Cryptology ePrint Archive: Report 2019/956

Security of Hedged Fiat-Shamir Signatures under Fault Attacks

Diego F. Aranha and Claudio Orlandi and Akira Takahashi and Greg Zaverucha

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.

Category / Keywords: public-key cryptography / signature schemes, fault attacks, Fiat-Shamir signatures, deterministic signatures, randomness failures, hedged cryptography, provable security

Original Publication (with major differences): IACR-EUROCRYPT-2020

Date: received 21 Aug 2019, last revised 23 Feb 2021

Contact author: gregz at microsoft com, orlandi at cs au dk, dfaranha at cs au dk, takahashi at cs au dk

Available format(s): PDF | BibTeX Citation

Note: Updated HVZK definition; revised the c-HVZK analysis of Picnic; added Appendix D

Version: 20210223:201006 (All versions of this report)

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