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 22019-12-18T00:03:06  <aj> gmaxwell: slightly cheaper HTLC reveal (for sha256 preimage so you can't do a scriptless script) single musig(a,b) is cheaper than sig(a) plus script code to enforce op_csv delay
 32019-12-18T00:03:25  <aj> sipa: yeah, was kinda hoping you'd say that
 42019-12-18T00:05:36  <sipa> aj: so this is for applications where the participants would never agree to spend using the key path, but you're paying the cost for revealing a key anyway?
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 72019-12-18T01:28:51  <gmaxwell> oh, I see, so the 2of2 wants to sign, but only with a CSV, basically a kind of delegation to self plus CSV.
 82019-12-18T01:52:31  <gmaxwell> kinda lame that their CSV has to be pre-commited and isn't just part of their signature.
 92019-12-18T01:52:47  <gmaxwell> otherwise it could just be a keypath spend plus an added CSV.
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122019-12-18T01:59:29  <aj> gmaxwell: can't be a keypath spend because you want to reveal the sha256 preimage, the csv you can enforce via the signature
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532019-12-18T14:30:15  <_andrewtoth_> 243748
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592019-12-18T15:36:28  <pinheadmz> Where can I learn more about this?
602019-12-18T15:36:29  <pinheadmz>  For points P on the secp256k1 curve it holds that has_square_y(P) = not has_square_y(-P).
612019-12-18T15:37:02  <pinheadmz> Is this a property of all elliptic curves? i.e. for each X there exists one Y that is a quadratic residue and one that is not
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642019-12-18T16:14:20  <waxwing> pinheadmz, see note 6 in bip-schnorr; it's true because -1 is not a square mod p where p is the order of the finite field used for the coordinates. that's true because p is 3 mod 4.
652019-12-18T16:14:58  <waxwing> there's a note about that at the start of this wiki section: https://en.wikipedia.org/wiki/Quadratic_residue#Prime_modulus
662019-12-18T16:15:16  <waxwing> well not the start
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702019-12-18T16:57:58  <sipa> pinheadmz: or more mechanically, you can test that there is no point with x coordinate zero
712019-12-18T16:58:17  <sipa> (loading pubkey 0x020000... will fail)
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732019-12-18T17:08:43  <pinheadmz> brilliant, thanks
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