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Boolean Ring Cryptographic Equation Solving

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Selected Areas in Cryptography (SAC 2020)

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Abstract

This paper considers multivariate polynomial equation systems over GF(2) that have a small number of solutions. This paper gives a new method EGHAM2 for solving such systems of equations that uses the properties of the Boolean quotient ring to potentially reduce memory and time complexity relative to existing XL-type or Gröbner basis algorithms applied in this setting. This paper also establishes a direct connection between solving such a multivariate polynomial equation system over GF(2), an \(\mathtt{MQ}\) problem, and an instance of the LPN problem.

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Acknowledgements

We would like to thank the anonymous referees for their helpful comments.

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Authors and Affiliations

  1. Royal Holloway, University of London, London, UK

    Sean Murphy

  2. Birkbeck, University of London, London, UK

    Maura Paterson

  3. University of Cape Town, Cape Town, South Africa

    Christine Swart

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  1. Sean Murphy
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Correspondence to Sean Murphy .

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Editors and Affiliations

  1. University of Haifa, Haifa, Israel

    Orr Dunkelman

  2. University of Calgary, Calgary, AB, Canada

    Michael J. Jacobson, Jr.

  3. Dalhousie University, Halifax, NS, Canada

    Colin O'Flynn

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Murphy, S., Paterson, M., Swart, C. (2021). Boolean Ring Cryptographic Equation Solving. In: Dunkelman, O., Jacobson, Jr., M.J., O'Flynn, C. (eds) Selected Areas in Cryptography. SAC 2020. Lecture Notes in Computer Science(), vol 12804. Springer, Cham. https://doi.org/10.1007/978-3-030-81652-0_10

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  • DOI: https://doi.org/10.1007/978-3-030-81652-0_10

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