mirror of https://github.com/zcash/zips.git
1649 lines
64 KiB
TeX
1649 lines
64 KiB
TeX
\documentclass{article}
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\RequirePackage{amsmath}
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\RequirePackage{bytefield}
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\RequirePackage{graphicx}
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\RequirePackage{newtxmath}
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\RequirePackage{mathtools}
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\RequirePackage{xspace}
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\RequirePackage{url}
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\RequirePackage{changepage}
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\RequirePackage{lmodern}
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\RequirePackage[unicode,bookmarksnumbered,bookmarksopen,pdfview=Fit]{hyperref}
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\RequirePackage{nameref}
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\RequirePackage{enumitem}
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\RequirePackage{tabularx}
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\RequirePackage{hhline}
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\RequirePackage{comment}
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\RequirePackage{bold-extra}
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\setlength{\oddsidemargin}{-0.25in} % Left margin of 1 in + 0 in = 1 in
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\setlength{\textwidth}{7in} % Right margin of 8.5 in - 1 in - 6.5 in = 1 in
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\setlength{\topmargin}{-.75in} % Top margin of 2 in -0.75 in = 1 in
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\setlength{\textheight}{9.2in} % Lower margin of 11 in - 9 in - 1 in = 1 in
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\setlength{\parskip}{1.5ex}
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\setlength{\parindent}{0ex}
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\renewcommand{\arraystretch}{1.4}
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\overfullrule=2cm
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\setlist[itemize]{itemsep=0.5ex,topsep=0.2ex,after=\vspace{1.5ex}}
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\newcommand{\doctitle}{Zcash Protocol Specification}
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\newcommand{\docversion}{Version 2.0-alpha-2}
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\newcommand{\leadauthor}{Daira Hopwood}
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\newcommand{\coauthors}{Sean Bowe | Taylor Hornby | Nathan Wilcox}
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\hypersetup{
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pdfborderstyle={/S/U/W 0.7},
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pdfinfo={
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Title={\doctitle, \docversion},
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Author={\leadauthor\ | \coauthors}
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}
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}
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\renewcommand{\sectionautorefname}{\S\!}
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\renewcommand{\subsectionautorefname}{\S\!}
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\renewcommand{\subsubsectionautorefname}{\S\!}
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\newcommand{\crossref}[1]{\autoref{#1} \emph{`\nameref*{#1}\kern -0.1em'} on p.\,\pageref*{#1}}
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\mathchardef\mhyphen="2D
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\RequirePackage[usenames,dvipsnames]{xcolor}
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% https://en.wikibooks.org/wiki/LaTeX/Colors#The_68_standard_colors_known_to_dvips
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\newcommand{\eli}[1]{{\color{JungleGreen}\sf{Eli: #1}}}
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\newcommand{\sean}[1]{{\color{blue}\sf{Sean: #1}}}
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\newcommand{\taylor}[1]{{\color{red}\sf{Taylor: #1}}}
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\newcommand{\daira}[1]{{\color{RedOrange}\sf{Daira: #1}}}
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\newcommand{\nathan}[1]{{\color{ForestGreen}\sf{Nathan: #1}}}
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\newcommand{\todo}[1]{{\color{Sepia}\sf{TODO: #1}}}
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\newcommand{\changedcolor}{magenta}
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\newcommand{\setchanged}{\color{\changedcolor}}
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\newcommand{\changed}[1]{\texorpdfstring{{\setchanged{#1}}}{#1}}
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% bold but not extended
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\newcommand{\textbnx}[1]{{\fontseries{b}\selectfont #1}}
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% terminology
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\newcommand{\term}[1]{\textsl{#1}\xspace}
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\newcommand{\titleterm}[1]{#1}
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\newcommand{\termbf}[1]{\textbf{#1}\xspace}
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\newcommand{\conformance}[1]{\textbnx{#1}\xspace}
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\newcommand{\Zcash}{\termbf{Zcash}}
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\newcommand{\Zerocash}{\termbf{Zerocash}}
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\newcommand{\Bitcoin}{\termbf{Bitcoin}}
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\newcommand{\ZEC}{\termbf{ZEC}}
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\newcommand{\zatoshi}{\term{zatoshi}}
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\newcommand{\MUST}{\conformance{MUST}}
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\newcommand{\MUSTNOT}{\conformance{MUST NOT}}
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\newcommand{\SHOULD}{\conformance{SHOULD}}
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\newcommand{\SHOULDNOT}{\conformance{SHOULD NOT}}
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\newcommand{\note}{\term{note}}
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\newcommand{\notes}{\term{notes}}
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\newcommand{\Note}{Note}
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\newcommand{\Notes}{Notes}
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\newcommand{\noteCommitment}{\term{note commitment}}
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\newcommand{\noteCommitments}{\term{note commitments}}
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\newcommand{\NoteCommitment}{\titleterm{Note Commitment}}
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\newcommand{\NoteCommitments}{\titleterm{Note Commitments}}
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\newcommand{\noteCommitmentTree}{\term{note commitment tree}}
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\newcommand{\joinSplitDescription}{\term{JoinSplit description}}
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\newcommand{\joinSplitDescriptions}{\term{JoinSplit descriptions}}
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\newcommand{\sequenceOfJoinSplitDescriptions}{\changed{sequence of} \joinSplitDescription\changed{\term{s}}\xspace}
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\newcommand{\joinSplitTransfer}{\term{JoinSplit operation}}
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\newcommand{\joinSplitTransfers}{\term{JoinSplit operations}}
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\newcommand{\JoinSplitTransfer}{\titleterm{JoinSplit Operation}}
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\newcommand{\JoinSplitTransfers}{\titleterm{JoinSplit Operations}}
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\newcommand{\joinSplitSignature}{\term{JoinSplit signature}}
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\newcommand{\fullnode}{\term{full node}}
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\newcommand{\fullnodes}{\term{full nodes}}
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\newcommand{\anchor}{\term{anchor}}
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\newcommand{\anchors}{\term{anchors}}
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\newcommand{\block}{\term{block}}
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\newcommand{\blocks}{\term{blocks}}
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\newcommand{\transaction}{\term{transaction}}
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\newcommand{\transactions}{\term{transactions}}
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\newcommand{\blockchainview}{\term{blockchain view}}
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\newcommand{\mempool}{\term{mempool}}
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\newcommand{\treestate}{\term{treestate}}
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\newcommand{\treestates}{\term{treestates}}
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\newcommand{\nullifier}{\term{nullifier}}
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\newcommand{\nullifiers}{\term{nullifiers}}
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\newcommand{\Nullifier}{\titleterm{Nullifier}}
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\newcommand{\Nullifiers}{\titleterm{Nullifiers}}
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\newcommand{\nullifierSet}{\term{nullifier set}}
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\newcommand{\NullifierSet}{\titleterm{Nullifier Set}}
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% Daira: This doesn't adequately distinguish between zk stuff and transparent stuff
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\newcommand{\paymentAddress}{\term{payment address}}
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\newcommand{\paymentAddresses}{\term{payment addresses}}
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\newcommand{\viewingKey}{\term{viewing key}}
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\newcommand{\viewingKeys}{\term{viewing keys}}
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\newcommand{\spendingKey}{\term{spending key}}
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\newcommand{\spendingKeys}{\term{spending keys}}
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\newcommand{\keyTuple}{\term{key tuple}}
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\newcommand{\notePlaintext}{\term{note plaintext}}
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\newcommand{\notePlaintexts}{\term{note plaintexts}}
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\newcommand{\NotePlaintexts}{\titleterm{Note Plaintexts}}
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\newcommand{\notesCiphertext}{\term{transmitted notes ciphertext}}
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\newcommand{\authKeypair}{\term{authorization}}
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\newcommand{\transmitKeypair}{\term{transmission}}
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\newcommand{\discloseKey}{\term{disclosure key}}
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\newcommand{\incrementalMerkleTree}{\term{incremental Merkle tree}}
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\newcommand{\merkleRoot}{\term{root}}
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\newcommand{\merkleNode}{\term{node}}
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\newcommand{\merkleNodes}{\term{nodes}}
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\newcommand{\merkleLeaf}{\term{leaf}}
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\newcommand{\merkleLeaves}{\term{leaves}}
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\newcommand{\merklePath}{\term{path}}
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\newcommand{\merkleLayer}{\term{layer}}
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\newcommand{\merkleIndex}{\term{index}}
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\newcommand{\merkleIndices}{\term{indices}}
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\newcommand{\zkSNARK}{\term{zk-SNARK}}
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\newcommand{\zkSNARKs}{\term{zk-SNARKs}}
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\newcommand{\memo}{\term{memo field}}
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\newcommand{\Memos}{\titleterm{Memo Fields}}
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% conventions
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\newcommand{\bytes}[1]{\underline{\raisebox{-0.22ex}{}\smash{#1}}}
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\newcommand{\zeros}[1]{[0]^{#1}}
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\newcommand{\hexint}[1]{\mathbf{0x{#1}}}
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\newcommand{\dontcare}{\kern -0.06em\raisebox{0.1ex}{\footnotesize{$\times$}}}
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\newcommand{\ascii}[1]{\textbf{``\texttt{#1}"}}
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\newcommand{\CRH}{\mathsf{CRH}}
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\newcommand{\CRHbox}[1]{\CRH\left(\;\raisebox{-1.3ex}{\usebox{#1}}\;\right)}
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\newcommand{\SHA}{\mathtt{SHA256Compress}}
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\newcommand{\SHAName}{\term{SHA-256 compression}}
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\newcommand{\FullHash}{\mathtt{SHA256}}
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\newcommand{\FullHashName}{\term{SHA-256}}
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\newcommand{\BlakeHash}{\mathtt{BLAKE2b\kern 0.05em\mhyphen256}}
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\newcommand{\BlakeHashName}{\term{BLAKE2b\kern 0.05em-256}}
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\newcommand{\BlakeFullLength}{\term{BLAKE2b}}
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\newcommand{\FullHashbox}[1]{\FullHash\left(\;\raisebox{-1.3ex}{\usebox{#1}}\;\right)}
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\newcommand{\Justthebox}[2]{\;\raisebox{#2}{\usebox{#1}}\;}
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\newcommand{\setof}[1]{\{{#1}\}}
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\newcommand{\minimum}{\mathsf{min}}
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\newcommand{\floor}{\mathsf{floor}}
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\newcommand{\xor}{\oplus}
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% key pairs:
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\newcommand{\PaymentAddress}{\mathsf{addr_{pk}}}
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\newcommand{\SpendingKey}{\mathsf{addr_{sk}}}
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\newcommand{\PaymentAddressLeadByte}{\hexint{92}}
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\newcommand{\SpendingKeyLeadByte}{\hexint{??}}
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\newcommand{\NotePlaintextLeadByte}{\hexint{00}}
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\newcommand{\AuthPublic}{\mathsf{a_{pk}}}
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\newcommand{\AuthPrivate}{\mathsf{a_{sk}}}
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\newcommand{\AuthPublicOld}[1]{\mathsf{a^{old}_{pk,\mathnormal{#1}}}}
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\newcommand{\AuthPrivateOld}[1]{\mathsf{a^{old}_{sk,\mathnormal{#1}}}}
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\newcommand{\AuthPublicNew}[1]{\mathsf{a^{new}_{pk,\mathnormal{#1}}}}
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\newcommand{\AuthPrivateNew}[1]{\mathsf{a^{new}_{sk,\mathnormal{#1}}}}
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\newcommand{\AddressPublicNew}[1]{\mathsf{addr^{new}_{pk,\mathnormal{#1}}}}
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\newcommand{\enc}{\mathsf{enc}}
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\newcommand{\disclose}{\mathsf{disclose}}
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\newcommand{\shared}{\mathsf{shared}}
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\newcommand{\DHSecret}[1]{\mathsf{dhsecret}_{#1}}
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\newcommand{\DHSecretCompare}[1]{\mathsf{dhsecret}^*_{#1}}
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\newcommand{\EphemeralPublic}{\mathsf{epk}}
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\newcommand{\EphemeralPublicCompare}{\mathsf{epk}^*}
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\newcommand{\EphemeralPrivate}{\mathsf{esk}}
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\newcommand{\EphemeralPrivateClamped}{\mathsf{esk_{clamped}}}
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\newcommand{\TransmitPublic}{\mathsf{pk_{enc}}}
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\newcommand{\TransmitPublicNew}[1]{\mathsf{pk^{new}_{\enc,\mathnormal{#1}}}}
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\newcommand{\TransmitPrivate}{\mathsf{sk_{enc}}}
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\newcommand{\Value}{\mathsf{v}}
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\newcommand{\ValueNew}[1]{\mathsf{v^{new}_\mathnormal{#1}}}
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\newcommand{\pubKeyHash}{\mathsf{pubKeyHash}}
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\newcommand{\hSigInput}{\mathsf{hSigInput}}
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\newcommand{\dataToBeSigned}{\mathsf{dataToBeSigned}}
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% Notes
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\newcommand{\NoteTuple}[1]{\mathbf{n}_{#1}}
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\newcommand{\NotePlaintext}[1]{\mathbf{np}_{#1}}
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\newcommand{\NoteCommitRand}{\mathsf{r}}
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\newcommand{\NoteCommitRandOld}[1]{\mathsf{r^{old}_\mathnormal{#1}}}
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\newcommand{\NoteCommitRandNew}[1]{\mathsf{r^{new}_\mathnormal{#1}}}
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\newcommand{\NoteAddressRand}{\mathsf{\uprho}}
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\newcommand{\NoteAddressRandOld}[1]{\mathsf{\uprho^{old}_\mathnormal{#1}}}
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\newcommand{\NoteAddressRandNew}[1]{\mathsf{\uprho^{new}_\mathnormal{#1}}}
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\newcommand{\NoteAddressPreRand}{\mathsf{\upvarphi}}
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\newcommand{\NoteCommitS}{\mathsf{s}}
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\newcommand{\nf}{\mathsf{nf}}
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\newcommand{\nfOld}[1]{\nf^\mathsf{old}_\mathnormal{#1}}
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\newcommand{\Memo}{\mathsf{memo}}
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\newcommand{\CurveMultiply}{\mathsf{Curve25519}}
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\newcommand{\CurveBase}{\bytes{9}}
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\newcommand{\DecryptNote}{\mathtt{DecryptNote}}
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\newcommand{\Plaintext}{\mathbf{P}}
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\newcommand{\Ciphertext}{\mathbf{C}}
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\newcommand{\Key}{\mathsf{K}}
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\newcommand{\TransmitPlaintext}[1]{\Plaintext^\enc_{#1}}
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\newcommand{\TransmitCiphertext}[1]{\Ciphertext^\enc_{#1}}
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\newcommand{\TransmitKey}[1]{\Key^\enc_{#1}}
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\newcommand{\TransmitKeyCompare}[1]{\Key^*_{#1}}
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\newcommand{\DerivedKey}[1]{\Key^\disclose_{#1}}
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\newcommand{\DisclosePlaintext}[1]{\Plaintext^\disclose_{#1}}
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\newcommand{\DiscloseCiphertext}[1]{\Ciphertext^\disclose_{#1}}
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\newcommand{\SharedPlaintext}{\Plaintext^\shared}
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\newcommand{\KDF}{\mathsf{KDF}}
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\newcommand{\kdftag}{\mathsf{kdftag}}
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\newcommand{\kdfinput}{\mathsf{kdfinput}}
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\newcommand{\SymEncrypt}[1]{\mathsf{SymEncrypt}_{#1}}
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\newcommand{\SymDecrypt}[1]{\mathsf{SymDecrypt}_{#1}}
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\newcommand{\SymSpecific}{\mathsf{AEAD\_CHACHA20\_POLY1305}}
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\newcommand{\SymCipher}{\mathsf{ChaCha20}}
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\newcommand{\SymAuth}{\mathsf{Poly1305}}
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\newcommand{\Clamp}{\mathsf{clamp_{Curve25519}}}
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\newcommand{\PRF}[2]{\mathsf{{PRF}^{#2}_\mathnormal{#1}}}
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\newcommand{\PRFaddr}[1]{\PRF{#1}{addr}}
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\newcommand{\PRFnf}[1]{\PRF{#1}{\nf}}
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\newcommand{\PRFpk}[1]{\PRF{#1}{pk}}
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\newcommand{\PRFrho}[1]{\PRF{#1}{\NoteAddressRand}}
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\newcommand{\PRFdk}[1]{\PRF{#1}{dk}}
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\newcommand{\cm}{\mathsf{cm}}
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\newcommand{\cmNew}[1]{\mathsf{{cm}^{new}_\mathnormal{#1}}}
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\newcommand{\ReplacementCharacter}{\textsf{U+FFFD}}
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\newcommand{\CryptoBoxSeal}{\mathsf{crypto\_box\_seal}}
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\newcommand{\ECDSAr}{\mathsf{r}}
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\newcommand{\ECDSAs}{\mathsf{s}}
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% merkle tree
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\newcommand{\MerkleDepth}{\mathsf{d}}
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\newcommand{\MerkleNode}[2]{\mathsf{M}^{#1}_{#2}}
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\newcommand{\MerkleSibling}{\mathsf{sibling}}
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% bitcoin
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\newcommand{\vin}{\mathtt{vin}}
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\newcommand{\vout}{\mathtt{vout}}
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\newcommand{\nJoinSplit}{\mathtt{nJoinSplit}}
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\newcommand{\vJoinSplit}{\mathtt{vJoinSplit}}
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\newcommand{\vpubOldField}{\mathtt{vpub\_old}}
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\newcommand{\vpubNewField}{\mathtt{vpub\_new}}
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\newcommand{\vsum}[2]{\smashoperator[r]{\sum_{#1}^{#2}}}
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\newcommand{\anchorField}{\mathtt{anchor}}
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\newcommand{\joinSplitSig}{\mathtt{joinSplitSig}}
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\newcommand{\joinSplitPubKey}{\mathtt{joinSplitPubKey}}
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\newcommand{\nullifiersField}{\mathtt{nullifiers}}
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\newcommand{\commitments}{\mathtt{commitments}}
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\newcommand{\ephemeralKey}{\mathtt{ephemeralKey}}
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\newcommand{\encCiphertexts}{\mathtt{encCiphertexts}}
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\newcommand{\randomSeed}{\mathtt{randomSeed}}
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\newcommand{\rt}{\mathsf{rt}}
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\newcommand{\Varies}{\textit{Varies}}
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\newcommand{\heading}[1]{\multicolumn{1}{c|}{#1}}
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\newcommand{\type}[1]{\texttt{#1}}
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\newcommand{\sighashType}{\term{SIGHASH type}}
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\newcommand{\sighashTypes}{\term{SIGHASH types}}
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\newcommand{\SIGHASHALL}{\mathsf{SIGHASH\_ALL}}
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\newcommand{\scriptSig}{\mathtt{scriptSig}}
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% JoinSplit
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\newcommand{\hSig}{\mathsf{h_{Sig}}}
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\newcommand{\hSigText}{\texorpdfstring{$\hSig$}{hSig}}
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\newcommand{\h}[1]{\mathsf{h_{\mathnormal{#1}}}}
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\newcommand{\NOld}{\mathrm{N}^\mathsf{old}}
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\newcommand{\NNew}{\mathrm{N}^\mathsf{new}}
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\newcommand{\allN}[1]{\mathrm{1}..\mathrm{N}^\mathsf{#1}}
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\newcommand{\allOld}{\allN{old}}
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\newcommand{\allNew}{\allN{new}}
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\newcommand{\setofOld}{\setof{\allOld}}
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\newcommand{\setofNew}{\setof{\allNew}}
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\newcommand{\vmacs}{\mathtt{vmacs}}
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\newcommand{\zkproofSize}{\mathtt{zkproofSize}}
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\newcommand{\zkproof}{\mathtt{zkproof}}
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\newcommand{\JoinSplitCircuit}{\term{\texttt{JoinSplit} circuit}}
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\newcommand{\JoinSplitStatement}{\texttt{JoinSplit}}
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\newcommand{\JoinSplitProof}{\pi_{\JoinSplitStatement}}
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\newcommand{\vpubOld}{\mathsf{v_{pub}^{old}}}
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\newcommand{\vpubNew}{\mathsf{v_{pub}^{new}}}
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\newcommand{\cOld}[1]{\mathbf{n}_{#1}^\mathsf{old}}
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\newcommand{\cNew}[1]{\mathbf{n}_{#1}^\mathsf{new}}
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\newcommand{\cpNew}[1]{\mathbf{np}_{#1}^\mathsf{new}}
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\newcommand{\vOld}[1]{\mathsf{v}_{#1}^\mathsf{old}}
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\newcommand{\vNew}[1]{\mathsf{v}_{#1}^\mathsf{new}}
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\newcommand{\NP}{\mathsf{NP}}
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\newcommand{\treepath}[1]{\mathsf{path}_{#1}}
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\newcommand{\COMM}[1]{\mathsf{COMM}_{#1}}
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\newcommand{\COMMtrapdoor}{\term{\textsf{COMM} trapdoor}}
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\newcommand{\Commitment}{\mathtt{NoteCommitment}}
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\newcommand{\Receive}{\mathsf{Receive}}
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\begin{document}
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\title{\doctitle \\
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\Large \docversion \\
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\vspace{1ex} \large as intended for the \Zcash release of summer 2016}
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\author{\Large \leadauthor \\ \Large \coauthors}
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\date{\today}
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\maketitle
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\tableofcontents
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\newpage
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\section{Introduction}
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\Zcash is an implementation of the \term{Decentralized Anonymous Payment}
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scheme \Zerocash \cite{ZerocashOakland} with some adjustments to terminology,
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functionality and performance. It bridges the existing \emph{transparent}
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payment scheme used by \Bitcoin with a \emph{confidential} payment scheme
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protected by zero-knowledge succinct non-interactive arguments of knowledge
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(\zkSNARKs).
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Changes from the original \Zerocash are highlighted in \changed{\changedcolor}.
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\section{Caution}
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\Zcash security depends on consensus. Should your program diverge from
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consensus, its security is weakened or destroyed. The cause of the divergence
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doesn't matter: it could be a bug in your program, it could be an error in
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this documentation which you implemented as described, or it could be you do
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everything right but other software on the network behaves unexpectedly. The
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specific cause will not matter to the users of your software whose wealth is
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lost.
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Having said that, a specification of \emph{intended} behaviour is essential
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for security analysis, understanding of the protocol, and maintenance of
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Zcash Core and related software. If you find any mistake in this specification,
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please contact \texttt{<security@z.cash>}. While the production \Zcash network
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has yet to be launched, please feel free to do so in public even if you believe
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the mistake may indicate a security weakness.
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\section{Conventions}
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\subsection{Integers, Bit Sequences, and Endianness}
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All integers in \emph{\Zcash-specific} encodings are unsigned, have a fixed
|
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bit length, and are encoded in little-endian byte order. \changed{The definition of
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the encryption scheme based on $\SymSpecific$ \cite{rfc7539} in \crossref{inband}
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uses length fields encoded as little-endian. Also, Curve25519 public and
|
|
private keys are defined as byte sequences, which are converted from integers
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|
using little-endian encoding.}
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The notation $\hexint{}$ followed by a string of \textbf{boldface} hexadecimal
|
|
digits represents the corresponding integer converted from hexadecimal.
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|
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|
The notation $\ascii{...}$ represents the given string represented as a
|
|
sequence of bytes in US-ASCII. For example, $\ascii{abc}$ represents the
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byte sequence $[\hexint{61}, \hexint{62}, \hexint{63}]$.
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In bit layout diagrams, each box of the diagram represents a sequence of bits.
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The bit length is given explicitly in each box, except for the case of a single
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bit, or for the notation $\zeros{n}$ which represents the sequence of $n$ zero bits.
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The entire diagram represents the sequence of \emph{bytes} formed by first
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concatenating these bit sequences, and then treating each subsequence of 8 bits
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as a byte with the bits ordered from \emph{most significant} to
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\emph{least significant}. Thus the \emph{most significant} bit in each byte
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is toward the left of a diagram. Where bit fields are used, the text will
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clarify their position in each case.
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\begin{comment}
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\todo{Update example for big-bit-endian order.}
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\newsavebox{\exampleabox}
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\begin{lrbox}{\exampleabox}
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\setchanged
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\begin{bytefield}[bitwidth=1.3em]{32}
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\bitbox{1}{0} &
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\bitbox{1}{1} &
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\bitbox{1}{0} &
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\bitbox{1}{0} &
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\bitbox{16}{16 bit $\hexint{ABCD}$} &
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\bitbox{12}{12 bit $\hexint{123}$} &
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\end{bytefield}
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\end{lrbox}
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\newsavebox{\examplebbox}
|
|
\begin{lrbox}{\examplebbox}
|
|
\setchanged
|
|
\begin{bytefield}[bitwidth=1.3em]{32}
|
|
\bitbox{4}{4 bit $\hexint{2}$} &
|
|
\bitbox{4}{4 bit $\hexint{D}$} &
|
|
\bitbox{4}{4 bit $\hexint{C}$} &
|
|
\bitbox{4}{4 bit $\hexint{B}$} &
|
|
\bitbox{4}{4 bit $\hexint{A}$} &
|
|
\bitbox{4}{4 bit $\hexint{3}$} &
|
|
\bitbox{4}{4 bit $\hexint{2}$} &
|
|
\bitbox{4}{4 bit $\hexint{1}$} &
|
|
\end{bytefield}
|
|
\end{lrbox}
|
|
|
|
\newsavebox{\examplecbox}
|
|
\begin{lrbox}{\examplecbox}
|
|
\setchanged
|
|
\begin{bytefield}[bitwidth=1.3em]{32}
|
|
\bitbox{8}{8 bit $\hexint{D2}$} &
|
|
\bitbox{8}{8 bit $\hexint{BC}$} &
|
|
\bitbox{8}{8 bit $\hexint{3A}$} &
|
|
\bitbox{8}{8 bit $\hexint{12}$} &
|
|
\end{bytefield}
|
|
\end{lrbox}
|
|
|
|
For example, the following diagrams are all equivalent:
|
|
\begin{itemize}
|
|
\item[] $\Justthebox{\exampleabox}{-1.3ex}$
|
|
\item[] $\Justthebox{\examplebbox}{-1.3ex}$
|
|
\item[] $\Justthebox{\examplecbox}{-1.3ex}$
|
|
\end{itemize}
|
|
|
|
and represent the byte sequence $[\hexint{D2}, \hexint{BC}, \hexint{3A}, \hexint{12}]$.
|
|
\end{comment}
|
|
|
|
The notation $\allN{}$, used as a subscript, means the sequence of values
|
|
with indices $1$ through $\mathrm{N}$ inclusive. For example,
|
|
$\AuthPublicNew{\allNew}$ means the sequence $[\AuthPublicNew{\mathrm{1}},
|
|
\AuthPublicNew{\mathrm{2}}, ...\;\AuthPublicNew{\NNew}]$.
|
|
|
|
The symbol $\bot$ is used to indicate unavailable information or a failed decryption.
|
|
|
|
\subsection{Cryptographic Functions}
|
|
|
|
$\CRH$ is a collision-resistant hash function. In \Zcash, the $\SHAName$ function
|
|
is used which takes a 512-bit block and produces a 256-bit hash. This is
|
|
different from the $\FullHashName$ function, which hashes arbitrary-length sequences.
|
|
\cite{sha2}
|
|
|
|
$\PRF{x}{}$ is a pseudo-random function seeded by $x$. \changed{Four} \emph{independent}
|
|
$\PRF{x}{}$ are needed in our scheme: $\PRFaddr{x}$, $\PRFnf{x}$, $\PRFpk{x}$\changed{,
|
|
and $\PRFrho{x}$}.
|
|
|
|
It is required that $\PRFnf{x}$, $\PRFaddr{x}$\changed{, and $\PRFrho{x}$} be
|
|
collision-resistant across all $x$ --- i.e. it should not be feasible to find
|
|
$(x, y) \neq (x', y')$ such that $\PRFnf{x}(y) = \PRFnf{x'}(y')$, and similarly for
|
|
$\PRFaddr{}$ \changed{and $\PRFrho{}$}.
|
|
|
|
In \Zcash, the $\SHAName$ function is used to construct all of these
|
|
functions.
|
|
|
|
\newcommand{\iminusone}{\hspace{0.3pt}\scriptsize{$i$\hspace{0.6pt}-1}}
|
|
|
|
\newsavebox{\addrbox}
|
|
\begin{lrbox}{\addrbox}
|
|
\setchanged
|
|
\begin{bytefield}[bitwidth=0.06em]{512}
|
|
\bitbox{18}{1} &
|
|
\bitbox{18}{1} &
|
|
\bitbox{18}{0} &
|
|
\bitbox{18}{0} &
|
|
\bitbox{224}{252 bit $x$} &
|
|
\bitbox{56}{8 bit $t$} &
|
|
\bitbox{200}{$\zeros{248}$}
|
|
\end{bytefield}
|
|
\end{lrbox}
|
|
|
|
\newsavebox{\nfbox}
|
|
\begin{lrbox}{\nfbox}
|
|
\setchanged
|
|
\begin{bytefield}[bitwidth=0.06em]{512}
|
|
\bitbox{18}{1} &
|
|
\bitbox{18}{1} &
|
|
\bitbox{18}{1} &
|
|
\bitbox{18}{0} &
|
|
\bitbox{224}{252 bit $\AuthPrivate$} &
|
|
\bitbox{256}{256 bit $\NoteAddressRand$}
|
|
\end{bytefield}
|
|
\end{lrbox}
|
|
|
|
\newsavebox{\pkbox}
|
|
\begin{lrbox}{\pkbox}
|
|
\setchanged
|
|
\begin{bytefield}[bitwidth=0.06em]{512}
|
|
\bitbox{18}{0} &
|
|
\bitbox{18}{\iminusone} &
|
|
\bitbox{18}{0} &
|
|
\bitbox{18}{0} &
|
|
\bitbox{224}{252 bit $\AuthPrivate$} &
|
|
\bitbox{256}{256 bit $\hSig$}
|
|
\end{bytefield}
|
|
\end{lrbox}
|
|
|
|
\newsavebox{\rhobox}
|
|
\begin{lrbox}{\rhobox}
|
|
\setchanged
|
|
\begin{bytefield}[bitwidth=0.06em]{512}
|
|
\bitbox{18}{0} &
|
|
\bitbox{18}{\iminusone} &
|
|
\bitbox{18}{1} &
|
|
\bitbox{18}{0} &
|
|
\bitbox{224}{252 bit $\NoteAddressPreRand$} &
|
|
\bitbox{256}{256 bit $\hSig$}
|
|
\end{bytefield}
|
|
\end{lrbox}
|
|
|
|
\begin{equation*}
|
|
\begin{aligned}
|
|
&\setchanged \PRFaddr{x}(t) &\setchanged := \CRHbox{\addrbox} \\
|
|
\nf =\;& \PRFnf{\AuthPrivate}(\NoteAddressRand) &:= \CRHbox{\nfbox} \\
|
|
\h{i} =\;& \PRFpk{\AuthPrivate}(i, \hSig) &:= \CRHbox{\pkbox} \\
|
|
\setchanged \NoteAddressRandNew{i} =\;&\setchanged \PRFrho{\NoteAddressPreRand}(i, \hSig)
|
|
&\setchanged := \CRHbox{\rhobox}
|
|
\end{aligned}
|
|
\end{equation*}
|
|
|
|
\changed{
|
|
\subparagraph{Note:}
|
|
The first four bits --i.e. the most significant four bits of the first byte--
|
|
are used to distinguish different uses of $\CRH$, ensuring that the functions
|
|
are independent. In addition to the inputs shown here, the bits $\mathtt{1011}$
|
|
in this position are used to distinguish uses of the full $\FullHashName$ hash
|
|
function --- see \crossref{comm}.
|
|
(The specific bit patterns chosen here are motivated by the possibility of future
|
|
extensions that either increase $\NOld$ and/or $\NNew$ to 3, or that add an
|
|
additional bit to $\AuthPrivate$ to encode a new key type, or that require an
|
|
additional PRF.)
|
|
|
|
$\BlakeHashName$ (that is, $\BlakeFullLength$ with an output digest length of
|
|
32 bytes) is also used to construct a Key Derivation Function and as a
|
|
hash function for the computation of $\hSig$. The notation $\BlakeHash(p, x)$
|
|
represents the application of unkeyed $\BlakeHashName$ to a 16-byte personalization
|
|
string $p$ and input $x$, as defined in \cite{blake2}. Note that $\BlakeHashName$
|
|
is not the same as $\BlakeFullLength$ truncated to 256 bits.
|
|
}
|
|
|
|
|
|
\section{Concepts}
|
|
|
|
\subsection{Payment Addresses and Spending Keys}
|
|
|
|
A \keyTuple $(\SpendingKey, \PaymentAddress)$ is
|
|
generated by users who wish to receive payments under this scheme.
|
|
The \paymentAddress $\PaymentAddress$ is derived from the \spendingKey
|
|
$\SpendingKey$.
|
|
|
|
The following diagram depicts the relations between key components.
|
|
Arrows point from a component to any other component(s) that can be derived
|
|
from it.
|
|
|
|
\begin{center}
|
|
\includegraphics[scale=.8]{key_components}
|
|
\end{center}
|
|
|
|
The composition of \paymentAddresses and \spendingKeys
|
|
is a cryptographic protocol detail that should not normally be
|
|
exposed to users. However, user-visible operations should be provided
|
|
to obtain a \paymentAddress or \viewingKey from a \spendingKey.
|
|
|
|
\changed{$\AuthPrivate$ is 252 bits.}
|
|
$\AuthPublic$, $\TransmitPrivate$, and $\TransmitPublic$, are each 256 bits.
|
|
|
|
\changed{$\AuthPublic$, $\TransmitPrivate$ and $\TransmitPublic$ are derived
|
|
as follows:}
|
|
{\hfuzz=50pt
|
|
\begin{equation*}
|
|
\begin{aligned}
|
|
\AuthPublic &:= \changed{\PRFaddr{\AuthPrivate}(0)} \\
|
|
\TransmitPrivate &:= \changed{\Clamp(\PRFaddr{\AuthPrivate}(1))} \\
|
|
\TransmitPublic &:= \changed{\CurveMultiply(\TransmitPrivate, \CurveBase)}
|
|
\end{aligned}
|
|
\end{equation*}
|
|
}
|
|
|
|
\changed{
|
|
where
|
|
\begin{itemize}
|
|
\item $\CurveMultiply(\bytes{n}, \bytes{q})$ performs point
|
|
multiplication of the Curve25519 public key represented by the byte
|
|
sequence $\bytes{q}$ by the Curve25519 secret key represented by the
|
|
byte sequence $\bytes{n}$, as defined in section 2 of \cite{Curve25519};
|
|
\item $\CurveBase$ is the public byte sequence representing the Curve25519
|
|
base point;
|
|
\item $\Clamp(\bytes{x})$ takes a 32-byte sequence $\bytes{x}$ as input
|
|
and returns a byte sequence representing a Curve25519 private key, with
|
|
bits ``clamped'' as described in section 3 of \cite{Curve25519}:
|
|
``clear bits 0, 1, 2 of the first byte, clear bit 7 of the last byte,
|
|
and set bit 6 of the last byte.'' Here the bits of a byte are numbered
|
|
such that bit $b$ has numeric weight $2^b$.
|
|
\end{itemize}
|
|
}
|
|
|
|
Users can accept payment from multiple parties with a single
|
|
$\PaymentAddress$ and the fact that these payments are destined to
|
|
the same payee is not revealed on the blockchain, even to the
|
|
paying parties. \emph{However} if two parties collude to compare a
|
|
$\PaymentAddress$ they can trivially determine they are the same. In the
|
|
case that a payee wishes to prevent this they should create a distinct
|
|
\paymentAddress for each payer.
|
|
|
|
\subsection{\Notes}
|
|
|
|
A \note (denoted $\NoteTuple{}$) is a tuple $\changed{(\AuthPublic, \Value,
|
|
\NoteAddressRand, \NoteCommitRand)}$ which represents that a value $\Value$ is
|
|
spendable by the recipient who holds the \spendingKey $\AuthPrivate$ corresponding
|
|
to $\AuthPublic$, as described in the previous section.
|
|
|
|
\begin{itemize}
|
|
\item $\AuthPublic$ is a 32-byte \authKeypair public key of the recipient.
|
|
\item $\Value$ is a 64-bit unsigned integer representing the value of the
|
|
\note in \zatoshi (1 \ZEC = $10^8$ \zatoshi).
|
|
\item $\NoteAddressRand$ is a 32-byte $\PRFnf{\AuthPrivate}$ preimage.
|
|
\item $\NoteCommitRand$ is a 32-byte \COMMtrapdoor.
|
|
\end{itemize}
|
|
|
|
$\NoteCommitRand$ is randomly generated by the sender. \changed{$\NoteAddressRand$
|
|
is generated from a random seed $\NoteAddressPreRand$ using
|
|
$\PRFrho{\NoteAddressPreRand}$.} Only a commitment to these values is disclosed
|
|
publicly, which allows the tokens $\NoteCommitRand$ and $\NoteAddressRand$ to blind
|
|
the value and recipient \emph{except} to those who possess these tokens.
|
|
|
|
\subsubsection{\NoteCommitments} \label{comm}
|
|
|
|
The underlying $\Value$ and $\AuthPublic$ are blinded with $\NoteAddressRand$
|
|
and $\NoteCommitRand$ \changed{using the collision-resistant hash function $\FullHash$}.
|
|
The resulting hash $\cm = \Commitment(\NoteTuple{})$.
|
|
|
|
\newsavebox{\cmbox}
|
|
\begin{lrbox}{\cmbox}
|
|
\setchanged
|
|
\begin{bytefield}[bitwidth=0.036em]{840}
|
|
\bitbox{24}{1} &
|
|
\bitbox{24}{0} &
|
|
\bitbox{24}{1} &
|
|
\bitbox{24}{1} &
|
|
\bitbox{24}{0} &
|
|
\bitbox{24}{0} &
|
|
\bitbox{24}{0} &
|
|
\bitbox{24}{0} &
|
|
\bitbox{256}{256 bit $\AuthPublic$} &
|
|
\bitbox{128}{64 bit $\Value$} &
|
|
\bitbox{256}{256 bit $\NoteAddressRand$}
|
|
\bitbox{256}{256 bit $\NoteCommitRand$} &
|
|
\end{bytefield}
|
|
\end{lrbox}
|
|
|
|
\changed{
|
|
\hskip 1em $\cm := \FullHashbox{\cmbox}$
|
|
|
|
\subparagraph{Note:}
|
|
The leading byte of the $\FullHash$ input is $\hexint{B0}$.
|
|
}
|
|
|
|
\subsubsection{\Nullifiers}
|
|
|
|
A \nullifier (denoted $\nf$) is derived from the $\NoteAddressRand$ component
|
|
of a \note as $\PRFnf{\AuthPrivate}(\NoteAddressRand)$. A \note is spent by proving
|
|
knowledge of $\NoteAddressRand$ and $\AuthPrivate$ in zero knowledge while
|
|
disclosing its \nullifier $\nf$, allowing $\nf$ to be used to prevent double-spending.
|
|
|
|
\subsubsection{\NotePlaintexts{} and \Memos} \label{notept}
|
|
|
|
Transmitted \notes are stored on the blockchain in encrypted form, together with
|
|
a \noteCommitment $\cm$.
|
|
|
|
The \notePlaintexts associated with a \joinSplitDescription are encrypted to the
|
|
respective \transmitKeypair keys $\TransmitPublicNew{\allNew}$,
|
|
and the result forms part of a \notesCiphertext (see \crossref{inband}
|
|
for further details).
|
|
|
|
Each \notePlaintext (denoted $\NotePlaintext{}$) consists of
|
|
$(\Value, \NoteAddressRand, \NoteCommitRand\changed{, \Memo})$.
|
|
|
|
The first three of these fields are as defined earlier.
|
|
\changed{$\Memo$ is a 128-byte \memo associated with this \note.
|
|
|
|
The usage of the \memo is by agreement between the sender and recipient of the
|
|
\note. The \memo{} \SHOULD be encoded either as:
|
|
\begin{itemize}
|
|
\item a UTF-8 human-readable string \cite{Unicode}, padded with zero bytes; or
|
|
\item an arbitrary sequence of 128 bytes starting with a byte value of $\hexint{F5}$
|
|
or greater, which is therefore not a valid UTF-8 string.
|
|
\end{itemize}
|
|
|
|
In the former case, wallet software is expected to strip any trailing zero bytes
|
|
and then display the resulting \mbox{UTF-8} string to the recipient user, where applicable.
|
|
Incorrect UTF-8-encoded byte sequences should be displayed as replacement characters
|
|
(\ReplacementCharacter).
|
|
|
|
In the latter case, the contents of the \memo{} \SHOULDNOT be displayed. A start byte
|
|
of $\hexint{F5}$ is reserved for use by automated software by private agreement.
|
|
A start byte of $\hexint{F6}$ or greater is reserved for use in future \Zcash
|
|
protocol extensions.
|
|
}
|
|
|
|
The encoding of a \notePlaintext consists of, in order:
|
|
\begin{equation*}
|
|
\begin{bytefield}[bitwidth=0.029em]{1608}
|
|
\changed{
|
|
\bitbox{192}{8 bit $\NotePlaintextLeadByte$}
|
|
&}\bitbox{192}{$\Value$ (8 bytes)} &
|
|
\bitbox{256}{$\NoteAddressRand$ (32 bytes)} &
|
|
\bitbox{256}{$\NoteCommitRand$ (\changed{32} bytes)} &
|
|
\changed{\bitbox{800}{$\Memo$ (128 bytes)}}
|
|
\end{bytefield}
|
|
\end{equation*}
|
|
|
|
\begin{itemize}
|
|
\changed{
|
|
\item A byte, $\NotePlaintextLeadByte$, indicating this version of the
|
|
encoding of a \notePlaintext.
|
|
}
|
|
\item 8 bytes specifying $\Value$.
|
|
\item 32 bytes specifying $\NoteAddressRand$.
|
|
\item \changed{32} bytes specifying $\NoteCommitRand$.
|
|
\changed{
|
|
\item 128 bytes specifying $\Memo$.
|
|
}
|
|
\end{itemize}
|
|
|
|
|
|
\subsection{\NoteCommitment{} Tree} \label{merkle}
|
|
|
|
\begin{center}
|
|
\includegraphics[scale=.4]{incremental_merkle}
|
|
\end{center}
|
|
|
|
The \noteCommitmentTree is an \incrementalMerkleTree of depth $\MerkleDepth$ used to
|
|
store \noteCommitments that \joinSplitTransfers produce. Just as the \term{unspent
|
|
transaction output set} (UTXO) used in \Bitcoin, it is used to express the existence
|
|
of value and the capability to spend it. However, unlike the UTXO, it is \emph{not}
|
|
the job of this tree to protect against double-spending, as it is append-only.
|
|
|
|
Blocks in the blockchain are associated (by all nodes) with the \merkleRoot of this tree
|
|
after all of its constituent \joinSplitDescriptions' \noteCommitments have been
|
|
entered into the tree associated with the previous block.
|
|
|
|
Each \merkleNode in the \incrementalMerkleTree is associated with a 32-byte hash.
|
|
The \merkleLayer numbered $h$, counting from \merkleLayer $0$ at the \merkleRoot, has
|
|
$2^h$ \merkleNodes with \merkleIndices $0$ to $2^h-1$ inclusive. 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 $0 \leq h < \MerkleDepth$
|
|
and $0 \leq i < 2^h$,
|
|
|
|
\newsavebox{\merklebox}
|
|
\begin{lrbox}{\merklebox}
|
|
\begin{bytefield}[bitwidth=0.04em]{512}
|
|
\bitbox{256}{256 bit $\MerkleNode{h+1}{2i}$} &
|
|
\bitbox{256}{256 bit $\MerkleNode{h+1}{2i+1}$}
|
|
\end{bytefield}
|
|
\end{lrbox}
|
|
|
|
\hskip 2em $\MerkleNode{h}{i} := \CRHbox{\merklebox}$.
|
|
|
|
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 $\MerkleNode{\MerkleDepth}{i}$ in the
|
|
\incrementalMerkleTree is the sequence
|
|
|
|
\hskip 2em $[\MerkleNode{h}{\MerkleSibling(h, i)} \text{ for }
|
|
h \text{ from } \MerkleDepth \text{ down to } 1]$,
|
|
|
|
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 \merkleLeaf $\MerkleNode{\MerkleDepth}{i}$ is in a tree
|
|
with a given \merkleRoot $\rt = \MerkleNode{0}{0}$.
|
|
|
|
|
|
\subsection{\NullifierSet}
|
|
|
|
Transactions insert \nullifiers into a \nullifierSet which is maintained
|
|
alongside the UTXO by all nodes.
|
|
|
|
\eli{a tx is just a string, so it doesn't insert anything. Rather, nodes process
|
|
tx's and the ``good'' ones lead to the addition of \nullifiers to the
|
|
\nullifierSet.}
|
|
|
|
Transactions that attempt to insert a \nullifier into this set that already
|
|
exists within it are invalid as they are attempting to double-spend.
|
|
|
|
\eli{After defining \term{transaction}, one should define what a \term{legal tx} is
|
|
(this definition depends on a particular blockchain [view]) and only then can one
|
|
talk about ``attempts'' of transactions, and insertions of \nullifiers into the
|
|
\nullifierSet.}
|
|
|
|
\subsection{The Blockchain}
|
|
|
|
At a given point in time, the \blockchainview of each \fullnode consists of a
|
|
sequence of one or more valid \blocks. Each \block consists of a sequence of one or
|
|
more \transactions. In a given node's \blockchainview, \treestates are chained in an
|
|
obvious way:
|
|
|
|
\begin{itemize}
|
|
\item The input \treestate of the first \block is the empty \treestate.
|
|
\item The input \treestate of the first \transaction of a \block is the final
|
|
\treestate of the immediately preceding \block.
|
|
\item The input \treestate of each subsequent \transaction in a \block is the
|
|
output \treestate of the immediately preceding \transaction.
|
|
\item The final \treestate of a \block is the output \treestate of its last
|
|
\transaction.
|
|
\end{itemize}
|
|
|
|
An \anchor is a Merkle tree root of a \treestate, and uniquely identifies that
|
|
\treestate given the assumed security properties of the Merkle tree's hash function.
|
|
|
|
Each \transaction is associated with a \sequenceOfJoinSplitDescriptions.
|
|
\todo{They also have a transparent value flow that interacts with the \joinSplitDescription's
|
|
\changed{$\vpubOld$ and} $\vpubNew$.}
|
|
Inputs and outputs are associated with a value.
|
|
|
|
The total value of the outputs must not exceed the total value of the inputs.
|
|
|
|
The \anchor of the \changed{first} \joinSplitDescription in a \transaction must refer to
|
|
some earlier \block's final \treestate.
|
|
|
|
\changed{
|
|
The \anchor of each subsequent \joinSplitDescription may refer either to some earlier
|
|
\block's final \treestate, or to the output \treestate of the immediately preceding
|
|
\joinSplitDescription.
|
|
}
|
|
|
|
These conditions act as constraints on the blocks that a \fullnode will
|
|
accept into its \blockchainview.
|
|
|
|
We rely on Bitcoin-style consensus for \fullnodes to eventually converge on their
|
|
views of valid \blocks, and therefore of the sequence of \treestates in those
|
|
\blocks.
|
|
|
|
|
|
\subparagraph{Value pool}
|
|
|
|
Transaction inputs insert value into a \term{value pool}, and transaction outputs
|
|
remove value from this pool. The remaining value in the pool is available to miners
|
|
as a fee.
|
|
|
|
\section{\JoinSplitTransfers{} and Descriptions} \label{pourdesc}
|
|
|
|
A \joinSplitDescription is data included in a \transaction that describes a \joinSplitTransfer,
|
|
i.e. a confidential value transfer. This kind of value transfer is the primary
|
|
\Zcash-specific operation performed by \transactions; it uses, but should not be
|
|
confused with, the \JoinSplitCircuit used for the \zkSNARK proof and verification.
|
|
|
|
A \joinSplitTransfer spends $\NOld$ \notes $\cOld{\allOld}$ and transparent input
|
|
$\vpubOld$, and creates $\NNew$ \notes $\cNew{\allNew}$ and transparent output
|
|
$\vpubNew$.
|
|
|
|
\subparagraph{Consensus rule:}
|
|
Either $\vpubOld$ or $\vpubNew$ \MUST be zero.
|
|
|
|
\changed{
|
|
\Zcash \transactions have the following additional fields:
|
|
|
|
\begin{center}
|
|
\begin{tabularx}{0.9\textwidth}{|c|l|p{10.49em}|X|}
|
|
\hline
|
|
Bytes & \heading{Name} & \heading{Data Type} & \heading{Description} \\
|
|
\hhline{|=|=|=|=|}
|
|
|
|
\Varies & $\nJoinSplit$ & \type{compactSize uint} & The number of \joinSplitDescriptions
|
|
in $\vJoinSplit$. \\ \hline
|
|
|
|
$1026 \times \nJoinSplit$ & $\vJoinSplit$ &
|
|
\type{JoinSplitDescription} \type{[$\nJoinSplit$]} &
|
|
The \sequenceOfJoinSplitDescriptions in this \transaction. \\ \hline
|
|
|
|
33 $\dagger$ & $\joinSplitPubKey$ & \type{char[33]} & An encoding of a ECDSA public verification key,
|
|
using the secp256k1 curve and parameters defined in \cite{sec2-ecdsa} and
|
|
\cite{secp256k1}. \\ \hline
|
|
|
|
64 $\dagger$ & $\joinSplitSig$ & \type{char[64]} & A signature on a prefix of the \transaction encoding,
|
|
to be verified using $\joinSplitPubKey$. \\ \hline
|
|
\end{tabularx}
|
|
\end{center}
|
|
|
|
$\dagger$ The $\joinSplitPubKey$ and $\joinSplitSig$ fields are present if and only if
|
|
$\nJoinSplit > 0$.
|
|
|
|
The encoding of $\joinSplitPubKey$ and the data to be signed are specified in
|
|
more detail in \crossref{nonmalleability}.
|
|
}
|
|
|
|
Each \type{JoinSplitDescription} consists of:
|
|
|
|
\begin{center}
|
|
\begin{tabularx}{0.9\textwidth}{|c|l|l|X|}
|
|
\hline
|
|
Bytes & \heading{Name} & \heading{Data Type} & \heading{Description} \\
|
|
\hhline{|=|=|=|=|}
|
|
|
|
\setchanged 8 &\setchanged $\vpubOldField$ &\setchanged \type{int64\_t} &\mbox{}\setchanged
|
|
A value $\vpubOld$ that the \joinSplitTransfer removes from the value pool. \\ \hline
|
|
|
|
8 & $\vpubNewField$ & \type{int64\_t} & A value $\vpubNew$ that the \joinSplitTransfer inserts
|
|
into the value pool. \\ \hline
|
|
|
|
32 & $\anchorField$ & \type{char[32]} & A merkle root $\rt$ of the \noteCommitmentTree at
|
|
some block height in the past, or the merkle root produced by a previous \joinSplitTransfer in
|
|
this \transaction. \sean{We need to be more specific here.} \\ \hline
|
|
|
|
64 & $\nullifiersField$ & \type{char[32][$\NOld$]} & A sequence of \nullifiers of the input
|
|
\notes $\nfOld{\allOld}$. \\ \hline
|
|
|
|
64 & $\commitments$ & \type{char[32][$\NNew$]}. & A sequence of \noteCommitments for the
|
|
output \notes $\cmNew{\allNew}$. \\ \hline
|
|
|
|
\setchanged 32 &\setchanged $\ephemeralKey$ &\setchanged \type{char[32]} &\mbox{}\setchanged
|
|
A Curve25519 public key $\EphemeralPublic$. \\ \hline
|
|
|
|
434 & $\encCiphertexts$ & \type{char[217][$\NNew$]} & A sequence of ciphertext
|
|
components for the encrypted output \notes, $\TransmitCiphertext{\allNew}$. \\ \hline
|
|
|
|
\setchanged 32 &\setchanged $\randomSeed$ &\setchanged \type{char[32]} &\mbox{}\setchanged
|
|
A 256-bit seed that must be chosen independently at random for each \joinSplitDescription. \\ \hline
|
|
|
|
64 & $\vmacs$ & \type{char[32][$\NOld$]} & A sequence of message authentication tags
|
|
$\h{\allOld}$ that bind $\hSig$ to each $\AuthPrivate$ of the
|
|
$\joinSplitDescription$. \\ \hline
|
|
|
|
288 & $\zkproof$ & \type{char[288]} & An encoding, as determined by the libsnark library
|
|
\cite{libsnark}, of the zero-knowledge proof $\JoinSplitProof$. \\ \hline
|
|
|
|
\end{tabularx}
|
|
\end{center}
|
|
|
|
The $\ephemeralKey$ and $\encCiphertexts$ fields together form the \notesCiphertext.
|
|
|
|
\todo{Describe case where there are fewer than $\NOld$ real input \notes.}
|
|
|
|
\subsection{Computation of \hSigText} \label{hsig}
|
|
|
|
\newsavebox{\hsigbox}
|
|
\begin{lrbox}{\hsigbox}
|
|
\setchanged
|
|
\begin{bytefield}[bitwidth=0.04em]{1024}
|
|
\bitbox{256}{256 bit $\randomSeed$}
|
|
\bitbox{256}{\hfill 256 bit $\nfOld{\mathrm{1}}$\hfill...\;} &
|
|
\bitbox{256}{256 bit $\nfOld{\NOld}$} &
|
|
\bitbox{256}{256 bit $\pubKeyHash$}
|
|
\end{bytefield}
|
|
\end{lrbox}
|
|
|
|
\changed{
|
|
Given a \joinSplitDescription containing the fields $\randomSeed$ and
|
|
$\nullifiersField = \nfOld{\allOld}$, and embedded in a transaction
|
|
containing the field $\joinSplitPubKey$, we compute $\hSig$ for that
|
|
\joinSplitDescription as follows:
|
|
\begin{equation*}
|
|
\begin{aligned}
|
|
\pubKeyHash &:= \BlakeHash(\ascii{ZcashECDSAPubKey},\; \joinSplitPubKey) \\
|
|
\hSigInput &:= \Justthebox{\hsigbox}{-1.3ex} \\
|
|
\hSig &:= \BlakeHash(\ascii{ZcashComputehSig},\; \hSigInput)
|
|
\end{aligned}
|
|
\end{equation*}
|
|
}
|
|
|
|
\subsection{Merkle root validity}
|
|
|
|
A \joinSplitDescription is valid if $\rt$ is a \noteCommitmentTree root found in
|
|
either the blockchain or a merkle root produced by inserting the \noteCommitments
|
|
of a previous \joinSplitDescription in the \transaction to the \noteCommitmentTree
|
|
identified by that previous \joinSplitDescription's $\anchor$.
|
|
|
|
\subsection{Non-malleability} \label{nonmalleability}
|
|
|
|
\changed{
|
|
\Bitcoin defines several \sighashTypes that cover various parts of a transaction.
|
|
In \Zcash, all of these \sighashTypes are extended to cover the \Zcash-specific
|
|
fields $\nJoinSplit$, $\vJoinSplit$, and (if present) $\joinSplitPubKey$.
|
|
They \emph{do not} cover the field $\joinSplitSig$.
|
|
|
|
\subparagraph{Consensus rule:}
|
|
If $\nJoinSplit > 0$, the \transaction{} \MUSTNOT use \sighashTypes other than
|
|
$\SIGHASHALL$.
|
|
|
|
Let $\dataToBeSigned$ be the hash of the \transaction using the $\SIGHASHALL$
|
|
\sighashType. Note that this \emph{excludes} all of the $\scriptSig$ fields in
|
|
the non-\Zcash-specific parts of the \transaction.
|
|
|
|
In order to ensure that a \joinSplitDescription is cryptographically bound to the
|
|
transparent inputs and outputs corresponding to $\vpubNew$ and $\vpubOld$, and
|
|
to the other \joinSplitDescriptions in the same \transaction, an ephemeral ECDSA
|
|
key pair is generated for each \transaction, and the $\dataToBeSigned$ is
|
|
signed with the private signing key of this key pair. The corresponding public
|
|
verification key is included in the \transaction encoding as $\joinSplitPubKey$.
|
|
|
|
If $\nJoinSplit$ is zero, the $\joinSplitPubKey$ and $\joinSplitSig$ fields are
|
|
omitted. Otherwise, a \transaction has a correct \joinSplitSignature if:
|
|
\begin{itemize}
|
|
\item $\joinSplitSig$ can be verified as an encoding of a signature on
|
|
$\dataToBeSigned$, using the ECDSA public key encoded as $\joinSplitPubKey$; and
|
|
\item $\joinSplitSig$ has an $\ECDSAs$ value in the lower half of the possible range
|
|
(i.e. $\ECDSAs$ must be in the range from 0x1 to \linebreak
|
|
0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF5D576E7357A4501DDFE92F46681B20A0,
|
|
inclusive).
|
|
\end{itemize}
|
|
|
|
If $\ECDSAs$ is not in the given range, the signature is treated as invalid.
|
|
}
|
|
|
|
\newsavebox{\sigbox}
|
|
\begin{lrbox}{\sigbox}
|
|
\setchanged
|
|
\begin{bytefield}[bitwidth=0.075em]{512}
|
|
\bitbox{256}{256 bit $\ECDSAr$}
|
|
\bitbox{256}{256 bit $\ECDSAs$}
|
|
\end{bytefield}
|
|
\end{lrbox}
|
|
|
|
\newsavebox{\pubkeybox}
|
|
\begin{lrbox}{\pubkeybox}
|
|
\setchanged
|
|
\begin{bytefield}[bitwidth=0.075em]{264}
|
|
\bitbox{14}{0}
|
|
\bitbox{14}{0}
|
|
\bitbox{14}{0}
|
|
\bitbox{14}{0}
|
|
\bitbox{14}{0}
|
|
\bitbox{14}{0}
|
|
\bitbox{14}{1}
|
|
\bitbox{56}{1 bit $\tilde{y}_P$}
|
|
\bitbox{256}{256 bit $x_P$}
|
|
\end{bytefield}
|
|
\end{lrbox}
|
|
|
|
\changed{
|
|
The encoding of a signature is:
|
|
}
|
|
\begin{itemize}
|
|
\item[] $\Justthebox{\sigbox}{-1.3ex}$
|
|
\end{itemize}
|
|
|
|
\changed{
|
|
where $\ECDSAr$ and $\ECDSAs$ are as defined in \cite{sec2-ecdsa}.
|
|
|
|
The encoding of a public key is as defined in section E.2.3.2 of \cite{std1363}
|
|
for a compressed elliptic curve point with $x$-coordinate $x_P$ and compressed
|
|
$y$-coordinate $\tilde{y}_P$:
|
|
}
|
|
\begin{itemize}
|
|
\item[] $\Justthebox{\pubkeybox}{-1.3ex}$
|
|
\end{itemize}
|
|
|
|
\changed{
|
|
Note that only compressed public keys are valid.
|
|
}
|
|
|
|
The condition enforced by the \JoinSplitCircuit specified in \crossref{nonmalleablepour}
|
|
ensures that a holder of all of $\AuthPrivateOld{\allOld}$ for each
|
|
\joinSplitDescription has authorized the use of the private signing key corresponding
|
|
to $\joinSplitPubKey$ to sign this \transaction.
|
|
|
|
|
|
\subsection{Balance}
|
|
|
|
A \joinSplitTransfer can be seen, from the perspective of the \transaction, as
|
|
an input \changed{and an output simultaneously}.
|
|
\changed{$\vpubOld$ takes value from the value pool and}
|
|
$\vpubNew$ adds value to the value pool. As a result, \changed{$\vpubOld$ is
|
|
treated like an \emph{output} value, whereas} $\vpubNew$ is treated like an
|
|
\emph{input} value.
|
|
|
|
\changed{
|
|
Note that unlike original \Zerocash \cite{ZerocashOakland}, \Zcash does not have
|
|
a distinction between Mint and Pour operations. The addition of $\vpubOld$ to a
|
|
\joinSplitDescription subsumes the functionality of both Mint and Pour. Also,
|
|
\joinSplitDescriptions are indistinguishable regardless of the number of real input
|
|
\notes.
|
|
|
|
As stated in \crossref{pourdesc}, either $\vpubOld$ or $\vpubNew$ \MUST be zero.
|
|
No generality is lost because, if a \transaction in which both $\vpubOld$ and
|
|
$\vpubNew$ were nonzero were allowed, it could be replaced by an equivalent one
|
|
in which $\minimum(\vpubOld, \vpubNew)$ is subtracted from both of these values.
|
|
This restriction helps to avoid unnecessary distinctions between \transactions
|
|
according to client implementation.
|
|
}
|
|
|
|
\subsection{\NoteCommitments{} and \Nullifiers}
|
|
|
|
A \transaction that contains one or more \joinSplitDescriptions, when entered into the
|
|
blockchain, appends to the \noteCommitmentTree with all constituent
|
|
\noteCommitments. All of the constituent \nullifiers are also entered into the
|
|
\nullifierSet of the \blockchainview \emph{and} \mempool. A \transaction is not
|
|
valid if it attempts to add a \nullifier to the \nullifierSet that already
|
|
exists in the set.
|
|
|
|
\subsection{\JoinSplitCircuit{} and Proofs}
|
|
|
|
In \Zcash, $\NOld$ and $\NNew$ are both $2$.
|
|
|
|
A valid instance of $\JoinSplitProof$ assures that given a \term{primary input}:
|
|
|
|
\begin{itemize}
|
|
\item[] $(\rt, \nfOld{\allOld}, \cmNew{\allNew}, \changed{\vpubOld,\;}
|
|
\vpubNew, \hSig, \h{\allOld})$,
|
|
\end{itemize}
|
|
|
|
there exists a witness of \term{auxiliary input}:
|
|
|
|
\begin{itemize}
|
|
\item[] $(\treepath{\allOld}, \cOld{\allOld}, \AuthPrivateOld{\allOld},
|
|
\cNew{\allNew}\changed{, \NoteAddressPreRand})$
|
|
\end{itemize}
|
|
|
|
where:
|
|
|
|
\begin{itemize}
|
|
\item[] for each $i \in \setofOld$: $\cOld{i} = (\AuthPublicOld{i},
|
|
\vOld{i}, \NoteAddressRandOld{i}, \NoteCommitRandOld{i})$;
|
|
\item[] for each $i \in \setofNew$: $\cNew{i} = (\AuthPublicNew{i},
|
|
\vNew{i}, \NoteAddressRandNew{i}, \NoteCommitRandNew{i})$
|
|
\end{itemize}
|
|
|
|
such that the following conditions hold:
|
|
|
|
\subparagraph{Merkle path validity}
|
|
|
|
for each $i \in \setofOld$ \changed{$\mid$ $\vOld{i} \neq 0$}:
|
|
$\treepath{i}$ must be a valid \merklePath of depth $\MerkleDepth$, as defined in
|
|
\crossref{merkle}, from $\Commitment(\cOld{i})$ to \noteCommitmentTree root $\rt$.
|
|
|
|
\textbf{Note:} Merkle path validity covers both conditions 1. (a) and 1. (d) of the NP statement
|
|
given in section 4.2 of \cite{ZerocashOakland}.
|
|
|
|
\subparagraph{Balance}
|
|
|
|
$\changed{\vpubOld\; +} \vsum{i=1}{\NOld} \vOld{i} = \vpubNew + \vsum{i=1}{\NNew} \vNew{i}$.
|
|
|
|
\subparagraph{\Nullifier integrity}
|
|
|
|
for each $i \in \setofNew$:
|
|
$\nfOld{i} = \PRFnf{\AuthPrivateOld{i}}(\NoteAddressRandOld{i})$.
|
|
|
|
\subparagraph{Spend authority}
|
|
|
|
for each $i \in \setofOld$:
|
|
$\AuthPublicOld{i} = \changed{\PRFaddr{\AuthPrivateOld{i}}(0)}$.
|
|
|
|
\subparagraph{Non-malleability} \label{nonmalleablepour}
|
|
|
|
for each $i \in \setofOld$:
|
|
$\h{i} = \PRFpk{\AuthPrivateOld{i}}(i, \hSig)$.
|
|
|
|
\changed{
|
|
\subparagraph{Uniqueness of $\NoteAddressRandNew{i}$} \label{uniquerho}
|
|
|
|
for each $i \in \setofNew$:
|
|
$\NoteAddressRandNew{i} = \PRFrho{\NoteAddressPreRand}(i, \hSig)$.
|
|
}
|
|
|
|
\subparagraph{Commitment integrity}
|
|
|
|
for each $i \in \setofNew$: $\cmNew{i}$ = $\Commitment(\cNew{i})$.
|
|
|
|
|
|
\section{In-band secret distribution} \label{inband}
|
|
|
|
In order to transmit the secret $\Value$, $\NoteAddressRand$, and $\NoteCommitRand$
|
|
(necessary for the recipient to later spend) \changed{and also a \memo} to the
|
|
recipient \emph{without} requiring an out-of-band communication channel, the
|
|
\transmitKeypair public key $\TransmitPublic$ is used to encrypt these
|
|
secrets. The recipient's possession of the associated
|
|
$(\PaymentAddress, \SpendingKey)$ (which contains both $\AuthPublic$ and
|
|
$\TransmitPrivate$) is used to reconstruct the original \note \changed{ and \memo}.
|
|
|
|
All of the resulting ciphertexts are combined to form a \notesCiphertext.
|
|
|
|
\newsavebox{\kdftagbox}
|
|
\begin{lrbox}{\kdftagbox}
|
|
\setchanged
|
|
\begin{bytefield}[bitwidth=0.16em]{128}
|
|
\bitbox{64}{64 bit $\ascii{ZcashKDF}$} &
|
|
\bitbox{32}{8 bit $i\!-\!1$}
|
|
\bitbox{56}{$\zeros{56}$}
|
|
\end{bytefield}
|
|
\end{lrbox}
|
|
|
|
\newsavebox{\kdfinputbox}
|
|
\begin{lrbox}{\kdfinputbox}
|
|
\setchanged
|
|
\begin{bytefield}[bitwidth=0.04em]{1024}
|
|
\bitbox{256}{256-bit $\hSig$}
|
|
\bitbox{256}{256 bit $\DHSecret{i}$} &
|
|
\bitbox{256}{256 bit $\EphemeralPublic$} &
|
|
\bitbox{256}{256 bit $\TransmitPublicNew{i}$} &
|
|
\end{bytefield}
|
|
\end{lrbox}
|
|
|
|
\subsection{Encryption}
|
|
|
|
\changed{
|
|
Let $\SymEncrypt{\Key}(\Plaintext)$ be authenticated encryption using
|
|
$\SymSpecific$ \cite{rfc7539} encryption of plaintext $\Plaintext$, with empty
|
|
``associated data", all-zero nonce $\zeros{96}$, and 256-bit key $\Key$.
|
|
|
|
Similarly, let $\SymDecrypt{\Key}(\Ciphertext)$ be $\SymSpecific$
|
|
decryption of ciphertext $\Ciphertext$, with empty ``associated data",
|
|
all-zero nonce $\zeros{96}$, and 256-bit key $\Key$. The result is either
|
|
the plaintext byte sequence, or $\bot$ indicating failure to decrypt.
|
|
}
|
|
|
|
Define:
|
|
|
|
\hskip 1.5em $\KDF(i, \hSig, \DHSecret{i}, \EphemeralPublic, \TransmitPublicNew{i}) :=
|
|
\BlakeHash(\kdftag, \kdfinput)$
|
|
|
|
where:
|
|
|
|
\hskip 1.5em $\kdftag := \Justthebox{\kdftagbox}{-1.3ex}$
|
|
|
|
\hskip 1.5em $\kdfinput := \Justthebox{\kdfinputbox}{-1.3ex}$.
|
|
|
|
\vspace{2ex}
|
|
Let $\TransmitPublicNew{\allNew}$ be the \changed{Curve25519} public keys
|
|
for the intended recipient addresses of each new \note, and let
|
|
$\NotePlaintext{\allNew}$ be the \notePlaintexts. Let $\hSig$ be the
|
|
value computed in \crossref{hsig}.
|
|
|
|
Then to encrypt:
|
|
\begin{itemize}
|
|
\changed{
|
|
\item Generate a new Curve25519 (public, private) key pair
|
|
$(\EphemeralPublic, \EphemeralPrivate)$.
|
|
\item For $i \in \setofNew$,
|
|
\begin{itemize}
|
|
\item Let $\TransmitPlaintext{i}$ be the raw encoding of $\NotePlaintext{i}$.
|
|
\item Let $\DHSecret{i} := \CurveMultiply(\EphemeralPrivate,
|
|
\TransmitPublicNew{i})$.
|
|
\item Let $\TransmitKey{i} := \KDF(i, \hSig, \DHSecret{i}, \EphemeralPublic,
|
|
\TransmitPublicNew{i})$.
|
|
\item Let $\TransmitCiphertext{i} :=
|
|
\SymEncrypt{\TransmitKey{i}}(\TransmitPlaintext{i})$.
|
|
\end{itemize}
|
|
}
|
|
\end{itemize}
|
|
|
|
The resulting \notesCiphertext is $\changed{(\EphemeralPublic,
|
|
\TransmitCiphertext{\allNew})}$.
|
|
|
|
\subsection{Decryption by a Recipient}
|
|
|
|
Let $\PaymentAddress = (\AuthPublic, \TransmitPublic)$ be the recipient's
|
|
\paymentAddress, and let $\TransmitPrivate$ be the recipient's \changed{Curve25519}
|
|
private key. Let $\hSig$ be the value computed in \crossref{hsig}.
|
|
Let $\cmNew{\allNew}$ be the \noteCommitments of each output coin.
|
|
Then for each $i \in \setofNew$, the recipient will attempt to decrypt that ciphertext
|
|
component as follows:
|
|
|
|
\changed{
|
|
\begin{itemize}
|
|
\item Let $\DHSecret{i} := \CurveMultiply(\TransmitPrivate, \EphemeralPublic)$.
|
|
\item Let $\TransmitKey{i} := \KDF(i, \hSig, \DHSecret{i}, \EphemeralPublic,
|
|
\TransmitPublicNew{i})$.
|
|
\item Return $\DecryptNote(\TransmitKey{i}, \TransmitCiphertext{i}, \cmNew{i},
|
|
\AuthPublic).$
|
|
\end{itemize}
|
|
|
|
$\DecryptNote(\TransmitKey{i}, \TransmitCiphertext{i}, \cmNew{i}, \AuthPublic)$
|
|
is defined as follows:
|
|
|
|
\begin{itemize}
|
|
\item Let $\TransmitPlaintext{i} :=
|
|
\SymDecrypt{\TransmitKey{i}}(\TransmitCiphertext{i})$.
|
|
\item If $\TransmitPlaintext{i} = \bot$, return $\bot$.
|
|
\item Extract $\NotePlaintext{i} = (\ValueNew{i},
|
|
\NoteAddressRandNew{i}, \NoteCommitRandNew{i}, \Memo_i)$ from $\TransmitPlaintext{i}$.
|
|
\item If $\Commitment((\AuthPublic, \ValueNew{i}, \NoteAddressRandNew{i},
|
|
\NoteCommitRandNew{i})) \neq \cmNew{i}$, return $\bot$, else return $\NotePlaintext{i}$.
|
|
\end{itemize}
|
|
}
|
|
|
|
Note that this corresponds to step 3 (b) i. and ii. (first bullet point) of the
|
|
$\Receive$ algorithm shown in Figure 2 of \cite{ZerocashOakland}.
|
|
|
|
To test whether a \note is unspent in a particular \blockchainview also requires
|
|
the \authKeypair private key $\AuthPrivate$; the coin is unspent if and only if
|
|
$\nf = \PRFnf{\AuthPrivate}(\NoteAddressRand)$ is not in the \nullifierSet
|
|
for that \blockchainview.
|
|
|
|
Note that a \note can change from being unspent to spent on a given \blockchainview,
|
|
as \transactions are added to that view. Also, blockchain reorganisations can cause
|
|
the \transaction in which a \note was output to no longer be on the consensus
|
|
blockchain.
|
|
|
|
|
|
\changed{
|
|
\subsection{Commentary}
|
|
|
|
The public key encryption used in this part of the protocol is based loosely on
|
|
other encryption schemes based on Diffie-Hellman over an elliptic curve, such
|
|
as ECIES or the $\CryptoBoxSeal$ algorithm defined in libsodium \cite{cryptoboxseal}.
|
|
Note that:
|
|
}
|
|
\begin{itemize}
|
|
\changed{
|
|
\item The same ephemeral key is used for all encryptions to the recipient keys
|
|
in a given \joinSplitDescription.
|
|
\item In addition to the Diffie-Hellman secret, the KDF takes as input the
|
|
seed $\hSig$, the public keys of both parties, and the index $i$.
|
|
\item The nonce parameter to $\SymSpecific$ is not used.
|
|
\item The ``IETF" definition of $\SymSpecific$ from \cite{rfc7539} is
|
|
used; this uses a 32-bit block count and a 96-bit nonce, rather than a 64-bit
|
|
block count and 64-bit nonce as in the original definition of $\SymCipher$.
|
|
}
|
|
\end{itemize}
|
|
|
|
|
|
\section{Encoding Addresses and Keys}
|
|
|
|
This section describes how \Zcash encodes \paymentAddresses and \spendingKeys.
|
|
|
|
Addresses and keys can be encoded as a byte sequence; this is called
|
|
the \term{raw encoding}. This byte sequence can then be further encoded using
|
|
Base58Check. The Base58Check layer is the same as for upstream \Bitcoin
|
|
addresses \cite{Base58Check}.
|
|
|
|
SHA-256 compression function outputs are always represented as sequences of 32
|
|
bytes.
|
|
|
|
The language consisting of the following encoding possibilities is prefix-free.
|
|
|
|
\subsection{Transparent Payment Addresses}
|
|
|
|
These are encoded in the same way as in \Bitcoin \cite{Base58Check}.
|
|
|
|
\subsection{Transparent Private Keys}
|
|
|
|
These are encoded in the same way as in \Bitcoin \cite{Base58Check}.
|
|
|
|
\subsection{Protected Payment Addresses}
|
|
|
|
A \paymentAddress consists of $\AuthPublic$ and $\TransmitPublic$.
|
|
$\AuthPublic$ is a SHA-256 compression function output.
|
|
$\TransmitPublic$ is a \changed{Curve25519} public key, for use with the
|
|
encryption scheme defined in \crossref{inband}.
|
|
|
|
The raw encoding of a \paymentAddress consists of:
|
|
|
|
\begin{equation*}
|
|
\begin{bytefield}[bitwidth=0.07em]{520}
|
|
\changed{
|
|
\bitbox{72}{8 bit $\PaymentAddressLeadByte$}
|
|
&}\bitbox{256}{256 bit $\AuthPublic$} &
|
|
\bitbox{256}{\changed{256 bit} $\TransmitPublic$}
|
|
\end{bytefield}
|
|
\end{equation*}
|
|
|
|
\begin{itemize}
|
|
\changed{
|
|
\item A byte, $\PaymentAddressLeadByte$, indicating this version of the
|
|
raw encoding of a \Zcash public address.
|
|
}
|
|
\item 256 bits specifying $\AuthPublic$.
|
|
\item \changed{256 bits} specifying $\TransmitPublic$, \changed{using the
|
|
normal encoding of a Curve25519 public key \cite{Curve25519}}.
|
|
\end{itemize}
|
|
|
|
\daira{check that this lead byte is distinct from other Bitcoin stuff,
|
|
and produces `z' as the Base58Check leading character.}
|
|
|
|
\nathan{what about the network version byte?}
|
|
|
|
\subsection{Spending Keys}
|
|
|
|
A \spendingKey consists of $\AuthPrivate$, which is a sequence of 252 bits.
|
|
|
|
The raw encoding of a \spendingKey consists of, in order:
|
|
|
|
\begin{equation*}
|
|
\begin{bytefield}[bitwidth=0.07em]{264}
|
|
\changed{
|
|
\bitbox{72}{8 bit $\SpendingKeyLeadByte$}
|
|
\bitbox{32}{$\zeros{4}$} &
|
|
&}\bitbox{252}{\changed{252} bit $\AuthPrivate$}
|
|
\end{bytefield}
|
|
\end{equation*}
|
|
|
|
\begin{itemize}
|
|
\changed{
|
|
\item A byte $\SpendingKeyLeadByte$ indicating this version of the
|
|
raw encoding of a \Zcash \spendingKey.
|
|
\item 4 zero padding bits.
|
|
}
|
|
\item \changed{252} bits specifying $\AuthPrivate$.
|
|
\end{itemize}
|
|
|
|
The zero padding occupies the most significant 4 bits of the second byte.
|
|
|
|
\subparagraph{Note:} If an implementation represents $\AuthPrivate$
|
|
internally as a sequence of 32 bytes with the 4 bits of zero padding
|
|
intact, it will be in the correct form for use as an input to
|
|
$\PRFaddr{}$, $\PRFnf{}$, and $\PRFpk{}$ without need for bit-shifting.
|
|
Future key representations may make use of these padding bits.
|
|
|
|
\daira{check that this lead byte is distinct from other Bitcoin stuff,
|
|
and produces a suitable Base58Check leading character.}
|
|
|
|
\nathan{what about the network version byte?}
|
|
|
|
|
|
\section{Differences from the Zerocash paper}
|
|
|
|
\subsection{Transaction Structure} \label{trstructure}
|
|
|
|
\Zerocash introduces two new operations, which are described in
|
|
the paper as new transaction types, in addition to the original
|
|
transaction type of the cryptocurrency on which it is based
|
|
(e.g. \Bitcoin).
|
|
|
|
In \Zcash, there is only the original \Bitcoin transaction type,
|
|
which is extended to contain a sequence of zero or more
|
|
\Zcash-specific operations.
|
|
|
|
This allows for the possibility of chaining transfers of protected
|
|
value in a single \Zcash \transaction, e.g. to spend a protected \note
|
|
that has just been created. (In \Zcash, we refer to value stored in
|
|
UTXOs as ``transparent'', and value stored in \joinSplitTransfer output
|
|
\notes as ``protected''.)
|
|
This was not possible in the \Zerocash design without using multiple
|
|
transactions. It also allows transparent and protected transfers to
|
|
happen atomically --- possibly under the control of nontrivial script
|
|
conditions, at some cost in distinguishability.
|
|
|
|
\todo{Describe changes to signing.}
|
|
|
|
|
|
\subsection{Unification of Mints and Pours}
|
|
|
|
In the original \Zerocash protocol, there were two kinds of transaction
|
|
relating to protected \notes:
|
|
\begin{itemize}
|
|
\item a ``Mint'' transaction takes value from transparent UTXOs as
|
|
input and produces a new protected \note as output.
|
|
\item a ``Pour'' transaction takes up to $\NOld$ protected
|
|
\notes as input, and produces up to $\NNew$ protected \notes and a
|
|
transparent UTXO as output.
|
|
\end{itemize}
|
|
|
|
Only ``Pour'' transactions included a \zkSNARK proof.
|
|
|
|
In \Zcash, the sequence of operations added to a \transaction
|
|
(described in \crossref{trstructure}) consists only of \joinSplitTransfers.
|
|
A \joinSplitTransfer is a Pour operation generalized to take a transparent
|
|
UTXO as input, allowing \joinSplitTransfers to subsume the functionality of
|
|
Mints. An advantage of this is that a \Zcash \transaction that takes
|
|
input from an UTXO can produce up to $\NNew$ output \notes, improving
|
|
the indistinguishability properties of the protocol. A related change
|
|
conceals the input arity of the \joinSplitTransfer: an unused (zero-value)
|
|
input is indistinguishable from an input that takes value from a \note.
|
|
|
|
This unification also simplifies the fix to the Faerie Gold attack
|
|
described below, since no special case is needed for Mints.
|
|
|
|
|
|
\subsection{\Memos}
|
|
|
|
\Zcash adds a \memo sent from the creator of a \joinSplitDescription to
|
|
the recipient of each output \note. This feature is described in
|
|
more detail in \crossref{notept}.
|
|
|
|
|
|
\subsection{Faerie Gold attack and fix}
|
|
|
|
When a protected \note is created in \Zerocash, the creator is
|
|
supposed to choose a new $\NoteAddressRand$ value at random.
|
|
The \nullifier of the \note is derived from its \spendingKey
|
|
($\AuthPrivate$) and $\NoteAddressRand$. The \noteCommitment
|
|
is derived from the recipient address component $\AuthPublic$,
|
|
the value $\Value$, and the commitment trapdoor $\NoteCommitRand$,
|
|
as well as $\NoteAddressRand$. However nothing prevents creating
|
|
multiple \notes with different $\Value$ and $\NoteCommitRand$
|
|
(hence different \noteCommitments) but the same $\NoteAddressRand$.
|
|
|
|
An adversary can use this to mislead a \note recipient, by sending
|
|
two \notes both of which are verified as valid by $\Receive$ (as
|
|
defined in Figure 2 of \cite{ZerocashOakland}), but only one of
|
|
which can be spent.
|
|
|
|
We call this a ``Faerie Gold'' attack --- referring to various Celtic
|
|
legends in which faeries pay mortals in what appears to be gold,
|
|
but which soon after reveals itself to be leaves, gorse blossoms,
|
|
gingerbread cakes, or other less valuable things \cite{LG2004}.
|
|
|
|
This attack does not violate the security definitions given in
|
|
\cite{ZerocashOakland}. The issue could be framed as a problem
|
|
either with the definition of Completeness, or the definition of
|
|
Balance:
|
|
|
|
\begin{itemize}
|
|
\item The Completeness property asserts that a validly received
|
|
\note can be spent provided that its \nullifier does not appear
|
|
on the ledger. This does not take into account the possibility
|
|
that distinct \notes, which are validly received, could have the
|
|
same \nullifier. That is, the security definition depends on
|
|
a protocol detail --\nullifiers-- that is not part of the
|
|
intended abstract security property, and that could be implemented
|
|
incorrectly.
|
|
\item The Balance property only asserts that an adversary cannot
|
|
obtain \emph{more} funds than they have minted or received via
|
|
payments. It does not prevent an adversary from causing others'
|
|
funds to decrease. In a Faerie Gold attack, an adversary can cause
|
|
spending of a \note to reduce (to zero) the effective value of another
|
|
\note for which the attacker does not know the \spendingKey, which
|
|
violates an intuitive conception of global balance.
|
|
\end{itemize}
|
|
|
|
These problems with the security definitions need to be repaired,
|
|
but doing so is outside the scope of this specification. Here we
|
|
only describe how \Zcash addresses the immediate attack.
|
|
|
|
It would be possible to address the attack by requiring that a
|
|
recipient remember all of the $\NoteAddressRand$ values for all
|
|
\notes they have ever received, and reject duplicates (as proposed
|
|
in \cite{GGM2016}). However, this requirement would interfere
|
|
with the intended \Zcash feature that a holder of a \spendingKey
|
|
can recover access to (and be sure that they are able to spend) all
|
|
of their funds, even if they have forgotten everything but the
|
|
\spendingKey.
|
|
|
|
Instead, \Zcash enforces that an adversary must choose distinct values
|
|
for each $\NoteAddressRand$, by making use of the fact that all of the
|
|
\nullifiers in \joinSplitDescriptions that appear in a valid \blockchainview
|
|
must be distinct. The \nullifiers are used as input to $\BlakeHashName$
|
|
to derive a public value $\hSig$ which uniquely identifies the transaction,
|
|
as described in \crossref{hsig}. ($\hSig$ was already used in \Zerocash
|
|
in a way that requires it to be unique in order to maintain
|
|
indistinguishability of \joinSplitDescriptions; adding the \nullifiers
|
|
to the input of the hash used to calculate it has the effect of making
|
|
this uniqueness property robust even if the \transaction creator is an
|
|
adversary.)
|
|
|
|
The $\NoteAddressRand$ value for each output \note is then derived from
|
|
a random private seed $\NoteAddressPreRand$ and $\hSig$ using
|
|
$\PRFrho{\NoteAddressPreRand}$. The correct construction of
|
|
$\NoteAddressRand$ for each output \note is enforced by the circuit
|
|
(see \crossref{uniquerho}).
|
|
|
|
Now even if the creator of a \joinSplitDescription does not choose
|
|
$\NoteAddressPreRand$ randomly, uniqueness of \nullifiers and
|
|
collision resistance of both $\BlakeHashName$ and $\PRFrho{}$ will ensure
|
|
that the derived $\NoteAddressRand$ values are unique, at least for
|
|
any two \joinSplitDescriptions that get into a valid \blockchainview.
|
|
This is sufficient to prevent the Faerie Gold attack.
|
|
|
|
|
|
\subsection{Internal hash collision attack and fix}
|
|
|
|
The \Zerocash security proof requires that the composition of
|
|
$\COMM{\NoteCommitRand}$ and $\COMM{\NoteCommitS}$ is a computationally
|
|
binding commitment to its inputs $\AuthPublic$, $\Value$, and
|
|
$\NoteAddressRand$. However, the instantiation of $\COMM{\NoteCommitRand}$
|
|
and $\COMM{\NoteCommitS}$ in section 5.1 of the paper did not meet
|
|
the definition of a binding commitment at a 128-bit security level.
|
|
Specifically, the internal hash of $\AuthPublic$ and $\NoteAddressRand$
|
|
is truncated to 128 bits (motivated by providing statistical hiding
|
|
security). This allows an attacker, with a work factor on the order of
|
|
$2^{64}$, to find distinct values of $\NoteAddressRand$ with colliding
|
|
outputs of the truncated hash, and therefore the same \noteCommitment.
|
|
This would have allowed such an attacker to break the balance property
|
|
by double-spending \notes, potentially creating arbitrary amounts of
|
|
currency for themself.
|
|
|
|
\Zcash uses a simpler construction with a single $\FullHash$ evaluation
|
|
for the commitment. The motivation for the nested construction in \Zerocash
|
|
was to allow Mint transactions to be publically verified without requiring
|
|
a ZK proof (as described under step 3 in section 1.3 of
|
|
\cite{ZerocashOakland}). Since \Zcash combines ``Mint'' and ``Pour''
|
|
transactions into a generalized \joinSplitTransfer which always uses a ZK proof,
|
|
it does not require the nesting. A side benefit is that this reduces the
|
|
number of $\SHA$ evaluations needed to compute each \noteCommitment from
|
|
three to two, saving a total of four $\SHA$ evaluations in the
|
|
$\JoinSplitCircuit$.
|
|
|
|
Note that \Zcash \noteCommitments are not statistically hiding, and
|
|
so \Zcash does not support the ``everlasting anonymity'' property
|
|
described in section 8.1 of the \Zerocash paper \cite{ZerocashOakland},
|
|
even when used as described in that section. While it is possible to
|
|
define a statistically hiding, computationally binding commitment scheme
|
|
for this use at a 128-bit security level, the overhead of doing so
|
|
within the circuit was not considered to justify the benefits.
|
|
|
|
\subsection{Changes to PRF inputs and truncation}
|
|
|
|
\todo{}
|
|
|
|
%The need for collision resistance of \CRH(.) truncated to 253 bits was not
|
|
%explicitly stated in \ (This does not follow from collision resistance of $\CRH$.)
|
|
|
|
\subsection{In-band secret distribution}
|
|
|
|
\todo{}
|
|
|
|
\subsection{Miscellaneous}
|
|
|
|
\begin{itemize}
|
|
\item The paper defines a \note as a tuple $(\AuthPublic, \Value,
|
|
\NoteAddressRand, \NoteCommitRand, \NoteCommitS, \cm)$, whereas this specification
|
|
defines it as $(\AuthPublic, \Value, \NoteAddressRand, \NoteCommitRand)$.
|
|
This is just a clarification, because the instantiation of $\COMM{\NoteCommitS}$
|
|
in section 5.1 of the paper did not use $\NoteCommitS$ (and neither does the
|
|
new instantiation of $\Commitment$). $\cm$ can be computed from the other
|
|
fields.
|
|
\end{itemize}
|
|
|
|
|
|
\section{Acknowledgements}
|
|
|
|
The inventors of \Zerocash are Eli Ben-Sasson, Alessandro Chiesa,
|
|
Christina Garman, Matthew Green, Ian Miers, Eran Tromer, and Madars
|
|
Virza.
|
|
|
|
The authors would like to thank everyone with whom they have discussed
|
|
the \Zerocash protocol design; in addition to the inventors, this includes
|
|
Mike Perry, Isis Lovecruft, Leif Ryge, Andrew Miller, Zooko Wilcox,
|
|
Samantha Hulsey, and no doubt others.
|
|
|
|
The Faerie Gold attack was found by Zooko Wilcox.
|
|
The internal hash collision attack was found by Taylor Hornby.
|
|
|
|
|
|
\section{References}
|
|
|
|
\begingroup
|
|
\renewcommand{\section}[2]{}
|
|
\bibliographystyle{plain}
|
|
\bibliography{zcash}
|
|
\endgroup
|
|
|
|
\end{document}
|