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Glacius: Threshold Schnorr Signatures from DDH with Full Adaptive Security

Authors:
Renas Bacho , CISPA Helmholtz Center for Information Security
Sourav Das , University of Illinois Urbana-Champaign
Julian Loss , CISPA Helmholtz Center for Information Security
Ling Ren , University of Illinois Urbana-Champaign
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Conference: EUROCRYPT 2025
Abstract: Threshold signatures are one of the most important cryptographic primitives in distributed systems. The threshold Schnorr signature scheme, an efficient and pairing-free scheme, is a popular choice and is included in NIST's standards and recent call for threshold cryptography. Despite its importance, most threshold Schnorr signature schemes assume a static adversary in their security proof. A recent scheme proposed by Katsumata et al. (Crypto 2024) addresses this issue. However, it requires linear-sized signing keys and lacks the identifiable abort property, which makes it vulnerable to denial-of-service attacks. Other schemes with adaptive security either have reduced corruption thresholds or rely on non-standard assumptions such as the algebraic group model (AGM) or hardness of the algebraic one-more discrete logarithm (AOMDL) problem. In this work, we present Glacius, the first threshold Schnorr signature scheme that overcomes all these issues. Glacius is adaptively secure based on the hardness of decisional Diffie-Hellman (DDH) in the random oracle model (ROM), and it supports a full corruption threshold $t
BibTeX
@inproceedings{eurocrypt-2025-35076,
  title={Glacius: Threshold Schnorr Signatures from DDH with Full Adaptive Security},
  publisher={Springer-Verlag},
  author={Renas Bacho and Sourav Das and Julian Loss and Ling Ren},
  year=2025
}