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Improving Attacks on Round-Reduced Speck32/64 Using Deep Learning

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Advances in Cryptology – CRYPTO 2019 (CRYPTO 2019)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 11693))

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Abstract

This paper has four main contributions. First, we calculate the predicted difference distribution of Speck32/64 with one specific input difference under the Markov assumption completely for up to eight rounds and verify that this yields a globally fairly good model of the difference distribution of Speck32/64. Secondly, we show that contrary to conventional wisdom, machine learning can produce very powerful cryptographic distinguishers: for instance, in a simple low-data, chosen plaintext attack on nine rounds of Speck, we present distinguishers based on deep residual neural networks that achieve a mean key rank roughly five times lower than an analogous classical distinguisher using the full difference distribution table. Thirdly, we develop a highly selective key search policy based on a variant of Bayesian optimization which, together with our neural distinguishers, can be used to reduce the remaining security of 11-round Speck32/64 to roughly 38 bits. This is a significant improvement over previous literature. Lastly, we show that our neural distinguishers successfully use features of the ciphertext pair distribution that are invisible to all purely differential distinguishers even given unlimited data.

While our attack is based on a known input difference taken from the literature, we also show that neural networks can be used to rapidly (within a matter of minutes on our machine) find good input differences without using prior human cryptanalysis. Supplementary code and data for this paper is available at https://github.com/agohr/deep_speck.

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Notes

  1. 1.

    As an implementation remark, note that with the neural networks used in this paper, the individual terms in the sum of Eq. 3 are up to a scale factor just the neural network outputs before application of the final sigmoid activation.

  2. 2.

    Running the same code with different parameters, other attacks can be obtained. The code repository, for instance, contains parameters for a 12-round attack that is practical on a single PC (with the parameters used, average runtime is under an hour on a GeForce GTX 1080 Ti GPU and success rate is \(\approx \)40%).

  3. 3.

    Note that for our neural networks, this argument can be slightly strengthened if the final sigmoid activation is removed, since then distinguisher output on an individual ciphertext pair is just a linear combination of 64 somewhat independent intermediate network units.

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Acknowledgments

The author wishes to thank the anonymous reviewers for their questions and comments, as they helped him to improve the present paper.

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  1. Bundesamt für Sicherheit in der Informationstechnik (BSI), Bonn, Germany

    Aron Gohr

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  1. Aron Gohr
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Correspondence to Aron Gohr .

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  1. Georgia Institute of Technology, Atlanta, GA, USA

    Alexandra Boldyreva

  2. University of California at San Diego, La Jolla, CA, USA

    Daniele Micciancio

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Gohr, A. (2019). Improving Attacks on Round-Reduced Speck32/64 Using Deep Learning. In: Boldyreva, A., Micciancio, D. (eds) Advances in Cryptology – CRYPTO 2019. CRYPTO 2019. Lecture Notes in Computer Science(), vol 11693. Springer, Cham. https://doi.org/10.1007/978-3-030-26951-7_6

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