Cryptanalysis of a rank-based signature with short public keys

Abstract

Following Schnorr framework for obtaining digital signatures, Song et al. recently proposed a new instantiation of a signature scheme featuring small public keys from coding assumptions in rank metric, which was accepted at PKC’19. Their proposal makes use of rank quasi-cyclic (RQC) codes to reduce the public key size. We show that it is possible to turn a valid, legitimate signature into an efficiently solvable decoding problem, which allows to recover the randomness used for signing and hence the secret key, from a single signature, in about the same amount of time as required for signing.

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Notes

  1. 1.

    Their results got accepted on Dec. 21st 2018 at PKC’19, made available as ePrint 2019/053 (https://eprint.iacr.org/eprint-bin/getfile.pl?entry=2019/053&version=20190125:204017&file=053.pdf) on Jan. 25th 2019, a cryptanalysis implementation was publicly released on Jan. 30th 2019 (https://github.com/deneuville/cryptanalysisSHMW), Lau and Tan (https://arxiv.org/pdf/1902.00241.pdf) then Xagawa (https://eprint.iacr.org/2019/120.pdf) published independently a description of the attack. The paper has been withdrawn since, both from ePrint and PKC’19, around Feb. 26th 2019. This work merges the implementation of Aragon et al., and the works of Lau and Tan, and Xagawa.

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Correspondence to Jean-Christophe Deneuville.

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This work was partially supported by the French DGA.

Communicated by R. Steinwandt.

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Aragon, N., Blazy, O., Deneuville, JC. et al. Cryptanalysis of a rank-based signature with short public keys. Des. Codes Cryptogr. 88, 643–653 (2020). https://doi.org/10.1007/s10623-019-00702-0

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Keywords

  • Post-quantum cryptography
  • Coding theory
  • Rank metric
  • RQC
  • Signature
  • Cryptanalysis

Mathematics Subject Classification

  • 94A60
  • 11T71
  • 14G50