From 4c062451d3e977b136f61ca8a0481f02b571cdff Mon Sep 17 00:00:00 2001 From: Daira Hopwood Date: Fri, 8 Apr 2016 20:55:49 +0100 Subject: [PATCH] Minor refinements. refs #14 Signed-off-by: Daira Hopwood --- protocol/protocol.pdf | Bin 808097 -> 808092 bytes protocol/protocol.tex | 8 +++++--- 2 files changed, 5 insertions(+), 3 deletions(-) diff --git a/protocol/protocol.pdf b/protocol/protocol.pdf index 8b4e9908b7e0e3cfd8051462373d234477775091..4551142b75c99739af26ac8afc83621978e29bf1 100644 GIT binary patch delta 40167 zcmV(@K-RyZsWF_XF|diD1T-);H0FYg zP17dsv@@4`pe6dmoJ=Vqbw2m6?=Aom1O>|SrS0^^q(~4SyT9H2?E)r?cMG!k`il7L zmp50Re?{e@$P2~P;^uB4#X>WkQw_h?i#OTLrn-K6^X=zfDK%=vNG>GwV4F0%u7A2- za!#_QegUCO3-qUH?QR`TNa3vD@$Ap1M!Hnt$M~_DBrAM3WOnib-MDhF7&ez=x0E4N4gxNO$$20ODit8!o7)~Iw?`=ft}GoU)N;?^MU zwfkLns6uYCZ+6%4`~g3yK7ZK12V52-8S1v#*6;CsH5sZG@JrttH0}JY2NK|BBsRo; zFe<=)N{>1>+yt2Wp?==oj^&`?jTJOb2MvC-OobTjs+C7Q*E%P1BHZ#_SvMB4oM-FZ z@pfA+2Q04Z=G{y8%Ay&rwQuSimB`BdAj##f**;zyp5=Bt0t1ng@Sr- 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Let $\MerkleNode{h}{i}$ be the hash associated with the \merkleNode at \merkleIndex $i$ in \merkleLayer $h$. -Parent \merkleNodes are computed from their children as follows. For $0 \leq h < d$ +Parent \merkleNodes are computed from their children as follows. For $0 \leq h < \MerkleDepth$ and $0 \leq i < 2^h$, \newsavebox{\merklebox} @@ -771,7 +771,8 @@ When a \noteCommitment is added to the tree, it occupies the \merkleLeaf $\MerkleNode{\MerkleDepth}{i}$ for the next available $i$. As-yet unused \merkleLeaves are encoded as the sequence of 32 zero bytes. -A \merklePath from \merkleLeaf $i$ in the \incrementalMerkleTree is the sequence +A \merklePath from \merkleLeaf $\MerkleNode{\MerkleDepth}{i}$ in the +\incrementalMerkleTree is the sequence \hskip 2em $[\MerkleNode{h}{\MerkleSibling(h, i)} \text{ for } h \text{ from } \MerkleDepth \text{ down to } 1]$, @@ -781,7 +782,8 @@ where \hskip 2em $\MerkleSibling(h, i) = \floor\left(\frac{i}{2^{\MerkleDepth-h}}\right) \xor 1$ and $\xor$ denotes bitwise exclusive or. Given such a \merklePath, it is -possible to verify that the \merkleLeaf is in a tree with a given \merkleRoot. +possible to verify that \merkleLeaf $\MerkleNode{\MerkleDepth}{i}$ is in a tree +with a given \merkleRoot $\rt = \MerkleNode{0}{0}$. \subsection{\NullifierSet}