Thanh, T., & Lục Như, Q. (1744650000). Application of Grover’s quantum search algorithm attack on S-Des cryptography. Transport and Communications Science Journal, 76(3), 271-281. https://doi.org/10.47869/tcsj.76.3.6
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