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Security of Hedged Fiat-Shamir Signatures under Fault Attacks

Authors:
Diego F. Aranha , Department of Engineering, DIGIT, Aarhus University, Denmark
Claudio Orlandi , Department of Computer Science, DIGIT, Aarhus University, Denmark
Akira Takahashi , Department of Computer Science, DIGIT, Aarhus University, Denmark
Greg Zaverucha , Microsoft Research, USA
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DOI: 10.1007/978-3-030-45721-1_23 (login may be required)
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Presentation: Slides
Conference: EUROCRYPT 2020
Abstract: Deterministic generation of per-signature randomness has been a widely accepted solution to mitigate the catastrophic risk of randomness failure in Fiat--Shamir type signature schemes. However, recent studies have practically demonstrated that such de-randomized schemes, including EdDSA, are vulnerable to differential fault attacks, which enable adversaries to recover the entire secret signing key, by artificially provoking randomness reuse or corrupting computation in other ways. In order to balance concerns of both randomness failures and the threat of fault injection, some signature designs are advocating a ``hedged'' derivation of the per-signature randomness, by hashing the secret key, message, and a nonce. Despite the growing popularity of the hedged paradigm in practical signature schemes, to the best of our knowledge, there has been no attempt to formally analyze the fault resilience of hedged signatures. We perform a formal security analysis of the fault resilience of signature schemes constructed via the Fiat--Shamir transform. We propose a model to characterize bit-tampering fault attacks, and investigate their impact across different steps of the signing operation. We prove that, for some types of faults, attacks are mitigated by the hedged paradigm, while attacks remain possible for others. As concrete case studies, we then apply our results to XEdDSA, a hedged version of EdDSA used in the Signal messaging protocol, and to Picnic2, a hedged Fiat--Shamir signature scheme in Round 2 of the NIST Post-Quantum standardization process.
Video from EUROCRYPT 2020
BibTeX
@inproceedings{eurocrypt-2020-30200,
  title={Security of Hedged Fiat-Shamir Signatures under Fault Attacks},
  booktitle={39th Annual International Conference on the Theory and Applications of Cryptographic Techniques, Zagreb, Croatia, May 10–14, 2020, Proceedings},
  series={Lecture Notes in Computer Science},
  publisher={Springer},
  keywords={Fiat-Shamir transform;fault attack;provable security;deterministic signature;hedged cryptography;EdDSA;Picnic},
  volume={12105},
  doi={10.1007/978-3-030-45721-1_23},
  author={Diego F. Aranha and Claudio Orlandi and Akira Takahashi and Greg Zaverucha},
  year=2020
}