Paper 2023/899
Practical Schnorr Threshold Signatures Without the Algebraic Group Model
, Friedrich-Alexander-Universität Erlangen-Nürnberg, Friedrich-Alexander-Universität Erlangen-Nürnberg, Blockstream Research, Friedrich-Alexander-Universität Erlangen-NürnbergAbstract
Threshold signatures are digital signature schemes in which a set of $n$ signers specify a threshold $t$ such that any subset of size $t$ is authorized to produce signatures on behalf of the group. There has recently been a renewed interest in this primitive, largely driven by the need to secure highly valuable signing keys, e.g., DNSSEC keys or keys protecting digital wallets in the cryptocurrency ecosystem. Of special interest is FROST, a practical Schnorr threshold signature scheme, which is currently undergoing standardization in the IETF and whose security was recently analyzed at CRYPTO'22. We continue this line of research by focusing on FROST's unforgeability combined with a practical distributed key generation (DKG) algorithm. Existing proofs of this setup either use non-standard heuristics, idealized group models like the AGM, or idealized key generation. Moreover, existing proofs do not consider all practical relevant optimizations that have been proposed. We close this gap between theory and practice by presenting the Schnorr threshold signature scheme Olaf, which combines the most efficient known FROST variant FROST3 with a variant of Pedersen's DKG protocol (as commonly used for FROST), and prove its unforgeability. Our proof relies on the AOMDL assumption (a weaker and falsifiable variant of the OMDL assumption) and, like proofs of regular Schnorr signatures, on the random oracle model.
Note: Fixed typos.
Metadata
- Available format(s)
-
PDF
- Category
- Public-key cryptography
- Publication info
- Published by the IACR in CRYPTO 2023
- DOI
- 10.1007/978-3-031-38557-5_24
- Keywords
- Threshold SignaturesSchnorr SignaturesFROST
- Contact author(s)
-
hien chu @ fau de
paul gerhart @ fau de
crypto @ timruffing de
dominique schroeder @ fau de - History
- 2023-08-22: revised
- 2023-06-09: received
- See all versions
- Short URL
- https://ia.cr/2023/899
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2023/899,
author = {Hien Chu and Paul Gerhart and Tim Ruffing and Dominique Schröder},
title = {Practical Schnorr Threshold Signatures Without the Algebraic Group Model},
howpublished = {Cryptology {ePrint} Archive, Paper 2023/899},
year = {2023},
doi = {10.1007/978-3-031-38557-5_24},
url = {https://eprint.iacr.org/2023/899}
}
