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Improved Attacks for Characteristic-2 Parameters of the Cubic ABC Simple Matrix Encryption Scheme

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Post-Quantum Cryptography (PQCrypto 2017)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 10346))

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Abstract

In the last few years multivariate public key cryptography has experienced an infusion of new ideas for encryption. Among these new strategies is the ABC Simple Matrix family of encryption schemes which utilize the structure of a large matrix algebra to construct effectively invertible systems of nonlinear equations hidden by an isomorphism of polynomials. One promising approach to cryptanalyzing these schemes has been structural cryptanalysis, based on applying a strategy similar to MinRank attacks to the discrete differential. These attacks however have been significantly more expensive when applied to parameters using fields of characteristic 2, which have been the most common choice for published parameters. This disparity is especially great for the cubic version of the Simple Matrix Encryption Scheme.

In this work, we demonstrate a technique that can be used to implement a structural attack which is as efficient against parameters of characteristic 2 as are attacks against analogous parameters over higher characteristic fields. This attack demonstrates that, not only is the cubic simple matrix scheme susceptible to structural attacks, but that the published parameters claiming 80 bits of security are less secure than claimed (albeit only slightly.) Similar techniques can also be applied to improve structural attacks against the original Simple Matrix Encryption scheme, but they represent only a modest improvement over previous structural attacks. This work therefore demonstrates that choosing a field of characteristic 2 for the Simple Matrix Encryption Scheme or its cubic variant will not provide any additional security value.

The rights of this work are transferred to the extent transferable according to title 17 § 105 U.S.C.

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Authors and Affiliations

  1. National Institute of Standards and Technology, Gaithersburg, MD, USA

    Dustin Moody, Ray Perlner & Daniel Smith-Tone

  2. Department of Mathematics, University of Louisville, Louisville, KY, USA

    Daniel Smith-Tone

Authors
  1. Dustin Moody
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  2. Ray Perlner
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  3. Daniel Smith-Tone
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Corresponding author

Correspondence to Dustin Moody .

Editor information

Editors and Affiliations

  1. Technische Universiteit Eindhoven, Eindhoven, The Netherlands

    Tanja Lange

  2. Kyushu University , Fukuoka, Japan

    Tsuyoshi Takagi

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Moody, D., Perlner, R., Smith-Tone, D. (2017). Improved Attacks for Characteristic-2 Parameters of the Cubic ABC Simple Matrix Encryption Scheme. In: Lange, T., Takagi, T. (eds) Post-Quantum Cryptography . PQCrypto 2017. Lecture Notes in Computer Science(), vol 10346. Springer, Cham. https://doi.org/10.1007/978-3-319-59879-6_15

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  • DOI: https://doi.org/10.1007/978-3-319-59879-6_15

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-59878-9

  • Online ISBN: 978-3-319-59879-6

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