Foundations of Adaptor Signatures
Adaptor signatures extend the functionality of regular signatures through the computation of pre-signatures on messages for statements of NP relations. Pre-signatures are publicly verifiable; they simultaneously hide and commit to a signature of an underlying signature scheme on that message. Anybody possessing a corresponding witness for the statement can adapt the pre-signature to obtain the ``regular'' signature. Adaptor signatures have found numerous applications for conditional payments in blockchain systems, like payment channels~(CCS'20, CCS'21), private coin mixing (CCS'22, SP'23), and oracle-based payments (NDSS'23). In our work, we revisit the state of the security of adaptor signatures and their constructions. In particular, our two main contributions are: - Security Gaps and Definitions: We review the widely-used security model of adaptor signatures due to Aumayr et al. (ASIACRYPT'21), and identify gaps in their definitions that render known protocols for private coin-mixing and oracle-based payments insecure. We give simple counterexamples of adaptor signatures that are secure w.r.t. their definitions, but result in insecure instantiations of these protocols. To fill these gaps, we identify a minimal set of modular definitions that align with these practical applications. - Secure Constructions: Despite their popularity, all known constructions are (1) derived from identification schemes via the Fiat-Shamir transform in the random oracle model or (2) require modifications to the underlying signature verification algorithm, thus making the construction useless in the setting of cryptocurrencies. More concerningly, all known constructions were proven secure w.r.t. the insufficient definitions of Aumayr et al., leaving us with no provably secure adaptor signature scheme to use in applications. Firstly, in this work, we salvage all current applications by proving security of the widely-used Schnorr adaptor signatures under our proposed definitions. We then provide several new constructions, including presenting the first adaptor signature schemes for Camenisch-Lysyanskaya (CL), Boneh-Boyen-Shacham (BBS+), and Waters signatures; all of which are proven secure in the standard model. Our new constructions rely on a new abstraction of digital signatures, called dichotomic signatures, which covers the essential properties we need to build adaptor signatures. Proving the security of all constructions (including identification-based schemes) relies on a novel non-black-box proof technique. Both our digital signature abstraction and the proof technique could be of independent interest to the community.
Practical Schnorr Threshold Signatures Without the Algebraic Group Model
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.