From 89ed4c9aab0064af9555b615c6ff63672d1c3730 Mon Sep 17 00:00:00 2001 From: Jonas Nick Date: Thu, 27 Jun 2019 11:08:58 +0000 Subject: [PATCH] Mention how to deal with MuSig rounds in multi-hop locks --- md/images/multi-hop-locks.png | Bin 88716 -> 97208 bytes md/images/multi-hop-locks.txt | 16 ++++++++-------- md/multi-hop-locks.md | 10 ++++++++-- 3 files changed, 16 insertions(+), 10 deletions(-) diff --git a/md/images/multi-hop-locks.png b/md/images/multi-hop-locks.png index 5ec0ef941dbc97a9e12a608d2c5a11f9c01da22b..7ed567b262189175e512f560e33ace25a968eb11 100644 GIT binary patch literal 97208 zcmb@ubzGEP*ET$&h>C)WN(rbaA~hf=9R}S>$AF;HAPqwr2#AP?gwl;P0+ItrDyc(C zOAj^D4euI^%jMHWd+oJX9P3!8uabh~kwY|x5D3H(X{npH5Qqb! z2*lo<14Qu6^=*R@_;txnT*J=L>VdQQz58|u$$OUfZ0^|IyL-mK`HZoh-2(w6@`3ps zOFMfDa}Gl*i({Ppr{NAPXcY~+-`^t;P7(g9J(fe9N8JLdMH?B-DQ;pdRK*Qck2`4F zU(2Zfpcu>&M3sGN`jfSBYt}$c^^- zTq??lkeT0quf+>nw}bE@l6GQIi(bxs!>`JJ#^9#EOunQgPQ*c<>HL=~!57$WE|*I$(N@%?8ZRFx7>Y7LK27WY}& 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zcpri9wt2>kk9ZNEhOIM5acL2$KE6ZsO7Izo&H8pYL;yhspOeUN?DrZ!GOMYhQ)WZ4 zPHB_$KX=5EP=?gNk#11nqAhe9W&bLf*V#ZSW+8x|d^8_;Xl%FyQT!Nky uPMJ&m`ZAa%aQ6zVUY5Ho|INsi%Bob : add 2-of-2 MuSig(A,B) output with timelocked refund to A -Bob->Alice : txB, psig(B,txB,(z+y0)*G) -Alice->Bob : psig(A,txB,(z+y0)*G) -Bob->Carol : add 2-of-2 MuSig(B,C) output with timelocked refund to B -Carol->Bob : txC, psig(C,txC,(z+y0+y1)*G) -Bob->Carol : psig(B,txC,(z+y0+y1)*G) -Carol->Dave : add 2-of-2 MuSig(C,D) output with timelocked refund to C -Dave->Carol : txD, psig(D,txD,(z+y0+y1+y2)*G) +Alice->Bob : add 2-of-2 MuSig(A,B) output with timelocked refund to A,\ncreate txB spending this to B, nonce(A,txB) +Bob->Alice : nonce(B,txB), psig(B,txB,(z+y0)*G) +Alice->Bob : psig(A,txB,(z+y0)*G) +Bob->Carol : add 2-of-2 MuSig(B,C) output with timelocked refund to B,\ncreate txC spending this to C, nonce(B,txC) +Carol->Bob : nonce(C,txC), psig(C,txC,(z+y0+y1)*G) +Bob->Carol : psig(B,txC,(z+y0+y1)*G) +Carol->Dave : add 2-of-2 MuSig(C,D) output with timelocked refund to C,\ncreate txD spending this to D, nonce(C,txD) +Dave->Carol : nonce(D,txD), psig(D,txD,(z+y0+y1+y2)*G) Carol->Dave : psig(C,txD,(z+y0+y1+y2)*G) == Settlement == diff --git a/md/multi-hop-locks.md b/md/multi-hop-locks.md index 48f6208..0080cb5 100644 --- a/md/multi-hop-locks.md +++ b/md/multi-hop-locks.md @@ -14,7 +14,8 @@ In addition, scriptless script multi-hop locks enable improved proof of payment Notation --- -- `psig(i,m,T) := ki + H(R+T,m)*xi` is a partial 2-of-2 MuSig from user `i` for `m` with combined nonce `R` (note that `R` has nothing to do with the right lock `R` defined below and we won't use `R` to mean the nonce again). +- `nonce(i, m)` is the public nonce of user `i` for a MuSig signature on `m` (note that we don't call nonces `R` here to avoid confusion with the right lock `R`). +- `psig(i,m,T) := ki + H(nonce(i,m)+nonce(j,m)+T,m)*xi` is a partial 2-of-2 MuSig from user `i` with user `j` for `m`. - `adaptor_sig(i,m,T) := psig(i,m,t*G) + t` - `sig(m,T) = psig(i,m,T) + adaptor_sig(j,m,T)` is the completed 2-of-2 MuSig from user i and j. It can be computed from a partial signature and an adaptor signature. @@ -41,7 +42,12 @@ But otherwise scriptless script HTLCs are plain 2-of-2 MuSig outputs and the has For demonstration purposes we assume [eltoo](https://blockstream.com/eltoo.pdf)-style channels which means that both parties have symmetric state and there's no need for revocation. If the payment does not time out, the coins in the scriptless script HTLC output shared by two adjacent hops will be spent by the right hop. -Therefore, the right hop `j` prepares a transaction `txj` spending the HTLC and partially signs it as `psig(j,txj,Lj)` which is similar to a regular partial signature except that its left lock `Lj` is added to the combined signature nonce. +Therefore, the left hop `i` creates a transaction `txj` that spends the HTLC and sends to coins to an output that the right hop `j` controls. +Because the left hop is now aware of the message (i.e. the transaction digest of `txj`) it is going to sign, its public signature nonce can be sent to the right hop. +Nonce commitments have been exchanged earlier whenever convenient for both nodes such that the nonce commitment roundtrips are not on the critical path of the payment. + +Upon receiving notice of the new HTLC and the left hops public nonce, the right hop `j` creates transaction `txj` as well, combines both nonces and partially signs `txj` as `psig(j,txj,Lj)`. +This is similar to a regular partial signature except that its left lock `Lj` is added to the combined signature nonce. The left hop verifies the partial signature and sends its own partial signature for `txj` to the right hop in the following two cases: - the left hop is the payer