In this commit, we build on the prior two commits by adding the ability
to generate partial musig2 signatures, validate them individually, and
finally combine them into a single signature.
Much of the logic here is unoptimized, and will be optimized in a later
commit. In addition, we also want to eventually have a nicer API to
support the book keeping necessary during multi signing.
In this commit, we add the ability to generate the secret+public nonces,
as well as combine a series of nonces into a single combined nonce
(which is used when doing multi signing).
In this commit, we add the set of key aggregation routines for musig2.
This includes the main public key aggregation method, as well as the
aggregation coefficient which is used to compute "mu" when signing.
The logic in this implementation is based on the musig2 paper, as well
as this spec:
https://github.com/ElementsProject/secp256k1-zkp/blob/master/doc/musig-spec.mediawiki.
In this commit, we optimize our signature implementation slightly, by
defining pre-computed sha256(tag) variables for the commonly used
values. If a tag matches this, then we'll use that hash value to avoid
an extra round of hashing.
In this commit, we add an initial implementation of BIP-340. Mirroring
the recently added `ecsda` package, we create a new `schnorr` package
with a unique `Signature` type and `ParsePubkey` function. The new
`Signature` type implements the fixed-sized 64-byte signatures, and the
`ParsePubkey` method only accepts pubkeys that are 32-bytes in length,
with an implicit sign byte.
The signing implementation by default, deviates from BIP-340 as it opts
to use rfc6979 deterministic signatures by default, which means callers
don't need to always pass in their own `auxNonce` randomness. A set of
functional arguments allows callers to pass in their own value, which is
the way all the included test vectors function.
The other optional functional argument added is the `FastSign` option
that allows callers to skip the final step of verifying each signature
they generate.
