Security of Hedged Fiat-Shamir Signatures under Fault Attacks 📺
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.
Improving the Performance of the Picnic Signature Scheme 📺
Picnic is a digital signature algorithm designed to provide security against attacks by quantum computers. The design uses only symmetric-key primitives, and is an efficient instantiation of the MPC-in-the-head paradigm. In this work, we explore the Picnic design in great detail. We investigate and benchmark different parameter choices and show that there exist better parameter choices than those in the current specification. We also present improvements to the MPC protocol that shorten signatures and reduce signing time. The proposed MPC changes tailor the protocol to the circuit of interest in Picnic, but may also be of independent interest. Taken together, these changes give a new instantiation of Picnic that signs messages 7.9 to 13.9 times faster, and verifies signatures 4.5 to 5.5 times faster than the existing “Picnic2” design, while having nearly the same signature sizes.