On Mon, Jul 9, 2018 at 3:02 PM, Erik Aronesty via bitcoin-dev <bitcoin-dev@lists.linuxfoundation.org> wrote: > and where H(g*x) can > be considered their public index for the purposes of Shamir polynomial > interpolation
This is isomorphic to the insecure musig variant where keys are blinded by H(g*x) instead of a commitment to all keys. It is insecure because it vulnerable to an attacker knowing a victim pubkey P who uses wagner's algorithim to solve a random modular subset sum problem: -1H(P) = H(aP)/a + H(bP)/b + H(cP)/c + ... for some a,b,c... then claiming to be participants with keys aP, bP, cP, ..., xG (their own key) and canceling out key P, allowing the value to just be signed for with their key alone. AFAICT your suggestion is using simple multiplication in the place of a cryptographic hash. E.g. you have just suggested a schnorr signature where H() is just r*m in the field of size n. It doesn't have any new properties about how you can use it. The same linearities do and don't apply as the normal schnorr construction, but for any of the security proofs to hold we'd have to believe that multiplication in the field of n is a suitable random oracle-- which is not very plausible. _______________________________________________ bitcoin-dev mailing list bitcoin-dev@lists.linuxfoundation.org https://lists.linuxfoundation.org/mailman/listinfo/bitcoin-dev
