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Links between Quantum Distinguishers Based on Simon’s Algorithm and Truncated Differentials

Authors:
Zejun Xiang , School of Cyber Science and Technology, Hubei University, Wuhan, Hubei, 430062, China; State Key Laboratory of Cryptology, P. O. Box 5159, Beijing, 100878, China
Xiaoyu Wang , Faculty of Mathematics and Statistics, Hubei University, Wuhan, Hubei, 430062, China
Bo Yu , College of Science, National University of Defense Technology, Changsha, Hunan, 410073, China
Bing Sun , College of Science, National University of Defense Technology, Changsha, Hunan, 410073, China; Center for Cryptologic Research, National University of Defense Technology, Changsha, Hunan, P.R. China, 410073
Shasha Zhang , School of Cyber Science and Technology, Hubei University, Wuhan, Hubei, 430062, China
Xiangyong Zeng , Faculty of Mathematics and Statistics, Hubei University, Wuhan, Hubei, 430062, China
Xuan Shen , College of Information and Communication, National University of Defense Technology, Wuhan, Hubei, 430010, China
Nian Li , School of Cyber Science and Technology, Hubei University, Wuhan, Hubei, 430062, China
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DOI: 10.46586/tosc.v2024.i2.296-321
URL: https://tosc.iacr.org/index.php/ToSC/article/view/11632
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Abstract: In this paper, we study the quantum security of block ciphers based on Simon’s period-finding quantum algorithm. We explored the relations between periodic functions and truncated differentials. The basic observation is that truncated differentials with a probability of 1 can be used to construct periodic functions, and two such constructions are presented with the help of a new notion called difference-annihilation matrix. This technique releases us from the tedious manual work of verifying the period of functions. Based on these new constructions, we find an 8-round quantum distinguisher for LBlock and a 9/10/11/13/15-round quantum distinguisher for SIMON-32/48/64/96/128 which are the best results as far as we know. Besides, to explore the security bounds of block cipher structures against Simon’s algorithm based quantum attacks, the unified structure, which unifies the Feistel, Lai-Massey, and most generalized Feistel structures, is studied. We estimate the exact round number of probability 1 truncated differentials that one can construct. Based on these results, one can easily check the quantum security of specific block ciphers that are special cases of unified structures, when the details of the non-linear building blocks are not considered.
BibTeX
@article{tosc-2024-34384,
  title={Links between Quantum Distinguishers Based on Simon’s Algorithm and Truncated Differentials},
  journal={IACR Transactions on Symmetric Cryptology},
  publisher={Ruhr-Universität Bochum},
  volume={024 No. 2},
  pages={296-321},
  url={https://tosc.iacr.org/index.php/ToSC/article/view/11632},
  doi={10.46586/tosc.v2024.i2.296-321},
  author={Zejun Xiang and Xiaoyu Wang and Bo Yu and Bing Sun and Shasha Zhang and Xiangyong Zeng and Xuan Shen and Nian Li},
  year=2024
}