sipa changed the topic of #bitcoin-wizards to: This channel is for discussing theoretical ideas with regard to cryptocurrencies, not about short-term Bitcoin development | http://bitcoin.ninja/ | This channel is logged. | For logs and more information, visit http://bitcoin.ninja
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<kallewoof>
Sorry for stupid question, but someone claimed that you can't securely do aggregation of signatures in Taproot (i.e. the "key spend" version) without knowing the internal private key. It seems to me that you can do so: Alice and Bob create k_a, k_b and share H(k_aG) and H(k_bG) with each other, then k_aG and k_bG, to get kG = (k_a + k_b)G. They generate and combine s_a = k_a + H(r,P,m)d_a and s_b = k_b + H(r,P,m)d_b to get
<kallewoof>
(k_a+k_b) + H(r,P,M)(d_a+d_b). For taproot, one of them would include the tweak in their part of the s, e.g. s_a = k_a + H(r,P,m)(t + d_a) to get s = (k_a+k_b) + H(r,P,m)(d_a + d_b + t). This seems to satisfy the equation. Is it broken or vulnerable to something?
<zmnscpxj>
Not that I know of.
<zmnscpxj>
First time I heard it was insecure
<sipa>
that's how i expect it to work; the tweaking at signing time can also be done by a third party that doesn't actually have a private key
<sipa>
i don't see why it would be insecure
<aj>
oh no, why is zman lowercase?
<kallewoof>
OK! Misunderstood then, thanks :)
<zmnscpxj>
maybe I am an impostor
<zmnscpxj>
In a little while I will be ranting about znn.
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<aj>
kallewoof: with r=kG and P=(d_aG+d_bG) and yeah, that looks right to me too
<zmnscpxj>
Fine, the OS insists on lowercasing my username, then I could not find out how this IRC client can override the nick
<kallewoof>
aj: right! Ok, cool :)
<zmnscpxj>
then I registered to freenode with the lowercased nick, so ----
<aj>
zmnscpxj: well, lowercase nicks are cool, so you've got that going for you
<sipa>
it's only a mild reduction in entropy
<zmnscpxj>
I suppose ....
<zmnscpxj>
It reduces by 1 bit for each character, this is an entire loss of 8 bits of entropy
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<UPPERNICK>
WRONG
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<zmnscpxj>
aj: you have been refuted
<aj>
i've been disputed, not refuted
<sipa>
i wonder who that was!
<zmnscpxj>
no, UPPERNICK was definitely cool.
<aj>
no, you'd need to find a lowercase nick that's not cool to refute me, not an uppercase nick that is cool
<zmnscpxj>
right, elementary logic
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<zmnscpxj>
lowercase -> cool, therefore !cool -> !lowercase, then !cool && lowercase refutes it
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<midnight>
lol I wish more driveby IRC people were that funny. oh well.
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<waxwing>
aj, i think you mean P=(d_aG + d_bG + tG)
<waxwing>
hmm segwit v1 witness bip number is a permutation of transaction digest for v0 bip number ...
<sipa>
waxwing: it's true for the sighash spec
<sipa>
(341 gives v1 sighash spec among other things, 143 gives v0 sighash spec)
<waxwing>
so did i miss something, why frame it in those terms kallewoof , if we do a 2 of 2 multisig wouldn't we just use musig directly on the key Q in Q = P + tG?, i.e. ignore t?
<waxwing>
or is there some reason you want to split it up ... oh to preserve a possible non-key path spend
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