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Algebraic Attacks on Round-Reduced Keccak

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Information Security and Privacy (ACISP 2021)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 13083))

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Abstract

Since Keccak was selected as the SHA-3 standard, both its hash mode and keyed mode have attracted lots of third-party cryptanalysis. Especially in recent years, there is progress in analyzing the collision resistance and preimage resistance of round-reduced Keccak. However, for the preimage attacks on round-reduced Keccak-384/512, we found that the linear relations leaked by the hash value are not well exploited when utilizing the current linear structures. To make full use of the \(320+64\times 2=448\) and 320 linear relations leaked by the hash value of Keccak-512 and Keccak-384, respectively, we propose a dedicated algebraic attack by expressing the output as a quadratic boolean equation system in terms of the input. Such a quadratic boolean equation system can be efficiently solved with linearization techniques. Consequently, we successfully improved the preimage attacks on 2/3/4 rounds of Keccak-384 and 2/3 rounds of Keccak-512.

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Notes

  1. 1.

    Note that the Keccak round function works on 64-bit words. In our implementation of Gauss elimination, we first encode the boolean coefficient matrix by treating every consecutive 64 bits as a 64-bit word in each row. Then, we perform the Gauss elimination on the encoded coefficient matrix. Such a way will not add extra cost to enumerate the solutions to the equation system after Gauss elimination.

  2. 2.

    The quadratic expression \((x_0\oplus x_1)x_2\) will be treated as one quadratic term rather than two different quadratic terms \((x_0x_2,x_0x_1)\).

  3. 3.

    This work is simple and we omit the details. Such a model was also used to verify the guessing strategy used in the preimage attack on 3-round Keccak-384.

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Acknowledgements

We thank the anonymous reviewers of ACISP 2021 for their useful comments. Fukang Liu is supported by Invitation Programs for Foreigner-based Researchers of NICT. In addition, he is also partially supported by the National Natural Science Foundation of China (No. 62072181) and the International Science and Technology Cooperation Projects (No. 61961146004). Takanori Isobe is supported by JST, PRESTO Grant Number JPMJPR2031, Grant-in-Aid for Scientific Research (B)(KAKENHI 19H02141) and SECOM science and technology foundation.

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Authors and Affiliations

  1. East China Normal University, Shanghai, China

    Fukang Liu & Zhonghao Yang

  2. University of Hyogo, Hyogo, Japan

    Fukang Liu & Takanori Isobe

  3. National Institute of Information and Communications Technology, Tokyo, Japan

    Takanori Isobe

  4. PRESTO, Japan Science and Technology Agency, Tokyo, Japan

    Takanori Isobe

  5. FHNW, Windisch, Switzerland

    Willi Meier

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  1. Fukang Liu
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  4. Zhonghao Yang
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  1. University of Wollongong, Wollongong, NSW, Australia

    Joonsang Baek

  2. Data61, CSIRO, Marsfield, NSW, Australia

    Sushmita Ruj

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Liu, F., Isobe, T., Meier, W., Yang, Z. (2021). Algebraic Attacks on Round-Reduced Keccak. In: Baek, J., Ruj, S. (eds) Information Security and Privacy. ACISP 2021. Lecture Notes in Computer Science(), vol 13083. Springer, Cham. https://doi.org/10.1007/978-3-030-90567-5_5

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  • DOI: https://doi.org/10.1007/978-3-030-90567-5_5

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