--- Log opened Tue Mar 24 00:00:31 2020
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07:52 < bsm117532> It seems to me that this monotone boolean function of pubkeys as a Schnorr threshold multisignature works as I had thought. (ignoring questions of efficiency)
07:53 < bsm117532> To elaborate: Let P = p1 p2 G + p2 p3 G + p1 p3 G be the 2-of-3 aggregate pubkey, where multiplication represents an AND operation and addition represents an OR operation.
07:53 < bsm117532> (You can therefore create any monotone boolean access structure as a single pubkey this way)
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07:54 < bsm117532> To sign: 1 and 2 create a signature by agreeing on k and computing s G = k G + H(k G | P | m) p1 p2 G
07:55 < bsm117532> (this is not a valid Schnorr signature since the effective pubkey p1 p2 G does not match the pubkey P inside the hash)
07:56 < bsm117532> They then need to malleate s to make it a valid signature. To do this they need to add the constant a = (p1 p3 + p2 p3) H(k G | P | m) G to s.
07:56 < bsm117532> If party 1 knows the combination p1 p3 G and party 2 knows the combination p2 p3 G, they can collaborate to create a.
07:57 < bsm117532> (each party knows the product of his private key with all necessary combinations of the other pubkeys)
07:59 < bsm117532> Does this work as a threshold multisignature algorithm? (up to sipa's point about DLEQ and efficiency due to choose(n,m) terms)
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09:21 < bsm117532> (NO) Since I need to share p1 p3 (which is a scalar) not p1 p3 G (which is an ECC point) to compute a. If the signatories knew this, they would be able to compute each other's private keys by (p1 p2)/p1 in Z_p.
09:22 < bsm117532> I need to insert some more hashes...
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--- Log closed Wed Mar 25 00:00:29 2020