Why does signature half aggregation break adaptor signatures?
6 minute readThere is this cool trick you can do with Schnorr signatures. It is called Adaptor Signature (AS). An adaptor signature is an extra signature that, combined with the original signature, allow for revealing a value that was previously hidden. You can use this trick to solve trust problems as they appear in atomic swaps, coin swaps and Discreet Log Contracts (DLCs).
Signature Aggregation (SA) is a way to aggregate multiple signatures into a single signature. The single aggregate signature is smaller (in bytes) than the original signatures combined. It reduces transaction weight, meaning we can have more transactions per block, which is always a good thing. It's like 7zip for transactions. Signature Half Aggregation is a variant of SA that only aggregates half of each signature. It offers less compression, but it has the benefit of not requiring any interaction with the signers, whereas full aggregation does require cooperation of all the signers.
So two cool tricks, but the latter breaks the former when it is used for blockwide signature aggregation. This article explains the math behind it and why SA breaks AS
I like it! I can think of a few use cases. There will be a day in the near future where I am going to use it, for sure.