I'm struggling to understand one detail in DahLIA's algorithm: the use of 
R2 as a check and not R1 (or both). Is it just that only one is needed? Is 
it just an optimization?

Thanks,
AdamISZ/waxwing

On Thursday, April 17, 2025 at 10:38:46 AM UTC-6 Jonas Nick wrote:

> Hi list,
>
> Cross-Input Signature Aggregation (CISA) has been a recurring topic here, 
> aiming
> to reduce transaction sizes and verification cost [0]. Tim Ruffing, Yannick
> Seurin and I recently published DahLIAS, the first interactive aggregate
> signature scheme with constant-size signatures (64 bytes) compatible with
> secp256k1.
>
> https://eprint.iacr.org/2025/692.pdf
>
> Recall that in an aggregate signature scheme, each signer contributes 
> their own
> message, which distinguishes it from multi- and threshold signatures, 
> where all
> signers sign the same message. This makes aggregate signature schemes the
> natural cryptographic primitive for cross-input signature aggregation 
> because
> each transaction input typically requires signing a different message.
>
> Previous candidates for constant-size aggregate signatures either:
> - Required cryptographic assumptions quite different from the discrete 
> logarithm
> problem on secp256k1 currently used in Bitcoin signatures (e.g., groups 
> with
> efficient pairings).
> - Were "folklore" constructions, lacking detailed descriptions and security
> proofs.
>
> Besides presenting DahLIAS, the paper provides a proof that a class of 
> these
> folklore constructions are indeed secure if the signer does _not_ use key
> tweaking (e.g., no Taproot commitments or BIP 32 derivation). Moreover, we 
> show
> that there exists a concrete attack against a folklore aggregate signature
> scheme derived from MuSig2 when key tweaking is used.
>
> In contrast, DahLIAS is proven to be compatible with key tweaking. 
> Moreover, it
> requires two rounds of communication for signing, where the first round 
> can be
> run before the messages to be signed are known. Verification of DahLIAS
> signatures is asymptotically twice as fast as half-aggregate Schnorr 
> signatures
> and as batch verification of individual Schnorr signatures.
>
> We believe DahLIAS offers an attractive building block for a potential CISA
> proposal and welcome any feedback or discussion.
>
> Jonas Nick, Tim Ruffing, Yannick Seurin
>
>
> [0] See, e.g., https://cisaresearch.org/ for a summary of various CISA
> discussions.
>

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