That's a great point. It's been solved in musig and that doesn't change the m of n multisig construction.

You use the same musig construction where you hash all keys and sum the multiples....and use that when computing k ... the shared blinding factor.... you're still improving the system .... Getting a nice Shamir m of n multisig.... with a single signature...and all the same properties otherwise.

On Thu, Jul 19, 2018, 9:11 AM Russell O'Connor <roconnor@blockstream.io> wrote:

On Thu, Jul 19, 2018 at 8:16 AM, Erik Aronesty via bitcoin-dev <bitcoin-dev@lists.linuxfoundation.org> wrote:
you can't birthday attack something where there's only a single variable that you can modify.

When engaging in a multiparty signature, the attacker can more than one variable to modify. When you are party to a multi-party signature (for example, in some sort of coin-join protocol) it could be that every other participant in the multi-party signature is, in fact, the same single attacker representing themselves as multiple participants. This is how the attacker gets their hands on multiple variables.