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Rotational Differential-Linear Distinguishers of ARX Ciphers with Arbitrary Output Linear Masks

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Advances in Cryptology – CRYPTO 2022 (CRYPTO 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13507))

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Abstract

The rotational differential-linear attacks, proposed at EUROCRYPT 2021, is a generalization of differential-linear attacks by replacing the differential part of the attacks with rotational differentials. At EUROCRYPT 2021, Liu et al. presented a method based on Morawiecki et al.’s technique (FSE 2013) for evaluating the rotational differential-linear correlations for the special cases where the output linear masks are unit vectors. With this method, some powerful (rotational) differential-linear distinguishers with output linear masks being unit vectors against FRIET, Xoodoo, and Alzette were discovered. However, how to compute the rotational differential-linear correlations for arbitrary output masks was left open. In this work, we partially solve this open problem by presenting an efficient algorithm for computing the (rotational) differential-linear correlation of modulo additions for arbitrary output linear masks, based on which a technique for evaluating the (rotational) differential-linear correlation of ARX ciphers is derived. We apply the technique to Alzette, SipHash, ChaCha, and SPECK. As a result, significantly improved (rotational) differential-linear distinguishers including deterministic ones are identified. All results of this work are practical and experimentally verified to confirm the validity of our methods. In addition, we try to explain the experimental distinguishers employed in FSE 2008, FSE 2016, and CRYPTO 2020 against ChaCha. The predicted correlations are close to the experimental ones.

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Acknowledgment

We thank the reviewers for their valuable comments. This work is supported by the National Key Research and Development Program of China (2018YFA0704704), the Natural Science Foundation of China (62032014), and the Fundamental Research Funds for the Central Universities.

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Authors and Affiliations

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

    Zhongfeng Niu & Yunwen Liu

  2. School of Cryptology, University of Chinese Academy of Sciences, Beijing, China

    Zhongfeng Niu, Siwei Sun & Yunwen Liu

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

    Zhongfeng Niu & Yunwen Liu

  4. College of Liberal Arts and Science, National University of Defense Technology, Changsha, China

    Yunwen Liu & Chao Li

  5. State Key Laboratory of Cryptology, P.O. Box 5159, Beijing, 100878, China

    Siwei Sun & Yunwen Liu

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  1. Zhongfeng Niu
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  2. Siwei Sun
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  4. Chao Li
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Correspondence to Siwei Sun .

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Editors and Affiliations

  1. New York University, New York, NY, USA

    Yevgeniy Dodis

  2. University of Florida, Gainesville, FL, USA

    Thomas Shrimpton

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Niu, Z., Sun, S., Liu, Y., Li, C. (2022). Rotational Differential-Linear Distinguishers of ARX Ciphers with Arbitrary Output Linear Masks. In: Dodis, Y., Shrimpton, T. (eds) Advances in Cryptology – CRYPTO 2022. CRYPTO 2022. Lecture Notes in Computer Science, vol 13507. Springer, Cham. https://doi.org/10.1007/978-3-031-15802-5_1

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