that quote is from the BIP-360 page
post quantum algorithms are a good thing. they are using merkle trees which layer hash functions. hashing the spend key into an address achieves the same thing, with the short time between posting a spend that reveals the key and when it is in a block. i have been working on a PQC signature algorithm, currently it's not very usable because it has a very high compute cost to generate but when i get back to working on it, i will figure out a way to do it. the signatures are only a little larger than elliptic curve keys, 128 bytes i think, so about 2x the size, but a lot less than FALCON's 600+ and all the rest, the signatures are absurdly large. mine uses a lattice algorithm on the bethe lattice. that's partly why the computation is so expensive, unlike standard lattices used for PQ signatures its a loop-free tree based structure. the cost of cracking it requires exploring branches of the tree and every layer deep you go, squares the cost of finding the exact path. regular lattices use ortholinear, they can loop and this is partly why they have so much bigger signatures. you can use paths in a bethe lattice to create compact signatures because it's just C^d where C is the coordination number (number of branches at each node) and d is the depth.
that's also why currently the algorithm is expensive to compute a signature. verification is quite fast though. there isn't any shortcuts because of the geometry of the bethe lattice.
anyway, it's something i will work on later.
in my opinion, BIP-360 is overthinking it. closing the quantum attack for the time between broadcast and block solutions is still better than nothing. you could even just change taproot so it sha256d the pubkey instead of leaving it naked. poelstra straight up lied about the security. he said it was fine because the secret is hashed in the tweak. but the spend authority on a branch of the root is the goddamn pubkey in the goddamn transaction. and luke didn't nack on it and now he's doing bip-110 but pepperidge farm remembers. coward. and this is also why bitcoin core devs should be shunned and ignored. they are either cowards or traitors.
