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Total Break of a Public Key Cryptosystem Based on a Group of Permutation Polynomials

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Advances in Information and Computer Security (IWSEC 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14128))

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Abstract

In this paper, we respond to the proposal of the Permutation Polynomial Encryption Scheme, introduced by Singh, Sarma, and Saikia in 2020. We simplify the private key and prove the scheme can be completely broken by a direct attack. Furthermore, we show that the direct attack also completely breaks the \(\ell \)IC cryptosystem. Although other attacks on this scheme were known, it was previously incorrectly asserted that Gröbner basis method is not feasible against \(\ell \)IC. We also highlight that this attack is effective against any generalization of these schemes that contain specific properties necessary for inversion.

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Authors and Affiliations

  1. University of Louisville, Louisville, KY, USA

    Max Cartor, Mark Lewis & Daniel Smith-Tone

  2. Clemson University, Clemson, SC, USA

    Ryann Cartor

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

    Daniel Smith-Tone

Authors
  1. Max Cartor
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  2. Ryann Cartor
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  3. Mark Lewis
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  4. Daniel Smith-Tone
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Corresponding author

Correspondence to Ryann Cartor .

Editor information

Editors and Affiliations

  1. Yokohama National University, Yokohama, Japan

    Junji Shikata

  2. Kobe University, Kobe, Japan

    Hiroki Kuzuno

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© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG

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Cartor, M., Cartor, R., Lewis, M., Smith-Tone, D. (2023). Total Break of a Public Key Cryptosystem Based on a Group of Permutation Polynomials. In: Shikata, J., Kuzuno, H. (eds) Advances in Information and Computer Security. IWSEC 2023. Lecture Notes in Computer Science, vol 14128. Springer, Cham. https://doi.org/10.1007/978-3-031-41326-1_8

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  • DOI: https://doi.org/10.1007/978-3-031-41326-1_8

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-41325-4

  • Online ISBN: 978-3-031-41326-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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