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1321 lines
51 KiB
1321 lines
51 KiB
\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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\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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\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-draft-4}
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\newcommand{\authors}{Sean Bowe | Daira Hopwood | 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={\authors}
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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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% terminology
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\newcommand{\term}[1]{\textsl{#1}\xspace}
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\newcommand{\termbf}[1]{\textbf{#1}\xspace}
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\newcommand{\conformance}[1]{\textmd{#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{\MAY}{\conformance{MAY}}
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\newcommand{\coin}{\term{coin}}
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\newcommand{\coins}{\term{coins}}
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\newcommand{\coinCommitment}{\term{coin commitment}}
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\newcommand{\coinCommitments}{\term{coin commitments}}
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\newcommand{\coinCommitmentTree}{\term{coin commitment tree}}
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\newcommand{\PourDescription}{\term{Pour description}}
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\newcommand{\PourDescriptions}{\term{Pour descriptions}}
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\newcommand{\sequenceOfPourDescriptions}{\changed{sequence of} \PourDescription\changed{\term{s}}}
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\newcommand{\PourTransfer}{\term{Pour transfer}}
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\newcommand{\PourTransfers}{\term{Pour transfers}}
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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{\script}{\term{script}}
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\newcommand{\serialNumber}{\term{serial number}}
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\newcommand{\serialNumbers}{\term{serial numbers}}
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\newcommand{\spentSerials}{\term{spent serial number 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{\coinPlaintext}{\term{coin plaintext}}
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\newcommand{\coinPlaintexts}{\term{coin plaintexts}}
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\newcommand{\coinsCiphertext}{\term{transmitted coins 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{\spentSerialsMap}{\term{spent serial numbers map}}
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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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% 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{\CRH}{\mathsf{CRH}}
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\newcommand{\CRHbox}[1]{\CRH\left(\;\raisebox{-1.3ex}{\usebox{#1}}\;\right)}
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\newcommand{\FullHash}{\mathtt{SHA256}}
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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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% 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{\CoinCommitmentLeadByte}{\hexint{C0}}
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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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% Coins
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\newcommand{\Coin}[1]{\mathbf{c}_{#1}}
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\newcommand{\CoinPlaintext}[1]{\mathbf{cp}_{#1}}
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\newcommand{\CoinCommitRand}{\mathsf{r}}
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\newcommand{\CoinCommitRandOld}[1]{\mathsf{r^{old}_\mathnormal{#1}}}
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\newcommand{\CoinCommitRandNew}[1]{\mathsf{r^{new}_\mathnormal{#1}}}
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\newcommand{\CoinAddressRand}{\mathsf{\uprho}}
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\newcommand{\CoinAddressRandOld}[1]{\mathsf{\uprho^{old}_\mathnormal{#1}}}
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\newcommand{\CoinAddressRandNew}[1]{\mathsf{\uprho^{new}_\mathnormal{#1}}}
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\newcommand{\CoinAddressPreRand}{\mathsf{\upvarphi}}
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\newcommand{\CoinCommitS}{\mathsf{s}}
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\newcommand{\hSigInputVersionByte}{\hexint{C1}}
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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{\DecryptCoin}{\mathtt{DecryptCoin}}
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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{\RandomSeed}{\mathsf{randomSeed}}
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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{\KDFLeadByte}{\hexint{C2}}
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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{\PRFsn}[1]{\PRF{#1}{sn}}
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\newcommand{\PRFpk}[1]{\PRF{#1}{pk}}
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\newcommand{\PRFrho}[1]{\PRF{#1}{\CoinAddressRand}}
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\newcommand{\PRFdk}[1]{\PRF{#1}{dk}}
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\newcommand{\SHA}{\mathtt{SHA256Compress}}
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\newcommand{\SHAName}{\term{SHA-256 compression}}
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\newcommand{\SHAOrig}{\term{SHA-256}}
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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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% merkle tree
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\newcommand{\MerkleDepth}{\mathsf{d}}
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\newcommand{\sn}{\mathsf{sn}}
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\newcommand{\snOld}[1]{\mathsf{{sn}^{old}_\mathnormal{#1}}}
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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{\vpour}{\mathtt{vpour}}
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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{\scriptSig}{\mathtt{scriptSig}}
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\newcommand{\scriptPubKey}{\mathtt{scriptPubKey}}
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\newcommand{\serials}{\mathtt{serials}}
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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{\discloseCiphertexts}{\mathtt{discloseCiphertexts}}
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\newcommand{\randomSeed}{\mathtt{randomSeed}}
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\newcommand{\rt}{\mathsf{rt}}
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% pour
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\newcommand{\hSig}{\mathsf{h_{Sig}}}
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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{\zkproof}{\mathtt{zkproof}}
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\newcommand{\PourCircuit}{\term{\texttt{POUR} circuit}}
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\newcommand{\PourStatement}{\texttt{POUR}}
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\newcommand{\PourProof}{\pi_{\PourStatement}}
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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{c}_{#1}^\mathsf{old}}
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\newcommand{\cNew}[1]{\mathbf{c}_{#1}^\mathsf{new}}
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\newcommand{\cpNew}[1]{\mathbf{cp}_{#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{\CoinCommitment}{\mathtt{CoinCommitment}}
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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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\author{\authors}
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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 as big-endian. \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
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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
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digits represents the corresponding integer converted from hexadecimal.
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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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If the content of the box is a byte sequence, it is implicitly converted to
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a sequence of bits using big-endian order. The bit sequences are then
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concatenated in the order shown from left to right, and the result is converted
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to a sequence of bytes, again using big-endian order.
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\newsavebox{\examplebox}
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\begin{lrbox}{\examplebox}
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\setchanged
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\begin{bytefield}[bitwidth=0.6em]{32}
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\bitbox{2}{0} &
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\bitbox{2}{1} &
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\bitbox{2}{0} &
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\bitbox{2}{0} &
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\bitbox{16}{16 bit $\hexint{ABCD}$} &
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\bitbox{12}{12 bit $\hexint{0123}$} &
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\end{bytefield}
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\end{lrbox}
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For example, the diagram
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\begin{itemize}
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\item[] $\Justthebox{\examplebox}{-1.3ex}$
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\end{itemize}
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represents the byte sequence $[\hexint{4A}, \hexint{BC}, \hexint{D1}, \hexint{23}]$.
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The notation $\allN{}$, used as a subscript, means the sequence of values
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|
with indices $1$ through $\mathrm{N}$ inclusive. For example,
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$\AuthPublicNew{\allNew}$ means the sequence $[\AuthPublicNew{\mathrm{1}},
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\AuthPublicNew{\mathrm{2}}, ...\;\AuthPublicNew{\NNew}]$.
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The symbol $\bot$ is used to indicate unavailable information or a failed decryption.
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\subsection{Cryptographic Functions}
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$\CRH$ is a collision-resistant hash function. In \Zcash, the $\SHAName$ function
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is used which takes a 512-bit block and produces a 256-bit hash. This is
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different from the $\SHAOrig$ function, which hashes arbitrary-length sequences.
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\cite{sha256}
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$\PRF{x}{}$ is a pseudo-random function seeded by $x$. \changed{Four} \emph{independent}
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$\PRF{x}{}$ are needed in our scheme: $\PRFaddr{x}$, $\PRFsn{x}$, $\PRFpk{x}$\changed{,
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and $\PRFrho{x}$}.
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It is required that $\PRFsn{x}$ \changed{and $\PRFrho{x}$} be collision-resistant
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across all $x$ --- i.e. it should not be feasible to find $(x, y) \neq (x', y')$
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such that $\PRFsn{x}(y) = \PRFsn{x'}(y')$\changed{, and similarly for $\PRFrho{}$}.
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In \Zcash, the $\SHAName$ function is used to construct all of these
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functions.
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\newcommand{\iminusone}{\hspace{0.3pt}\scriptsize{$i$\hspace{0.6pt}-1}}
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|
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|
\newsavebox{\addrbox}
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|
\begin{lrbox}{\addrbox}
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|
\setchanged
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|
\begin{bytefield}[bitwidth=0.06em]{512}
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\bitbox{18}{0} &
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\bitbox{18}{0} &
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\bitbox{18}{0} &
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\bitbox{18}{0} &
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\bitbox{224}{252 bit $x$} &
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\bitbox{200}{$\zeros{253}$} &
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\bitbox{56}{3 bit $t$} &
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\end{bytefield}
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\end{lrbox}
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\newsavebox{\snbox}
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|
\begin{lrbox}{\snbox}
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|
\setchanged
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|
\begin{bytefield}[bitwidth=0.06em]{512}
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|
\bitbox{18}{0} &
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|
\bitbox{18}{1} &
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\bitbox{18}{0} &
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\bitbox{18}{0} &
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\bitbox{224}{252 bit $\AuthPrivate$} &
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\bitbox{256}{256 bit $\CoinAddressRand$} &
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|
\end{bytefield}
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|
\end{lrbox}
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|
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\newsavebox{\pkbox}
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|
\begin{lrbox}{\pkbox}
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|
\setchanged
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|
\begin{bytefield}[bitwidth=0.06em]{512}
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|
\bitbox{18}{0} &
|
|
\bitbox{18}{\iminusone} &
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\bitbox{18}{0} &
|
|
\bitbox{18}{1} &
|
|
\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 $\CoinAddressPreRand$} &
|
|
\bitbox{256}{256 bit $\hSig$}
|
|
\end{bytefield}
|
|
\end{lrbox}
|
|
|
|
\begin{equation*}
|
|
\begin{aligned}
|
|
&\setchanged \PRFaddr{x}(t) &\setchanged := \CRHbox{\addrbox} \\
|
|
\sn =\;& \PRFsn{\AuthPrivate}(\CoinAddressRand) &:= \CRHbox{\snbox} \\
|
|
\h{i} =\;& \PRFpk{\AuthPrivate}(i, \hSig) &:= \CRHbox{\pkbox} \\
|
|
\setchanged \CoinAddressRandNew{i} =\;&\setchanged \PRFrho{\CoinAddressPreRand}(i, \hSig)
|
|
&\setchanged := \CRHbox{\rhobox}
|
|
\end{aligned}
|
|
\end{equation*}
|
|
|
|
\changed{
|
|
\subparagraph{Note:}
|
|
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 first four bits $\mathtt{1100}$
|
|
(i.e. a first byte of \textbf{0xC\dontcare}) are used to distinguish uses
|
|
of the full $\SHAOrig$ hash function -- see \crossref{comm} and \crossref{hsig}.
|
|
}
|
|
|
|
|
|
\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{Coins}
|
|
|
|
A \coin (denoted $\Coin{}$) is a tuple $\changed{(\AuthPublic, \Value,
|
|
\CoinAddressRand, \CoinCommitRand)}$ 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
|
|
\coin in \zatoshi (1 \ZEC = $10^8$ \zatoshi).
|
|
\item $\CoinAddressRand$ is a 32-byte $\PRFsn{\AuthPrivate}$ preimage.
|
|
\item $\CoinCommitRand$ is a 24-byte \COMMtrapdoor.
|
|
\end{itemize}
|
|
|
|
$\CoinCommitRand$ is randomly generated by the sender. \changed{$\CoinAddressRand$
|
|
is generated from a random seed $\CoinAddressPreRand$ using
|
|
$\PRFrho{\CoinAddressPreRand}$.} Only a commitment to these values is disclosed
|
|
publicly, which allows the tokens $\CoinCommitRand$ and $\CoinAddressRand$ to blind
|
|
the value and recipient \emph{except} to those who possess these tokens.
|
|
|
|
\subsubsection{Coin Commitments} \label{comm}
|
|
|
|
The underlying $\Value$ and $\AuthPublic$ are blinded with $\CoinAddressRand$
|
|
and $\CoinCommitRand$ using the collision-resistant hash function \changed{$\FullHash$}.
|
|
The resulting hash $\cm = \CoinCommitment(\Coin{})$.
|
|
|
|
\newsavebox{\cmbox}
|
|
\begin{lrbox}{\cmbox}
|
|
\setchanged
|
|
\begin{bytefield}[bitwidth=0.042em]{776}
|
|
\bitbox{128}{8 bit $\CoinCommitmentLeadByte$} &
|
|
\bitbox{256}{256 bit $\AuthPublic$} &
|
|
\bitbox{128}{64 bit $\Value$} &
|
|
\bitbox{256}{256 bit $\CoinAddressRand$}
|
|
\bitbox{192}{192 bit $\CoinCommitRand$} &
|
|
\end{bytefield}
|
|
\end{lrbox}
|
|
|
|
\changed{
|
|
\hskip 1.5em $\cm := \FullHashbox{\cmbox}$
|
|
}
|
|
|
|
\subsubsection{Serial numbers}
|
|
|
|
A \serialNumber (denoted $\sn$) equals
|
|
$\PRFsn{\AuthPrivate}(\CoinAddressRand)$. A \coin is spent by proving
|
|
knowledge of $\CoinAddressRand$ and $\AuthPrivate$ in zero knowledge while
|
|
disclosing $\sn$, allowing $\sn$ to be used to prevent double-spending.
|
|
|
|
\subsubsection{Coin plaintexts and memo fields} \label{coinpt}
|
|
|
|
Transmitted coins are stored on the blockchain in encrypted form, together with
|
|
a \coinCommitment $\cm$.
|
|
|
|
The \coinPlaintexts associated with a \PourDescription are encrypted to the
|
|
respective \transmitKeypair keys $\TransmitPublicNew{\allNew}$,
|
|
and the result forms part of a \coinsCiphertext (see \crossref{inband}
|
|
for further details).
|
|
|
|
Each \coinPlaintext (denoted $\CoinPlaintext{}$) consists of
|
|
$(\changed{\AuthPublic,\;}\Value, \CoinAddressRand, \CoinCommitRand\changed{, \Memo})$.
|
|
|
|
The first \changed{four} of these fields are as defined earlier.
|
|
\changed{$\Memo$ is a 64-byte \memo associated with this \coin.
|
|
|
|
The usage of the $\memo$ is by agreement between the sender and recipient of the
|
|
\coin. It should be encoded as a UTF-8 human-readable string \cite{Unicode}, padded
|
|
with zero bytes. Wallet software is expected to strip any trailing zero bytes and
|
|
then display the resulting UTF-8 string to the recipient user, where applicable.
|
|
Incorrect UTF-8-encoded byte sequences should be displayed as replacement characters
|
|
(\ReplacementCharacter). This does not preclude uses of the \memo by automated
|
|
software, but specification of such usage is not in the scope of this document.
|
|
}
|
|
|
|
The encoding of a \coinPlaintext consists of, in order:
|
|
\begin{equation*}
|
|
\begin{bytefield}[bitwidth=0.035em]{1288}
|
|
\changed{
|
|
\bitbox{256}{$\AuthPublic$ (32 bytes)}&
|
|
&}\bitbox{168}{$\Value$ (8 bytes)} &
|
|
\bitbox{256}{$\CoinAddressRand$ (32 bytes)} &
|
|
\bitbox{192}{$\CoinCommitRand$ (\changed{24} bytes)} &
|
|
\changed{\bitbox{512}{$\Memo$ (64 bytes)}}
|
|
\end{bytefield}
|
|
\end{equation*}
|
|
|
|
\begin{itemize}
|
|
\changed{
|
|
\item 32 bytes specifying $\AuthPublic$.
|
|
}
|
|
\item 8 bytes specifying a big-endian encoding of $\Value$.
|
|
\item 32 bytes specifying $\CoinAddressRand$.
|
|
\item \changed{24} bytes specifying $\CoinCommitRand$.
|
|
\changed{
|
|
\item 64 bytes specifying $\Memo$.
|
|
}
|
|
\end{itemize}
|
|
|
|
|
|
\subsection{Coin Commitment Tree}
|
|
|
|
\begin{center}
|
|
\includegraphics[scale=.4]{incremental_merkle}
|
|
\end{center}
|
|
|
|
The \coinCommitmentTree is an \incrementalMerkleTree of depth $\MerkleDepth$ used to
|
|
store \coinCommitments that \PourTransfers 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 root of this tree
|
|
after all of its constituent \PourDescriptions' \coinCommitments have been
|
|
entered into the tree associated with the previous block.
|
|
|
|
\subsection{Spent Serials Map}
|
|
|
|
Transactions insert \serialNumbers into a \spentSerialsMap 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 serials to the spent serials
|
|
map.}
|
|
|
|
Transactions that attempt to insert a \serialNumber into this map 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 serial numbers into the
|
|
spent serials map.}
|
|
|
|
\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 \sequenceOfPourDescriptions.
|
|
\todo{They also have a transparent value flow that interacts with the Pour
|
|
\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} \PourDescription in a \transaction must refer to
|
|
some earlier \block's final \treestate.
|
|
|
|
\changed{
|
|
The \anchor of each subsequent \PourDescription may refer either to some earlier
|
|
\block's final \treestate, or to the output \treestate of the immediately preceding
|
|
\PourDescription.
|
|
}
|
|
|
|
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{Pour Transfers and Descriptions} \label{pourdesc}
|
|
|
|
A \PourDescription is data included in a \block that describes a \PourTransfer,
|
|
i.e. a confidential value transfer. This kind of value transfer is the primary
|
|
\Zerocash-specific operation performed by transactions; it uses, but should not be
|
|
confused with, the \PourCircuit used for the \zkSNARK proof and verification.
|
|
|
|
A \PourTransfer spends $\NOld$ \coins $\cOld{\allOld}$ and creates $\NNew$ \coins
|
|
$\cNew{\allNew}$. \Zcash transactions have an additional field $\vpour$, which is
|
|
a \sequenceOfPourDescriptions.
|
|
|
|
Each \PourDescription consists of:
|
|
|
|
\begin{list}{}{}
|
|
\changed{
|
|
\item $\vpubOldField$ which is a value $\vpubOld$ that the \PourTransfer removes
|
|
from the value pool.
|
|
}
|
|
|
|
\item $\vpubNewField$ which is a value $\vpubNew$ that the \PourTransfer inserts
|
|
into the value pool.
|
|
|
|
\item $\anchorField$ which is a merkle root $\rt$ of the \coinCommitmentTree at
|
|
some block height in the past, or the merkle root produced by a previous pour in
|
|
this transaction. \sean{We need to be more specific here.}
|
|
|
|
\item $\scriptPubKey$ which is a \script that creates conditions for acceptance of a
|
|
\PourDescription in a transaction.
|
|
|
|
\item $\scriptSig$ which is a \script used to satisfy the conditions of the
|
|
$\scriptPubKey$.
|
|
|
|
\item $\serials$ which is an $\NOld$ size sequence of serials $\snOld{\allOld}$.
|
|
|
|
\item $\commitments$ which is a $\NNew$ size sequence of \coinCommitments
|
|
$\cmNew{\allNew}$.
|
|
|
|
\item $\ephemeralKey$ which is a Curve25519 public key $\EphemeralPublic$.
|
|
|
|
\item $\encCiphertexts$ which is a $\NNew$ size sequence of ciphertext
|
|
components, $\TransmitCiphertext{\allNew}$.
|
|
|
|
\changed{
|
|
(The preceding two fields form the \coinsCiphertext.)
|
|
|
|
\item $\randomSeed$ which is a random 256-bit seed $\RandomSeed$.
|
|
}
|
|
|
|
\item $\vmacs$ which is a $\NOld$ size sequence of message authentication tags
|
|
$\h{\allOld}$ that bind $\hSig$ to each $\AuthPrivate$ of the
|
|
$\PourDescription$.
|
|
|
|
\item $\zkproof$ which is the zero-knowledge proof $\PourProof$.
|
|
|
|
\end{list}
|
|
|
|
\todo{Describe case where there are fewer than $\NOld$ real input coins.}
|
|
|
|
\subparagraph{Computation of $\hSig$} \label{hsig}
|
|
|
|
\newsavebox{\hsigbox}
|
|
\begin{lrbox}{\hsigbox}
|
|
\setchanged
|
|
\begin{bytefield}[bitwidth=0.034em]{1064}
|
|
\bitbox{160}{8 bit $\hSigInputVersionByte$} &
|
|
\bitbox{256}{\hfill 256 bit $\snOld{\mathrm{1}}$\hfill...\;} &
|
|
\bitbox{256}{256 bit $\snOld{\NOld}$} &
|
|
\bitbox{256}{$\RandomSeed$}
|
|
\bitbox{256}{$\scriptPubKey$}
|
|
\end{bytefield}
|
|
\end{lrbox}
|
|
|
|
\changed{
|
|
Given a \PourDescription, we define:
|
|
|
|
\hskip 1.5em $\hSig := \FullHashbox{\hsigbox}$
|
|
}
|
|
|
|
\subparagraph{Merkle root validity}
|
|
|
|
A \PourDescription is valid if $\rt$ is a \coinCommitmentTree root found in
|
|
either the blockchain or a merkle root produced by inserting the \coinCommitments
|
|
of a previous $\PourDescription$ in the transaction to the \coinCommitmentTree
|
|
identified by that previous $\PourDescription$'s $\anchor$.
|
|
|
|
\subparagraph{Non-malleability}
|
|
|
|
A \PourDescription is valid if the script formed by appending $\scriptPubKey$ to
|
|
$\scriptSig$ returns $true$. The $\scriptSig$ is cryptographically bound to
|
|
$\PourProof$.
|
|
|
|
\subparagraph{Balance}
|
|
|
|
A \PourTransfer 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 transfers. The addition of $\vpubOld$ to a
|
|
\PourDescription subsumes the functionality of Mint. Also, \PourDescriptions
|
|
are indistinguishable regardless of the number of real input \coins.
|
|
}
|
|
|
|
\subparagraph{Commitments and Serials}
|
|
|
|
A \transaction that contains one or more \PourDescriptions, when entered into the
|
|
blockchain, appends to the \coinCommitmentTree with all constituent
|
|
\coinCommitments. All of the constituent \serialNumbers are also entered into the
|
|
\spentSerialsMap of the \blockchainview \emph{and} \mempool. A \transaction is not
|
|
valid if it attempts to add a \serialNumber to the \spentSerialsMap that already
|
|
exists in the map.
|
|
|
|
\subsection{Pour Circuit and Proofs}
|
|
|
|
In \Zcash, $\NOld$ and $\NNew$ are both $2$.
|
|
|
|
A valid instance of $\PourProof$ assures that given a \term{primary input}:
|
|
|
|
\begin{itemize}
|
|
\item[] $(\rt, \snOld{\allOld}, \cmNew{\allNew}, \changed{\vpubOld,\;}
|
|
\vpubNew, \hSig, \h{\allOld})$,
|
|
\end{itemize}
|
|
|
|
there exists a witness of \term{auxiliary input}:
|
|
|
|
\begin{itemize}
|
|
\item[] $(\treepath{\allOld}, \cOld{\allOld}, \AuthPrivateOld{\allOld},
|
|
\cpNew{\allNew}\changed{, \CoinAddressPreRand})$
|
|
\end{itemize}
|
|
|
|
where:
|
|
|
|
\begin{itemize}
|
|
\item[] for each $i \in \setofOld$: $\cOld{i} = (\AuthPublicOld{i},
|
|
\vOld{i}, \CoinAddressRandOld{i}, \CoinCommitRandOld{i})$;
|
|
\item[] for each $i \in \setofNew$: $\cNew{i} = (\AuthPublicNew{i},
|
|
\vNew{i}, \CoinAddressRandNew{i}, \CoinCommitRandNew{i})$
|
|
\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 path of depth $\MerkleDepth$ from \linebreak
|
|
$\CoinCommitment(\cOld{i})$ to \coinCommitmentTree root $\rt$.
|
|
|
|
\subparagraph{Balance}
|
|
|
|
$\changed{\vpubOld\; +} \vsum{i=1}{\NOld} \vOld{i} = \vpubNew + \vsum{i=1}{\NNew} \vNew{i}$.
|
|
|
|
\subparagraph{Serial integrity}
|
|
|
|
for each $i \in \setofNew$:
|
|
$\snOld{i} = \PRFsn{\AuthPrivateOld{i}}(\CoinAddressRandOld{i})$.
|
|
|
|
\subparagraph{Spend authority}
|
|
|
|
for each $i \in \setofOld$:
|
|
$\AuthPublicOld{i} = \changed{\PRFaddr{\AuthPrivateOld{i}}(0)}$.
|
|
|
|
\subparagraph{Non-malleability}
|
|
|
|
for each $i \in \setofOld$:
|
|
$\h{i} = \PRFpk{\AuthPrivateOld{i}}(i, \hSig)$.
|
|
|
|
\changed{
|
|
\subparagraph{Uniqueness of $\CoinAddressRandNew{i}$} \label{uniquerho}
|
|
|
|
for each $i \in \setofNew$:
|
|
$\CoinAddressRandNew{i} = \PRFrho{\CoinAddressPreRand}(i, \hSig)$.
|
|
}
|
|
|
|
\subparagraph{Commitment integrity}
|
|
|
|
for each $i \in \setofNew$: $\cmNew{i}$ = $\CoinCommitment(\cNew{i})$.
|
|
|
|
|
|
\section{In-band secret distribution} \label{inband}
|
|
|
|
In order to transmit the secret $\Value$, $\CoinAddressRand$, and $\CoinCommitRand$
|
|
(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 \coin \changed{ and \memo}.
|
|
|
|
All of the resulting ciphertexts are combined to form a \coinsCiphertext.
|
|
|
|
\newsavebox{\kdfbox}
|
|
\begin{lrbox}{\kdfbox}
|
|
\setchanged
|
|
\begin{bytefield}[bitwidth=0.035em]{840}
|
|
\bitbox{160}{8 bit $\KDFLeadByte$} &
|
|
\bitbox{256}{256 bit $\DHSecret{i}$} &
|
|
\bitbox{256}{256 bit $\EphemeralPublic$} &
|
|
\bitbox{256}{256 bit $\TransmitPublicNew{i}$} &
|
|
\bitbox{160}{8 bit $i-1$}
|
|
\end{bytefield}
|
|
\end{lrbox}
|
|
|
|
\subsection{Encryption}
|
|
|
|
\changed{
|
|
Let $\SymEncrypt{\Key}(\Plaintext)$ be authenticated encryption using a variation
|
|
of $\SymSpecific$ \cite{rfc7539} encryption of plaintext $\Plaintext$, with empty
|
|
``associated data", all-zero nonce $\zeros{96}$, and 256-bit key $\Key$. The variation
|
|
is that the $\SymCipher$ keystream is used to encrypt the plaintext starting immediately
|
|
after the 32 bytes of the $\SymAuth$ key, without discarding 32 bytes as in \cite{rfc7539}.
|
|
|
|
Similarly, let $\SymDecrypt{\Key}(\Ciphertext)$ be decryption using the same
|
|
$\SymSpecific$ variation 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 $\KDF(\DHSecret{i}, \EphemeralPublic, \TransmitPublicNew{i}, i) :=$
|
|
{\parskip=0.3ex
|
|
|
|
\hskip 5em $\FullHashbox{\kdfbox}$.
|
|
\vskip 1ex}
|
|
}
|
|
|
|
Let $\TransmitPublicNew{\allNew}$ be the \changed{Curve25519} public keys
|
|
for the intended recipient addresses of each new \coin, and let
|
|
$\CoinPlaintext{\allNew}$ be the \coinPlaintexts.
|
|
|
|
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 $\CoinPlaintext{i}$.
|
|
\item Let $\DHSecret{i} := \CurveMultiply(\EphemeralPrivate,
|
|
\TransmitPublicNew{i})$.
|
|
\item Let $\TransmitKey{i} := \KDF(\DHSecret{i}, \EphemeralPublic,
|
|
\TransmitPublicNew{i}, i)$.
|
|
\item Let $\TransmitCiphertext{i} :=
|
|
\SymEncrypt{\TransmitKey{i}}(\TransmitPlaintext{i})$.
|
|
\end{itemize}
|
|
}
|
|
\end{itemize}
|
|
|
|
The resulting \coinsCiphertext is $\changed{(\EphemeralPublic,
|
|
\TransmitCiphertext{\allNew})}$.
|
|
|
|
\subsection{Decryption by a Recipient}
|
|
|
|
Let $(\TransmitPublic, \TransmitPrivate)$ be the recipient's \changed{Curve25519}
|
|
(public, private) key pair, and let $\cmNew{\allNew}$ be the coin
|
|
commitments 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 $\TransmitKey{i} := \KDF(\DHSecret{i}, \EphemeralPublic,
|
|
\TransmitPublicNew{i}, i)$.
|
|
\item Return $\DecryptCoin(\TransmitKey{i}, \TransmitCiphertext{i}, \cmNew{i}).$
|
|
\end{itemize}
|
|
|
|
$\DecryptCoin(\TransmitKey{i}, \TransmitCiphertext{i}, \cmNew{i})$ is defined as follows:
|
|
|
|
\begin{itemize}
|
|
\item Let $\TransmitPlaintext{i} :=
|
|
\SymDecrypt{\TransmitKey{i}}(\TransmitCiphertext{i})$.
|
|
\item If $\TransmitPlaintext{i} = \bot$, return $\bot$.
|
|
\item Extract $\CoinPlaintext{i} = (\AuthPublicNew{i}, \ValueNew{i},
|
|
\CoinAddressRandNew{i}, \CoinCommitRandNew{i}, \Memo_i)$ from $\TransmitPlaintext{i}$.
|
|
\item If $\CoinCommitment((\AuthPublicNew{i}, \ValueNew{i}, \CoinAddressRandNew{i},
|
|
\CoinCommitRandNew{i})) \neq \cmNew{i}$, return $\bot$, else return $\CoinPlaintext{i}$.
|
|
\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 \coin is unspent in a particular \blockchainview also requires
|
|
the \authKeypair private key $\AuthPrivate$; the coin is unspent if and only if
|
|
$\sn = \PRFsn{\AuthPrivate}(\CoinAddressRand)$ is not in the \spentSerials
|
|
for that \blockchainview.
|
|
|
|
Note that a coin may change from being unspent to spent on a given \blockchainview,
|
|
as transactions are added to that view. Also, blockchain reorganisations may cause
|
|
the transaction in which a coin 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 \PourDescription.
|
|
\item In addition to the Diffie-Hellman secret, the KDF takes as input the
|
|
public keys of both parties, and the index $i$.
|
|
\item The nonce parameter to $\SymSpecific$ is not used.
|
|
}
|
|
\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{Private 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 $\AuthPrivate$.
|
|
|
|
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}
|
|
|
|
Note that, consistent with big-endian encoding, the zero padding occupies
|
|
the high-order 4 bits of the second byte.
|
|
|
|
\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 transaction, e.g. to spend a protected coin that
|
|
has just been created. (In \Zcash, we refer to value stored in UTXOs
|
|
as ``transparent'', and value stored in Pour output coins 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.
|
|
|
|
|
|
\subsection{Unification of Mints and Pours}
|
|
|
|
In the original \Zerocash protocol, there were two kinds of transaction
|
|
relating to protected coins:
|
|
\begin{itemize}
|
|
\item a ``Mint'' transaction takes value from transparent UTXOs as
|
|
input and produces a new protected coin as output.
|
|
\item a ``Pour'' transaction takes up to $\NOld$ protected
|
|
coins as input, and produces up to $\NNew$ protected coins 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 Pours.
|
|
A Pour is generalized to take a transparent UTXO as input, allowing
|
|
Pours to subsume the functionality of Mints. An advantage of this
|
|
is that a transaction that takes input from an UTXO can produce
|
|
up to $\NNew$ output coins, improving the indistinguishability
|
|
properties of the protocol. A related change conceals the input
|
|
arity of the Pour: an unused (zero-value) input is
|
|
indistinguishable from an input that takes value from a coin.
|
|
|
|
This unification also simplifies the fix to the Faerie Gold attack
|
|
described below, since no special case is needed for Mints.
|
|
|
|
|
|
\subsection{Memo fields}
|
|
|
|
\Zerocash adds a memo field sent from the creator of a Pour to
|
|
the recipient of each output coin. This feature is described in
|
|
more detail in \crossref{coinpt}.
|
|
|
|
|
|
\subsection{Faerie Gold attack and fix}
|
|
|
|
When a protected \coin is created in \Zerocash, the creator is
|
|
supposed to choose a new $\CoinAddressRand$ value at random.
|
|
The \serialNumber of the \coin is derived from its \spendingKey
|
|
($\AuthPrivate$) and $\CoinAddressRand$. The \coinCommitment
|
|
is derived from the recipient address component $\AuthPublic$,
|
|
the value $\Value$, and the commitment trapdoor $\CoinCommitRand$,
|
|
as well as $\CoinAddressRand$. However nothing prevents creating
|
|
multiple \coins with different $\Value$ and $\CoinCommitRand$
|
|
(hence different \coinCommitments) but the same $\CoinAddressRand$.
|
|
|
|
An adversary can use this to mislead a coin recipient, by sending
|
|
two coins 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
|
|
\coin can be spent provided that its \serialNumber does not appear
|
|
on the ledger. This does not take into account the possibility
|
|
that distinct \coins, which are validly received, could have the
|
|
same \serialNumber. That is, the security definition depends on
|
|
a protocol detail --\serialNumbers-- 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 \coin to reduce (to zero) the effective value of another
|
|
\coin 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 $\CoinAddressRand$ values for all
|
|
coins 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 $\CoinAddressRand$, by making use of the fact that all of the
|
|
\serialNumbers in \PourDescriptions that appear in a valid \blockchainview
|
|
must be distinct. The \serialNumbers are used as input to $\FullHash$
|
|
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 \PourDescriptions; adding the \serialNumbers
|
|
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 $\CoinAddressRand$ value for each output coin is then derived from
|
|
a random private seed $\CoinAddressPreRand$ and $\hSig$ using
|
|
$\PRFrho{\CoinAddressPreRand}$. The correct construction of
|
|
$\CoinAddressRand$ for each output coin is enforced by the circuit
|
|
(see \crossref{uniquerho}).
|
|
|
|
Now even if the creator of a \PourDescription does not choose
|
|
$\CoinAddressPreRand$ randomly, uniqueness of \serialNumbers and
|
|
collision resistance of both $\FullHash$ and $\PRFrho{}$ will ensure
|
|
that the derived $\CoinAddressRand$ values are unique, at least for
|
|
any two \PourDescriptions 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
|
|
$\COMM{\CoinCommitRand}$ and $\COMM{\CoinCommitS}$ is a computationally
|
|
binding commitment to its inputs $\AuthPublic$, $\Value$, and
|
|
$\CoinAddressRand$. However, the instantiation of $\COMM{\CoinCommitRand}$
|
|
and $\COMM{\CoinCommitS}$ 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 $\CoinAddressRand$
|
|
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 $\CoinAddressRand$ with colliding
|
|
outputs of the truncated hash, and therefore the same \coinCommitment.
|
|
This would have allowed such an attacker to break the balance property
|
|
by double-spending coins, 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 Pour 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 \coinCommitment from
|
|
three to two, saving a total of four $\SHA$ evaluations in the
|
|
$\PourCircuit$.
|
|
|
|
Note that \Zcash coin commitments 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 \Leading{253}{\CRH(.)} to be collision-resistant 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 coin as a tuple $(\AuthPublic, \Value,
|
|
\CoinAddressRand, \CoinCommitRand, \CoinCommitS, \cm)$, whereas this specification
|
|
defines it as $(\AuthPublic, \Value, \CoinAddressRand, \CoinCommitRand)$.
|
|
This is just a clarification, because the instantiation of $\COMM{\CoinCommitS}$
|
|
in section 5.1 of the paper did not use $\CoinCommitS$ (and neither does the
|
|
new instantiation of $\CoinCommitment$). $\cm$ 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}
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\bibliography{zcash}
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\endgroup
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\end{document}
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