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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<t-bast>
My main question is: is it safe to re-use a MuSig nonce (R) once collaboratively generated to sign multiple messages?
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<t-bast>
in the multi-hop-locks example, if each pair of participants needs to generate R only once and can then re-use it for each HTLC, it's great
<t-bast>
if they need to re-generate a shared nonce for each HTLC, it becomes very expensive
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<t-bast>
it seems to me that participants can safely re-use a nonce for signing multiple messages safely, but I can't prove it and I didn't find a section in the MuSig paper talking about this
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<t-bast>
hum actually scratch that, it looks like re-using nonce with schnorr signature almost trivially reveals the private key if the attacker knows both messages...
<nickler>
A nonce is an arbitrary number that can be used just once. Please don't reuse it in scriptless scripts, ecdsa signatures or anywhere else.
<t-bast>
so each "add 2-of-2 MuSig() output with timelocked refund" arrow means that you have to do to 3 roundtrips right? 2 to generate a new MuSig nonce and then the arrows displayed on the picture?
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<t-bast>
thx for your answer, I agree that usually nonces should never be re-used but I stumbled upon this paper which allows nonce re-use with Schnorr, so I was hoping it would be somehow possible: https://eprint.iacr.org/2018/069.pdf
<t-bast>
because otherwise I'm really concerned with the latency hit it imposes on lightning payments...
<nickler>
t-bast: the first round, exchanging nonce commitments can be done earlier whenever there's time for it
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<t-bast>
nickler: good point, correct me if I'm wrong but nothing prevents two channels participants to generate multiple nonces at once right? I'm thinking that at channel creation the two channel participants could generate a batch of X nonces (with only 2 round trips) and then slowly using them as HTLCs come in
<t-bast>
nickler: and when the reserve of nonces is getting low they could generate a next batch of nonces
<t-bast>
nickler: btw you're only mentioning the first round (commitments) but it should be safe to exchange the nonces themselves ahead of time too right?
<nickler>
but thanks for mentioning the roundtrips, I'll update the diagram
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<t-bast>
Interesting, thanks for mentioning that. The attacker (channel participant) would probably be able to grind HTLCs by trying a lot of amounts until it successfully executes wagner's attack, and then can use that HTLC on the other participant...
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<t-bast>
But at least the commitments can be pre-generated, that's one less roundtrip during the payment ;)
<t-bast>
thanks for your answers nickler
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<nickler>
fwiw the nonce-reuse paper doesn't apply to secp256k1 because there are no subgroups. Also requires signatures to be larger
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<t-bast>
yeah, I was thinking that it would be too good to be true if it could be easily adapted to secp256k1 and without any cost...but wanted to mention it just in case ;)
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