Post-quantum solutions for Bitcoin

[kayabaNerve]

The most trivial solution to implement over Bitcoin would likely be Lamport signatures. These are also the least amenable to threshold signatures, effectively mandating FHE with a threshold-split signing key. Such a solution would be universal to all cryptocurrencies we wish to integrate however.

With the adoption of covenants, we likely could implement any threshold scheme we want (such as Raccoon's, Mayo/UOV's or a dedicated threshold scheme (not a single-signer scheme with a threshold scheme later produced)). The sole question will be the complexity of building such a script and verifying it on-Bitcoin (along with the on-chain costs). Lamport signatures win in that regard, solely having a horrible off-chain complexity.

Bitcoin will presumably enshrine some post-quantum signature standard, and more-efficient threshold schemes for popular candidates will also likely be posited, giving us some flexibility.