[bitcoin-dev] BIP draft: Half-Aggregation of BIP-340 Signatures

[Jonas Nick <jonasdnick@gmail.com>]

Half-aggregation has been mentioned several times on this list in various
contexts. To have a solid basis for discussing applications of half-aggregation,
I think it's helpful to have a concrete specification of the scheme and a place
for collecting supplemental information like references to cryptographic
security proofs. You can find the BIP draft at

https://github.com/ElementsProject/cross-input-aggregation/blob/master/half-aggregation.mediawiki

Similar to BIP-340, this BIP draft specifies only the cryptographic scheme and
does not prescribe specific applications. It has not received an extensive
security review yet. Thanks to Elliott Jin and Tim Ruffing for the review so
far. One new feature that the specified scheme has is "incremental aggregation"
which allows aggregating additional BIP-340 signatures into an existing
half-aggregate signature.

While BIP-340 has a pseudocode specification and a reference implementation in
python, this BIP draft has a formal specification written in hacspec [0] and
auxiliary pseudocode. The formal specification is a mathematically precise
description of the scheme, which paves the way for computer-aided formal proofs.
Software tools ("proof assistants") allow proving properties about the formal
specification ("no integer overflow") and apply formal software verification
("implementation is behaviorally equivalent to the spec"). I don't have concrete
plans (nor the skillset) to use these techniques. Still, I think this is an
exciting area to explore because it has the potential to increase the Bitcoin
ecosystem's robustness significantly and has little downside. Since hacspec's
syntax is a subset of Rust's syntax, one can use the standard rust toolchain to
compile, execute and test the specification.

You can find a blog post that gives a broader context at
https://blog.blockstream.com/half-aggregation-of-bip-340-signatures/

[0] https://github.com/hacspec/hacspec