An Attack on Some Signature Schemes Constructed From Five-Pass Identification Schemes

Daniel Kales, Greg Zaverucha

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We present a generic forgery attack on signature schemes constructed from 5-round identification schemes made non-interactive with the Fiat-Shamir transform. The attack applies to ID schemes that use parallel repetition to decrease the soundness error. The attack can be mitigated by increasing the number of parallel repetitions, and our analysis of the attack facilitates parameter selection.

We apply the attack to MQDSS, a post-quantum signature scheme relying on the hardness of the MQ-problem. Concretely, forging a signature for the L1 instance of MQDSS, which should provide 128 bits of security, can be done in 2^95 operations. We verify the validity of the attack by implementing it for round-reduced versions of MQDSS, and the designers have revised their parameter choices accordingly.

We also survey other post-quantum signature algorithms and find the attack succeeds against PKP-DSS (a signature scheme based on the hardness of the permuted kernel problem) and list other schemes that may be affected. Finally, we use our analysis to choose parameters and investigate the performance of a 5-round variant of the Picnic scheme.
Original languageEnglish
Title of host publication19th International Conference on Cryptology and Network Security
PublisherSpringer
Publication statusAccepted/In press - 14 Sep 2020

Keywords

  • signatures
  • post-quantum cryptography
  • Fiat-Shamir heuristic

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    Kales, D., & Zaverucha, G. (Accepted/In press). An Attack on Some Signature Schemes Constructed From Five-Pass Identification Schemes. In 19th International Conference on Cryptology and Network Security Springer.