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Optimizing Rectangle Attacks: A Unified and Generic Framework for Key Recovery

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Advances in Cryptology – ASIACRYPT 2022 (ASIACRYPT 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13791))

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Abstract

The rectangle attack has shown to be a very powerful form of cryptanalysis against block ciphers. Given a rectangle distinguisher, one expects to mount key recovery attacks as efficiently as possible. In the literature, there have been four algorithms for rectangle key recovery attacks. However, their performance vary from case to case. Besides, numerous are the applications where the attacks lack optimality. In this paper, we investigate the rectangle key recovery in depth and propose a unified and generic key recovery algorithm, which supports any possible attacking parameters. Notably, it not only covers the four previous rectangle key recovery algorithms, but also unveils five types of new attacks which were missed previously. Along with the new key recovery algorithm, we propose a framework for automatically finding the best attacking parameters, with which the time complexity of the rectangle attack will be minimized using the new algorithm. To demonstrate the efficiency of the new key recovery algorithm, we apply it to Serpent, CRAFT, SKINNY and Deoxys-BC-256 based on existing distinguishers and obtain a series of improved rectangle attacks.

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Notes

  1. 1.

    If both \((P_1,P_2)\) and \((P_3,P_4)\) satisfy \(\alpha \) difference, then we can form two quartets: \((P_1,P_2,P_3,P_4)\) and \((P_1,P_2,P_4,P_3)\).

  2. 2.

    The number of filters for plaintext pairs is \(n-r^*_b\) while it is \(n-r^*_f+\mu \) for ciphertext pairs.

  3. 3.

    “Key bridging” is borrowed from [DKS10a, DKS15] which originally connects two subkeys separated by several key mixing steps.

  4. 4.

    https://drive.google.com/file/d/1gZpqtm4pg6ezZ4TrS9cRirnRz9YbqjgL/view?usp=sharing.

  5. 5.

    The key counters can be set flexibly. Thus the memory cost for them is elastic.

  6. 6.

    In [DQSW22], a rectangle attack on 10-round Serpent was also given. However, the authors seem to mistake \(m_f,r_f\) for \(m_b,r_b\). So we do not include their result in Table 3.

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Acknowledgement

The authors would like to thank anonymous reviewers for their helpful comments and suggestions. The work of this paper was supported by the National Natural Science Foundation of China (Grants 62022036, 62132008, 62202460, 62172410, 61732021), the National Key Research and Development Program (No. 2022YFB2701900, No. 2018YFA0704704 and No. 2018YFB0803801). Jian Weng was supported by Major Program of Guangdong Basic and Applied Research Project under Grant No. 2019B030302008, National Natural Science Foundation of China under Grant No. 61825203, Guangdong Provincial Science and Technology Project under Grant No. 2021A0505030033, National Joint Engineering Research Center of Network Security Detection and Protection Technology, and Guangdong Key Laboratory of Data Security and Privacy Preserving.

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Authors and Affiliations

  1. College of Cyber Security, Jinan University, Guangzhou, China

    Ling Song & Jian Weng

  2. State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, China

    Nana Zhang, Qianqian Yang, Danping Shi, Jiahao Zhao & Lei Hu

  3. National Joint Engineering Research Center of Network Security Detection and Protection Technology, Jinan University, Guangzhou, China

    Ling Song & Jian Weng

  4. Guangdong Key Laboratory of Data Security and Privacy Preserving, Jinan University, Guangzhou, China

    Jian Weng

  5. School of Cyber Security, University of Chinese Academy of Sciences, Beijing, China

    Nana Zhang, Qianqian Yang, Danping Shi, Jiahao Zhao & Lei Hu

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  1. Ling Song
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  1. Indian Institute of Technology Madras, Chennai, India

    Shweta Agrawal

  2. Chinese Academy of Sciences, Beijing, China

    Dongdai Lin

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Song, L. et al. (2022). Optimizing Rectangle Attacks: A Unified and Generic Framework for Key Recovery. In: Agrawal, S., Lin, D. (eds) Advances in Cryptology – ASIACRYPT 2022. ASIACRYPT 2022. Lecture Notes in Computer Science, vol 13791. Springer, Cham. https://doi.org/10.1007/978-3-031-22963-3_14

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  • DOI: https://doi.org/10.1007/978-3-031-22963-3_14

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