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The Nested Subset Differential Attack

A Practical Direct Attack Against LUOV Which Forges a Signature Within 210 Minutes

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Advances in Cryptology – EUROCRYPT 2021 (EUROCRYPT 2021)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 12696))

Abstract

In 2017, Ward Beullens et al. submitted Lifted Unbalanced Oil and Vinegar [3], which is a modification to the Unbalanced Oil and Vinegar Scheme by Patarin. Previously, Ding et al. proposed the Subfield Differential Attack [22] which prompted a change of parameters by the authors of LUOV for the second round of the NIST post quantum standardization competition [4].

In this paper we propose a modification to the Subfield Differential Attack called the Nested Subset Differential Attack which fully breaks half of the parameter sets put forward. We also show by experimentation that this attack is practically possible to do in under 210 min for the level I security parameters and not just a theoretical attack. The Nested Subset Differential attack is a large improvement of the Subfield differential attack which can be used in real world circumstances. Moreover, we will only use what is called the “lifted” structure of LUOV, and our attack can be thought as a development of solving “lifted” quadratic systems.

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Author information

Authors and Affiliations

  1. Tsinghua University, Beijing, China

    Jintai Ding

  2. University of Cincinnati, Cincinnati, OH, USA

    Joshua Deaton &  Vishakha

  3. Academia Sinica, Taipei, Taiwan

    Bo-Yin Yang

Authors
  1. Jintai Ding
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  2. Joshua Deaton
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  3. Vishakha
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  4. Bo-Yin Yang
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Corresponding author

Correspondence to Joshua Deaton .

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Editors and Affiliations

  1. Inria, Paris, France

    Anne Canteaut

  2. UCLouvain, Louvain-la-Neuve, Belgium

    François-Xavier Standaert

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Ding, J., Deaton, J., Vishakha, Yang, BY. (2021). The Nested Subset Differential Attack. In: Canteaut, A., Standaert, FX. (eds) Advances in Cryptology – EUROCRYPT 2021. EUROCRYPT 2021. Lecture Notes in Computer Science(), vol 12696. Springer, Cham. https://doi.org/10.1007/978-3-030-77870-5_12

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  • DOI: https://doi.org/10.1007/978-3-030-77870-5_12

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