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Yi ZHANG, Kai ZHANG, and Ting CUI, “Related-Key Zero-Correlation Linear Attacks on Block Ciphers with Linear Key Schedules,” Chinese Journal of Electronics, vol. 33, no. 3, pp. 1–11, 2024 doi: 10.23919/cje.2022.00.419
Citation: Yi ZHANG, Kai ZHANG, and Ting CUI, “Related-Key Zero-Correlation Linear Attacks on Block Ciphers with Linear Key Schedules,” Chinese Journal of Electronics, vol. 33, no. 3, pp. 1–11, 2024 doi: 10.23919/cje.2022.00.419

Related-Key Zero-Correlation Linear Attacks on Block Ciphers with Linear Key Schedules

doi: 10.23919/cje.2022.00.419
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  • Author Bio:

    Yi ZHANG received the B.S. degree in cryptology from PLA SSF Information Engineering University, Zhengzhou, China, in 2016. He is currently a master candidate of the Department of Applied Mathematics, PLA SSF Information Engineering University, Zhengzhou, China. His current research interests include block cipher design and cryptanalysis. (Email: yizhang0796@foxmail.com)

    Kai ZHANG received the Ph.D. degree in cryptology from the Information Science and Technology Institute, Zhengzhou, China, in 2016. His main research interests include design and analysis of symmetric ciphers. His works have been published in several refereed journals and he has been serving as a referee for several famous international journals in the area of information security and cryptology. (Email: zhkai2010@139.com)

    Ting CUI is currently a Professor at the Department of Applied Mathematics, PLA SSF Information Engineering University, China. His current research interests include cryptography and cyberspace security. His works have been published in several refereed journals and he has been serving as a referee for several famous international journals in the area of information security and cryptology. (Email: cuiting_1209@hotmail.com)

  • Corresponding author: Email: cuiting_1209@hotmail.com
  • Received Date: 2022-12-07
  • Accepted Date: 2023-03-13
  • Available Online: 2023-07-17
  • Related-key model is a favourable approach to improve attacks on block ciphers with a simple key schedule. However, to the best of our knowledge, there are a few results in which zero-correlation linear attacks take advantage of the related-key model. We ascribe this phenomenon to the lack of consideration of the key input in zero-correlation linear attacks. Concentrating on the linear key schedule of a block cipher, we generalize the zero-correlation linear attack by using a related-key setting. Specifically, we propose the creation of generalized linear hulls (GLHs) when the key input is involved; moreover, we indicate the links between GLHs and conventional linear hulls (CLHs). Then, we prove that the existence of zero-correlation GLHs is completely determined by the corresponding CLHs and the linear key schedule. In addition, we introduce a method to construct zero-correlation GLHs by CLHs and transform them into an integral distinguisher. The correctness is verified by applying it to SIMON16/16, a SIMON-like toy cipher. Based on our method, we find 12/13/14/15/15/17/20/22-round related-key zero-correlation linear distinguishers of SIMON32/64, SIMON48/72, SIMON48/96, SIMON64/96, SIMON64/128, SIMON96/144, SIMON128/192 and SIMON128/256, respectively. As far as we know, these distinguishers are one, two, or three rounds longer than current best zero-correlation linear distinguishers of SIMON.
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