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ZZZzzz…] 18:57 -!- Chris_Stewart_5 [~chris@unaffiliated/chris-stewart-5/x-3612383] has joined ##taproot-bip-review 19:13 -!- Chris_Stewart_5 [~chris@unaffiliated/chris-stewart-5/x-3612383] has quit [Ping timeout: 265 seconds] 19:32 -!- ZmnSCPxj [~ZmnSCPxj@180.190.53.119] has joined ##taproot-bip-review 19:36 < ZmnSCPxj> Given that R is sometimes called an "ephemeral key", why cannot we compose R using the same function as MuSig pubkey aggregation? 19:36 < ZmnSCPxj> i.e. MuSig(A, B) = h(sort({A, B}) | A) * A + h(sort({A, B}) | B) * B 19:37 < ZmnSCPxj> Then just use the same for R contributions from each aggregate member? 19:39 < ZmnSCPxj> Hmmm. 19:39 < ZmnSCPxj> Because you can still perform a Wagner attack on this method of aggregating R. 19:40 < aj> it's usually H( H(A,B), 1 ) not H(sort(A,B), A) isn't it? (to cope with duplicate keys) 19:41 < ZmnSCPxj> My understanding of MuSig is that it requires some canonical ordering of the keys, which is done by sorting the keys 19:42 < ZmnSCPxj> And duplicate keys are handled fine by a sort, they just get duplicated right next to each other 19:42 < aj> sure, but the |A part doesn't distinguish between them 19:46 < ZmnSCPxj> I see, but MuSig paper uses that. 19:47 < ZmnSCPxj> a[i] = h[agg](L, X[i]), then MuSig(X[1..n]) = sum where i = 1 to n of a[i] * X[i] 19:48 < ZmnSCPxj> And L is "uniquely encoded, e.g. lexicographical order", i.e. sorted 19:50 -!- jeremyrubin [~jr@c-67-180-60-249.hsd1.ca.comcast.net] has joined ##taproot-bip-review 19:50 < aj> yeah; but requires X[i] to be distinct. https://github.com/ElementsProject/secp256k1-zkp/blob/secp256k1-zkp/src/modules/musig/musig.md uses ,i and assumes P_i have some fixed ordering not necessarily sorted, i think 19:53 < aj> (i mean having the same key twice at the same level in a musig does seem pretty daft) 19:56 -!- jeremyrubin [~jr@c-67-180-60-249.hsd1.ca.comcast.net] has quit [Ping timeout: 240 seconds] 19:59 < gmaxwell> SECURE HARDER. TWO KEYS MORE STRONG THAN ONE KEY! 20:05 < aj> you've heard of 2-of-3 multisig, now try our battle hardened 5-of-3 multisig? 20:06 < aj> provides full access to all funds even with total loss of up to two of the original three keys! 20:18 -!- arik_ [~arik@c-73-162-137-55.hsd1.ca.comcast.net] has joined ##taproot-bip-review 20:24 -!- jeremyrubin [~jr@c-67-180-60-249.hsd1.ca.comcast.net] has joined ##taproot-bip-review 20:53 -!- davterra [~dulyNoded@37.120.149.156] has quit [Ping timeout: 252 seconds]