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Cryptanalysis of a code-based one-time signature

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Abstract

In 2012, Lyubashevsky introduced a new framework for building lattice-based signature schemes without resorting to any trapdoor [such as Gentry C, Peikert C, Vaikuntanathan V, in: Ladner and Dwork (eds) 40th ACM STOC, ACM Press, Victoria, pp. 197–206, 2008 or Hoffstein J, Pipher J, Silverman JH in: Pfitzmann (ed) EUROCRYPT 2001. LNCS, vol. 2045, pp 211–228, Springer, Heidelberg, 2001]. The idea is to sample a set of short lattice elements and construct the public key as a Short Integer Solution (SIS for short) instance. Signatures are obtained using a small subset sum of the secret key, hidden by a (large) Gaussian mask. (Information leakage is dealt with using rejection sampling.) Recently, Persichetti proposed an efficient adaptation of this framework to coding theory (Persichetti E in Cryptography 2(4):30, 2018). In this paper, we show that this adaptation cannot be secure, even for one-time signatures (OTS), due to an inherent difference between bounds in Hamming and Euclidean metrics. The attack consists in rewriting a signature as a noisy syndrome decoding problem, which can be handled efficiently using the extended bit flipping decoding algorithm. We illustrate our results by breaking Persichetti’s OTS scheme built upon this approach (Persichetti 2018): using a single signature, we recover the secret (signing) key in about the same amount of time as required for a couple of signature verifications.

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Notes

  1. See https://csrc.nist.gov/projects/post-quantum-cryptography.

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Acknowledgements

The authors are grateful to the WCC 2019 and DCC reviewers for their careful reading and relevant comments that helped improving the quality of the present work.

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Authors and Affiliations

  1. École Nationale de l’Aviation Civile, Federal University of Toulouse, Toulouse, France

    Jean-Christophe Deneuville

  2. XLIM-MATHIS, University of Limoges, Limoges, France

    Philippe Gaborit

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  1. Jean-Christophe Deneuville
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  2. Philippe Gaborit
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Correspondence to Jean-Christophe Deneuville.

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The first version of this work [30] was presented in the “Eleventh International Workshop on Coding and Cryptography (WCC 2019)”.

This is one of several papers published in Designs, Codes and Cryptography comprising the “Special Issue on Coding and Cryptography 2019”.

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Deneuville, JC., Gaborit, P. Cryptanalysis of a code-based one-time signature. Des. Codes Cryptogr. 88, 1857–1866 (2020). https://doi.org/10.1007/s10623-020-00737-8

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  • DOI: https://doi.org/10.1007/s10623-020-00737-8

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