mirror of https://github.com/zcash/zips.git
1102 lines
41 KiB
TeX
1102 lines
41 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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\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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\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]{{\setchanged{#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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% 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{\discloseKeypair}{\term{disclosure}}
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\newcommand{\keyPrivateAlgorithm}{\term{key-private encryption scheme}}
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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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% key pairs:
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\newcommand{\PaymentAddress}{\mathsf{addr_{pk}}}
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\newcommand{\ViewingKey}{\mathsf{addr_{viewkey}}}
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\newcommand{\SpendingKey}{\mathsf{addr_{sk}}}
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\newcommand{\PaymentAddressLeadByte}{\mathbf{0x92}}
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\newcommand{\ViewingKeyLeadByte}{\mathbf{0x??}}
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\newcommand{\SpendingKeyLeadByte}{\mathbf{0x93}}
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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{\alleged}{\mathsf{alleged}}
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\newcommand{\disclose}{\mathsf{disclose}}
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\newcommand{\PublicKey}[1]{\mathsf{pk_\mathnormal{#1}}}
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\newcommand{\PrivateKey}[1]{\mathsf{sk_\mathnormal{#1}}}
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\newcommand{\EphemeralPublic}[1]{\mathsf{epk_\mathnormal{#1}}}
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\newcommand{\EphemeralPrivate}[1]{\mathsf{esk_\mathnormal{#1}}}
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\newcommand{\TransmitPublic}{\PublicKey{\enc}}
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\newcommand{\TransmitPublicNew}[1]{\mathsf{pk^{new}_{\enc,\mathnormal{#1}}}}
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\newcommand{\TransmitPrivate}{\PrivateKey{\enc}}
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\newcommand{\DisclosePublic}{\PublicKey{\disclose}}
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\newcommand{\DisclosePrivate}{\PrivateKey{\disclose}}
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\newcommand{\TransmitEphemeralPublic}{\EphemeralPublic{\enc}}
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\newcommand{\TransmitEphemeralPrivate}{\EphemeralPrivate{\enc}}
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\newcommand{\DiscloseEphemeralPublic}{\EphemeralPublic{\disclose}}
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\newcommand{\DiscloseEphemeralPrivate}{\EphemeralPrivate{\disclose}}
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\newcommand{\Value}{\mathsf{v}}
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% Coins
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\newcommand{\Coin}{\mathbf{c}}
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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{\TransmitPlaintextVersionByte}{\mathbf{0x00}}
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\newcommand{\hSigInputVersionByte}{\mathbf{0x00}}
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\newcommand{\Memo}{\mathsf{memo}}
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\newcommand{\CryptoBox}{\mathsf{crypto\_box}}
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\newcommand{\CryptoBoxOpen}{\mathsf{crypto\_box\_open}}
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\newcommand{\CryptoBoxSeal}{\mathsf{crypto\_box\_seal}}
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\newcommand{\CryptoBoxSpecific}{\mathsf{crypto\_box\_curve25519xsalsa20poly1305}}
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\newcommand{\Plaintext}[1]{\mathbf{P}^\enc_{#1}}
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\newcommand{\AllegedPlaintext}[1]{\mathbf{P}^\alleged_{#1}}
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\newcommand{\DisclosePlaintext}{\mathbf{P}^\disclose}
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\newcommand{\TransmitCiphertext}[1]{\mathbf{C}^\enc_{#1}}
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\newcommand{\DiscloseCiphertext}{\mathbf{C}^\disclose}
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\newcommand{\Tag}[1]{\mathsf{tag}_{#1}}
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\newcommand{\Nonce}{\mathsf{nonce}}
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\newcommand{\Prenonce}{\mathsf{prenonce}}
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\newcommand{\Encrypt}[1]{\mathsf{Encrypt}_{#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{\FullHash}{\mathtt{SHA256}}
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\newcommand{\FullHashbox}[1]{\FullHash\left(\;\raisebox{-1.3ex}{\usebox{#1}}\;\right)}
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\newcommand{\Justthebox}[1]{\;\raisebox{-1.3ex}{\usebox{#1}}\;}
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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{\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{\InternalHashK}{\mathsf{k}}
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\newcommand{\InternalHash}{\mathsf{InternalH}}
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\newcommand{\Leading}[1]{\mathtt{Leading}_{#1}}
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\newcommand{\ReplacementCharacter}{\textsf{U+FFFD}}
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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{\encEphemeral}{\mathtt{encEphemeral}}
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\newcommand{\encCiphertexts}{\mathtt{encCiphertexts}}
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\newcommand{\discloseEphemeral}{\mathtt{discloseEphemeral}}
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\newcommand{\discloseCiphertext}{\mathtt{discloseCiphertext}}
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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{\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{\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}[1]{\mathtt{CoinCommitment}(#1)}
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\begin{document}
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\title{Zcash Protocol Specification \\
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\Large Version 2.0-draft-2}
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\author{Sean Bowe | Daira Hopwood | Taylor Hornby}
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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 \todo{address}. While the production \Zcash network has yet
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to be launched, please feel free to do so in public even if you believe the
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mistake may indicate a security weakness.
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\section{Concepts}
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\subsection{Integers, Bit Sequences, and Endianness}
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All integers visible in \Zcash-specific encodings are unsigned, have a fixed
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bit length, and are encoded as big-endian.
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In bit layout diagrams, each box of the diagram represents a sequence of 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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\nathan{An example would help here. It would be illustrative if it had
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a few differently-sized fields.}
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$\Leading{k}(x)$, where $k$ is an integer and $x$ is a bit sequence, returns
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the leading (initial) $k$ bits of its input.
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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 strings.
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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 $\PRFrho{x}$}. It is required that $\PRFsn{x}$ \changed{and $\PRFrho{x}$} be
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collision-resistant across all $x$ --- i.e. it should not be feasible to find
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$(x, y) \neq (x', y')$ such that $\PRFsn{x}(y) = \PRFsn{x'}(y')$\changed{, and similarly
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for $\PRFrho{}$}.
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In \Zcash, the $\SHAName$ function is used to construct all four of these
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functions. The bits $\mathtt{00}$, $\mathtt{01}$, $\mathtt{10}$\changed{, and
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$\mathtt{11}$} are included (respectively) within the blocks that are hashed,
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ensuring that the functions are independent.
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\newcommand{\iminusone}{\hspace{0.3pt}\scriptsize{$i$\hspace{0.6pt}-1}}
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\newsavebox{\addrbox}
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\begin{lrbox}{\addrbox}
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\begin{bytefield}[bitwidth=0.065em]{512}
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\bitbox{242}{256 bit $\AuthPrivate$} &
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\bitbox{18}{0} &
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\bitbox{18}{0} &
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\bitbox{222}{$0^{254}$} &
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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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\begin{bytefield}[bitwidth=0.065em]{512}
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\bitbox{242}{256 bit $\AuthPrivate$} &
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\bitbox{18}{0} &
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\bitbox{18}{1} &
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\bitbox{222}{$\Leading{254}(\CoinAddressRand)$} &
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\end{bytefield}
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\end{lrbox}
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\newsavebox{\pkbox}
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\begin{lrbox}{\pkbox}
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\begin{bytefield}[bitwidth=0.065em]{512}
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\bitbox{242}{256 bit $\AuthPrivate$} &
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\bitbox{18}{1} &
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\bitbox{18}{0} &
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\bitbox{18}{\iminusone} &
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\bitbox{204}{$\Leading{253}(\hSig)$}
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\end{bytefield}
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\end{lrbox}
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\newsavebox{\rhobox}
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\begin{lrbox}{\rhobox}
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\setchanged
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\begin{bytefield}[bitwidth=0.065em]{512}
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\bitbox{242}{256 bit $\CoinAddressPreRand$} &
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\bitbox{18}{1} &
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\bitbox{18}{1} &
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\bitbox{18}{\iminusone} &
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\bitbox{204}{$\Leading{253}(\hSig)$}
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\end{bytefield}
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\end{lrbox}
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\nathan{Note: If we change input arity (i.e. $\NOld$), we need to be aware of how it
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is associated with this bit-packing.}
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\begin{equation*}
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\begin{aligned}
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\AuthPublic &:= \PRFaddr{\AuthPrivate}(0) &= \CRHbox{\addrbox} \\
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\sn &:= \PRFsn{\AuthPrivate}(\CoinAddressRand) &= \CRHbox{\snbox} \\
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\h{i} &:= \PRFpk{\AuthPrivate}(i, \hSig) &= \CRHbox{\pkbox} \\
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\setchanged \CoinAddressRandNew{i} &\setchanged := \PRFrho{\CoinAddressPreRand}(i, \hSig)
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&\setchanged = \CRHbox{\rhobox}
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\end{aligned}
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\end{equation*}
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\daira{Should we instead define $\CoinAddressRand$ to be 254 bits and $\hSig$ to be
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253 bits?}
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\subsection{Payment Addresses\changed{, Viewing Keys,} and Spending Keys}
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A \keyTuple $(\PaymentAddress, \changed{\ViewingKey,\;} \SpendingKey)$ is generated
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by users who wish to receive payments under this scheme. The parts of
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the \keyTuple are composed from \changed{three} distinct keypairs, called the
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\authKeypair, \transmitKeypair \changed{, and \discloseKeypair} keypairs.
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\begin{itemize}
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\item The \paymentAddress $\PaymentAddress$ is a pair
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$(\AuthPublic, \TransmitPublic)$, containing the \emph{public}
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components of the \authKeypair and \transmitKeypair keypairs
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respectively.
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\changed{
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\item The \viewingKey $\ViewingKey$ is a pair
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$(\TransmitPrivate, \DisclosePrivate)$, containing the \emph{private}
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components of the \transmitKeypair and \discloseKeypair keypairs
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respectively.
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}
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\item The \spendingKey $\SpendingKey$ is a \changed{triple}
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$(\AuthPrivate, \TransmitPrivate\changed{, \DisclosePrivate})$,
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containing the \emph{private} components of the \authKeypair,
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\transmitKeypair\changed{, and \discloseKeypair} keypairs respectively.
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\end{itemize}
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The following diagram depicts the relations between key components.
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Arrows point from a private component to the corresponding public
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component derived from it.
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\begin{center}
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\includegraphics[scale=.5]{key_components}
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\end{center}
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Note that a \spendingKey holder can derive
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$(\AuthPublic, \TransmitPublic\changed{, \DisclosePublic})$,
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\changed{and a \viewingKey holder can derive $(\TransmitPublic, \DisclosePublic)$,}
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even though these components are not formally part of the respective keys.
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Implementations \MAY cache these derived public components, provided that
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they are deleted if the corresponding private component is deleted.
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The composition of \paymentAddresses\changed{, \viewingKeys,} and \spendingKeys
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is a cryptographic protocol detail that should not normally be
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exposed to users. However, user-visible operations should be provided
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to:
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\begin{itemize}
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\changed{
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\item obtain a \viewingKey from a \spendingKey; and
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}
|
|
\item obtain a \paymentAddress from a \spendingKey.
|
|
\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 $\authKeypair$ key pair
|
|
$(\AuthPublic, \AuthPrivate)$ such that
|
|
$\AuthPublic = \PRFaddr{\AuthPrivate}(0)$.
|
|
|
|
$\CoinCommitRand$ 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{In-band secret distribution}
|
|
|
|
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}.
|
|
\changed{To also transmit these values to a \viewingKey holder for outgoing
|
|
\PourTransfers, the \discloseKeypair public key $\DisclosePublic$ is used to
|
|
encrypt the ephemeral secret and address public keys from the preceding
|
|
encryptions.} The encryptions are combined to form a \coinsCiphertext.
|
|
|
|
\changed{
|
|
The encryption algorithm is defined in terms of $\CryptoBox$ (specifically,
|
|
$\CryptoBoxSpecific$) \cite{cryptobox} as follows.
|
|
}
|
|
|
|
\newsavebox{\prenoncebox}
|
|
\begin{lrbox}{\prenoncebox}
|
|
\setchanged
|
|
\begin{bytefield}[bitwidth=0.05em]{520}
|
|
\bitbox{120}{64 bit $\Tag{i}$} &
|
|
\bitbox{256}{256 bit $\EphemeralPublic{}$}
|
|
\bitbox{256}{256 bit $\PublicKey{i}$}
|
|
\end{bytefield}
|
|
\end{lrbox}
|
|
|
|
\newsavebox{\noncebox}
|
|
\begin{lrbox}{\noncebox}
|
|
\setchanged
|
|
\begin{bytefield}[bitwidth=0.085em]{192}
|
|
\bitbox{128}{$\Leading{128}(\Prenonce)$} &
|
|
\bitbox{64}{64 bit $\Tag{i}$}
|
|
\end{bytefield}
|
|
\end{lrbox}
|
|
|
|
\newsavebox{\tagibox}
|
|
\begin{lrbox}{\tagibox}
|
|
\setchanged
|
|
\begin{bytefield}[bitwidth=0.09em]{64}
|
|
\bitbox{64}{64 bit $i-1$}
|
|
\end{bytefield}
|
|
\end{lrbox}
|
|
|
|
\newsavebox{\tagdbox}
|
|
\begin{lrbox}{\tagdbox}
|
|
\setchanged
|
|
\begin{bytefield}[bitwidth=0.09em]{64}
|
|
\bitbox{64}{$1^{64}$}
|
|
\end{bytefield}
|
|
\end{lrbox}
|
|
|
|
\newsavebox{\disclosebox}
|
|
\begin{lrbox}{\disclosebox}
|
|
\setchanged
|
|
\begin{bytefield}[bitwidth=0.04em]{1536}
|
|
\bitbox{256}{256 bit $\TransmitEphemeralPrivate$}
|
|
\bitbox{256}{256 bit $\TransmitPublicNew{\mathrm{1}}$}
|
|
\bitbox{40}{...}
|
|
\bitbox{256}{256 bit $\TransmitPublicNew{\NNew}$}
|
|
\end{bytefield}
|
|
\end{lrbox}
|
|
|
|
Let $\TransmitPublicNew{\mathrm{1}..\NNew}$ be the \changed{Curve25519} public keys
|
|
for the intended recipient addresses of each new \coin,
|
|
\changed{let $\PublicKey{\disclose}$ be the sender's \discloseKeypair public key,}
|
|
and let $\Plaintext{1..\NNew}$ be the \coinPlaintexts.
|
|
|
|
\changed{
|
|
Define:
|
|
\begin{equation*}
|
|
\begin{aligned}
|
|
\Prenonce(\Tag{i}, \EphemeralPublic, \PublicKey{i}) &:= \FullHashbox{\prenoncebox} \\
|
|
\Nonce(\Tag{i}, \EphemeralPublic, \PublicKey{i}) &:= \Justthebox{\noncebox} \\
|
|
\Tag{i} &:= \Justthebox{\tagibox} \\
|
|
\Tag{\disclose} &:= \Justthebox{\tagdbox} \\
|
|
\DisclosePlaintext &:= \Justthebox{\disclosebox}
|
|
\end{aligned}
|
|
\end{equation*}
|
|
}
|
|
|
|
Then to encrypt:
|
|
|
|
\begin{itemize}
|
|
\changed{
|
|
\item Generate two new independent Curve25519 (public, private) key pairs:
|
|
$(\TransmitEphemeralPublic, \TransmitEphemeralPrivate)$ and
|
|
$(\DiscloseEphemeralPublic, \DiscloseEphemeralPrivate)$.
|
|
\item For $i$ in $\{1..\NNew\}$, let $\TransmitCiphertext{i} =
|
|
\CryptoBox(\Plaintext{i}, \PublicKey{i}, \EphemeralPrivate,
|
|
\Nonce(\Tag{i}, \TransmitEphemeralPublic, \TransmitPublicNew{i}))$
|
|
\item Let $\DiscloseCiphertext = \CryptoBox(\DisclosePlaintext,
|
|
\DisclosePublic, \DiscloseEphemeralPrivate,
|
|
\Nonce(\Tag{\disclose}, \DiscloseEphemeralPublic, \DisclosePublic))$
|
|
}
|
|
\end{itemize}
|
|
|
|
The resulting \coinsCiphertext is $\changed{(\TransmitEphemeralPublic,}\;
|
|
\TransmitCiphertext{\mathrm{1}..\NNew}\changed{, \DiscloseEphemeralPublic,
|
|
\DiscloseCiphertext)}$.
|
|
|
|
Let $(\TransmitPublic, \TransmitPrivate)$ be the recipient's \changed{Curve25519}
|
|
(public, private) key pair. Then for each $i$ in $\{1..\NNew\}$, the recipient
|
|
will attempt to decrypt that ciphertext component as follows:
|
|
|
|
\begin{itemize}
|
|
\changed{
|
|
\item $\AllegedPlaintext{i} := \CryptoBoxOpen(\TransmitCiphertext{i},
|
|
\TransmitEphemeralPublic, \TransmitPrivate,
|
|
\Nonce(\Tag{i}, \TransmitEphemeralPublic, \TransmitPublic))$
|
|
\item \todo{validation}
|
|
}
|
|
\end{itemize}
|
|
|
|
\changed{
|
|
Similarly, let $(\DisclosePublic, \DisclosePrivate)$ be a \viewingKey holder's
|
|
Curve25519 (public, private) key pair. Then for each \PourDescription in its
|
|
\blockchainview, the \viewingKey holder will attempt to decrypt the corresponding
|
|
\coinsCiphertext as follows:
|
|
}
|
|
|
|
\begin{itemize}
|
|
\changed{
|
|
\item Let $\DisclosePlaintext :=
|
|
\CryptoBoxOpen(\DiscloseCiphertext, \DiscloseEphemeralPublic,
|
|
\DisclosePrivate, \Nonce(\Tag{i}, \DiscloseEphemeralPublic, \DisclosePublic))$
|
|
\item Extract $\TransmitEphemeralPrivate$ and $\TransmitPublicNew{\mathrm{1}..\NNew}$
|
|
from $\DisclosePlaintext$.
|
|
\item For $i$ in $\{1..\NNew\}$,
|
|
\begin{itemize}
|
|
\item let $\AllegedPlaintext{i} :=
|
|
\CryptoBoxOpen(\TransmitCiphertext{i}, \TransmitEphemeralPrivate,
|
|
\TransmitPublicNew{i}, \Nonce(\Tag{i}, \TransmitEphemeralPublic, \TransmitPublicNew{i}))$
|
|
\item \todo{validation}
|
|
\end{itemize}
|
|
}
|
|
\end{itemize}
|
|
|
|
Any ciphertext components that fail to decrypt \MUST be ignored. Once a component
|
|
has been decrypted, it \MUST be validated as described in section ``Coin Commitments''.
|
|
|
|
\changed{
|
|
This is based loosely on the $\CryptoBoxSeal$ algorithm defined in libsodium
|
|
\cite{cryptoboxseal}, but with the following differences:
|
|
\begin{itemize}
|
|
\item The same ephemeral key is used for all encryptions to the recipient keys
|
|
in a given \PourDescription.
|
|
\item The nonce for each ciphertext component depends on the index $i$.
|
|
The particular nonce construction is chosen so that a known-nonce
|
|
distinguisher for $\mathsf{Salsa20}$ would not directly lead to a break
|
|
of the IK-CCA (key privacy) property.
|
|
\item $\FullHash$ (the full hash, not the compression function) is used instead
|
|
of $\mathsf{blake2b}$.
|
|
\item The ephemeral secret $\TransmitEphemeralPrivate$ is included together with
|
|
the \transmitKeypair public keys of the recipients, encrypted to the
|
|
\discloseKeypair public key. This allows a \viewingKey holder to decrypt
|
|
and validate these ciphertexts (if the sender constructs the \PourDescription
|
|
honestly). It also ensures (without assuming honesty of the sender) that if
|
|
the \viewingKey holder can decrypt a given component, then the indicated
|
|
recipient also has enough information to decrypt it and will receive the
|
|
same \coinPlaintext.
|
|
\end{itemize}
|
|
}
|
|
|
|
\subsubsection{Coin Commitments}
|
|
|
|
The underlying $\Value$ and $\AuthPublic$ are blinded with $\CoinAddressRand$
|
|
and $\CoinCommitRand$ using the collision-resistant hash function $\CRH$ in a
|
|
multi-layered process. The resulting hash $\cm = \CoinCommitment{\Coin}$.
|
|
|
|
\newsavebox{\ihbox}
|
|
\begin{lrbox}{\ihbox}
|
|
\begin{bytefield}[bitwidth=0.08em]{512}
|
|
\bitbox{256}{256 bit $\AuthPublic$} &
|
|
\bitbox{256}{256 bit $\CoinAddressRand$}
|
|
\end{bytefield}
|
|
\end{lrbox}
|
|
|
|
\newsavebox{\ihkbox}
|
|
\begin{lrbox}{\ihkbox}
|
|
\begin{bytefield}[bitwidth=0.08em]{512}
|
|
\bitbox{384}{384 bit $\CoinCommitRand$} &
|
|
\bitbox{128}{$\Leading{128}(\InternalHash)$}
|
|
\end{bytefield}
|
|
\end{lrbox}
|
|
|
|
\newsavebox{\cmbox}
|
|
\begin{lrbox}{\cmbox}
|
|
\begin{bytefield}[bitwidth=0.08em]{512}
|
|
\bitbox{64}{64 bit $\Value$} &
|
|
\bitbox{192}{192 bit padding} &
|
|
\bitbox{256}{256 bit $\InternalHashK$}
|
|
\end{bytefield}
|
|
\end{lrbox}
|
|
|
|
\begin{equation*}
|
|
\begin{aligned}
|
|
\InternalHash &:= \CRHbox{\ihbox} \\
|
|
\InternalHashK &:= \CRHbox{\ihkbox} \\
|
|
\cm &:= \CRHbox{\cmbox}
|
|
\end{aligned}
|
|
\end{equation*}
|
|
|
|
\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.
|
|
|
|
\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}
|
|
|
|
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 $\cOld{1..\NOld}$ and creates $\NNew$ \coins
|
|
$\cNew{1..\NNew}$. \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 $\scriptSig$ which is a \script that creates conditions for acceptance of a
|
|
\PourDescription in a transaction.
|
|
|
|
\item $\scriptPubKey$ which is a \script used to satisfy the conditions of the
|
|
$\scriptSig$.
|
|
|
|
\item $\serials$ which is an $\NOld$ size sequence of serials $\snOld{\mathrm{1}..\NOld}$.
|
|
|
|
\item $\commitments$ which is a $\NNew$ size sequence of \coinCommitments
|
|
$\cmNew{\mathrm{1}..\NNew}$.
|
|
|
|
\changed{
|
|
\item $\encEphemeral$ which is a Curve25519 public key $\TransmitEphemeralPublic$.
|
|
|
|
\item $\encCiphertexts$ which is a $\NNew$ size sequence of ciphertext
|
|
components, $\TransmitCiphertext{\mathrm{1}..\NNew}$.
|
|
|
|
\item $\discloseEphemeral$ which is a Curve25519 public key $\DiscloseEphemeralPublic$.
|
|
|
|
\item $\discloseCiphertext$ which is the ciphertext component
|
|
$\DiscloseCiphertext$.
|
|
|
|
(The preceding four fields together form the \coinsCiphertext.)
|
|
}
|
|
|
|
\item $\vmacs$ which is a $\NOld$ size sequence of message authentication tags
|
|
$\h{\mathrm{1}..\NOld}$ that bind $\hSig$ to each $\AuthPrivate$ of the
|
|
$\PourDescription$.
|
|
|
|
\item $\zkproof$ which is the zero-knowledge proof $\PourProof$.
|
|
|
|
\end{list}
|
|
|
|
\subparagraph{Computation of $\hSig$}
|
|
|
|
\newsavebox{\hsigbox}
|
|
\begin{lrbox}{\hsigbox}
|
|
\setchanged
|
|
\begin{bytefield}[bitwidth=0.045em]{808}
|
|
\bitbox{80}{$\hSigInputVersionByte$} &
|
|
\bitbox{256}{256 bit $\snOld{0}$} &
|
|
\bitbox{24}{...} &
|
|
\bitbox{256}{256 bit $\snOld{\NOld-1}$} &
|
|
\bitbox{256}{$\scriptPubKey$}
|
|
\end{bytefield}
|
|
\end{lrbox}
|
|
|
|
\changed{
|
|
Given a \PourDescription, we define:
|
|
|
|
\begin{itemize}
|
|
\item[] $\hSig := \FullHashbox{\hsigbox}$
|
|
\end{itemize}
|
|
}
|
|
|
|
\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}
|
|
$(\rt, \snOld{\mathrm{1}..\NOld}, \cmNew{\mathrm{1}..\NNew}, \changed{\vpubOld,\;}
|
|
\vpubNew, \hSig, \h{1..\NOld})$, a witness of \term{auxiliary input}
|
|
$(\treepath{1..\NOld}, \cOld{1..\NOld}, \AuthPrivateOld{\mathrm{1}..\NOld},
|
|
\cNew{1..\NNew}\changed{, \CoinAddressPreRand})$ exists, where:
|
|
|
|
\begin{list}{}{}
|
|
|
|
\item for each $i \in \{1..\NOld\}$: $\cOld{i}$ = $(\AuthPublicOld{i},
|
|
\vOld{i}, \CoinAddressRandOld{i}, \CoinCommitRandOld{i})$
|
|
|
|
\item for each $i \in \{1..\NNew\}$: $\cNew{i}$ = $(\AuthPublicNew{i},
|
|
\vNew{i}, \CoinAddressRandNew{i}, \CoinCommitRandNew{i})$
|
|
|
|
\item The following conditions hold:
|
|
|
|
\end{list}
|
|
|
|
\subparagraph{Merkle path validity}
|
|
|
|
for each $i \in \{1..\NOld\}$ \changed{$\mid$ $\vOld{i} \neq 0$}: $\treepath{i}$ must be a valid path
|
|
of depth $\MerkleDepth$ from \linebreak $\CoinCommitment{\cOld{i}}$ to Coin
|
|
commitment merkle tree root $\rt$.
|
|
|
|
\subparagraph{Balance}
|
|
|
|
$\changed{\vpubOld +} \vsum{i=1}{\NOld} \vOld{i} = \vpubNew + \vsum{i=1}{\NNew} \vNew{i}$.
|
|
|
|
\subparagraph{Serial integrity}
|
|
|
|
for each $i \in \{1..\NNew\}$:
|
|
$\snOld{i} = \PRFsn{\AuthPrivateOld{i}}(\CoinAddressRandOld{i})$.
|
|
|
|
\subparagraph{Spend authority}
|
|
|
|
for each $i \in \{1..\NOld\}$:
|
|
$\AuthPublicOld{i} = \PRFaddr{\AuthPrivateOld{i}}(0)$.
|
|
|
|
\subparagraph{Non-malleability}
|
|
|
|
for each $i \in \{1..\NOld\}$: $\h{i}$ = $\PRFpk{\AuthPrivateOld{i}}(i, \hSig)$
|
|
|
|
\changed{
|
|
\subparagraph{Uniqueness of $\CoinAddressRandNew{i}$}
|
|
|
|
for each $i \in \{1..\NNew\}$: $\CoinAddressRandNew{i}$ = $\PRFrho{\CoinAddressPreRand}(i, \hSig)$
|
|
}
|
|
|
|
\subparagraph{Commitment integrity}
|
|
|
|
for each $i \in \{1..\NNew\}$: $\cmNew{i}$ = $\CoinCommitment{\cNew{i}}$
|
|
|
|
\section{Encoding Addresses, Private keys, Coins, and Pour descriptions}
|
|
|
|
This section describes how \Zcash encodes public addresses, private keys,
|
|
coins, and \PourDescriptions.
|
|
|
|
Addresses, keys, and coins, can be encoded as a byte string; this is called
|
|
the \term{raw encoding}. This byte string 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 strings of 32
|
|
bytes.
|
|
|
|
The language consisting of the following encoding possibilities is prefix-free.
|
|
|
|
\subsection{Transparent Public 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{Confidential Public 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 section ``In-band secret distribution".
|
|
|
|
\subsubsection{Raw Encoding}
|
|
|
|
The raw encoding of a confidential address consists of:
|
|
|
|
\begin{equation*}
|
|
\begin{bytefield}[bitwidth=0.07em]{520}
|
|
\changed{
|
|
\bitbox{48}{$\PaymentAddressLeadByte$}
|
|
&}\bitbox{256}{$\AuthPublic$ (32 bytes)} &
|
|
\bitbox{256}{A \changed{32-byte} encoding of $\TransmitPublic$}
|
|
\end{bytefield}
|
|
\end{equation*}
|
|
|
|
\begin{itemize}
|
|
\changed{
|
|
\item A byte, $\PaymentAddressLeadByte$, indicating this version of the
|
|
raw encoding of a \Zcash public address.
|
|
}
|
|
\item 32 bytes specifying $\AuthPublic$.
|
|
\item \changed{32 bytes} 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{Confidential Address Secrets}
|
|
|
|
A confidential address secret consists of $\AuthPrivate$ and
|
|
$\TransmitPrivate$. $\AuthPrivate$ is a SHA-256 compression function
|
|
output. $\TransmitPrivate$ is a \changed{Curve25519} private key, for use with
|
|
the encryption scheme defined in section ``In-band secret distribution".
|
|
|
|
\subsubsection{Raw Encoding}
|
|
|
|
The raw encoding of a confidential address secret consists of, in order:
|
|
|
|
\begin{equation*}
|
|
\begin{bytefield}[bitwidth=0.07em]{520}
|
|
\changed{
|
|
\bitbox{48}{$\SpendingKeyLeadByte$}
|
|
&}\bitbox{256}{$\AuthPrivate$ (32 bytes)} &
|
|
\bitbox{256}{$\TransmitPrivate$ (32 bytes)}
|
|
\end{bytefield}
|
|
\end{equation*}
|
|
|
|
\begin{itemize}
|
|
\changed{
|
|
\item A byte $\SpendingKeyLeadByte$ indicating this version of the
|
|
raw encoding of a \Zcash private key.
|
|
}
|
|
\item 32 bytes specifying $\AuthPrivate$.
|
|
\item 32 bytes specifying $\TransmitPrivate$.
|
|
\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{Coins}
|
|
|
|
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 $\PublicKey{\mathrm{1}..\NNew}$,
|
|
and the result forms a \coinsCiphertext.
|
|
|
|
Each \coinPlaintext consists of $(\changed{\AuthPublic, }\Value, \CoinAddressRand,
|
|
\CoinCommitRand\changed{, \Memo})$, where:
|
|
|
|
\begin{itemize}
|
|
\changed{
|
|
\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 48-byte \COMMtrapdoor.
|
|
\changed{
|
|
\item $\Memo$ is a 64-byte \memo associated with this \coin.
|
|
}
|
|
\end{itemize}
|
|
|
|
\changed{
|
|
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.
|
|
}
|
|
|
|
Note that the value $\CoinCommitS$ described as being part of a \coin in the
|
|
\Zerocash paper is not encoded because the instantiation of $\COMM{\CoinCommitS}$
|
|
does not use it.
|
|
|
|
\subsubsection{Raw Encoding}
|
|
|
|
The raw encoding of a \coinPlaintext consists of, in order:
|
|
|
|
\begin{equation*}
|
|
\begin{bytefield}[bitwidth=0.03em]{1480}
|
|
\changed{
|
|
\bitbox{88}{$\TransmitPlaintextVersionByte$}&
|
|
\bitbox{256}{$\AuthPublic$ (32 bytes)}&
|
|
&}\bitbox{168}{$\Value$ (8 bytes)} &
|
|
\bitbox{256}{$\CoinAddressRand$ (32 bytes)} &
|
|
\bitbox{384}{$\CoinCommitRand$ (48 bytes)} &
|
|
\changed{\bitbox{512}{$\Memo$ (64 bytes)}}
|
|
\end{bytefield}
|
|
\end{equation*}
|
|
|
|
\begin{itemize}
|
|
\changed{
|
|
\item A byte $\TransmitPlaintextVersionByte$ indicating this version of the raw
|
|
encoding of a \coinPlaintext.
|
|
\item 32 bytes specifying $\AuthPublic$.
|
|
}
|
|
\item 8 bytes specifying a big-endian encoding of $\Value$.
|
|
\item 32 bytes specifying $\CoinAddressRand$.
|
|
\item 48 bytes specifying $\CoinCommitRand$.
|
|
\changed{
|
|
\item 64 bytes specifying $\Memo$.
|
|
}
|
|
\end{itemize}
|
|
|
|
\section{Pours (within a transaction on the blockchain)}
|
|
|
|
TBD.
|
|
|
|
\changed{Describe case where there are fewer than $\NOld$ real input coins.}
|
|
|
|
\section{Transactions}
|
|
|
|
TBD.
|
|
|
|
|
|
\changed{
|
|
\section{Differences from the Zerocash paper}
|
|
|
|
\begin{itemize}
|
|
\item Instead of ECIES, we use an encryption scheme based on $\CryptoBox$,
|
|
defined in section ``In-band secret distribution".
|
|
\item Faerie Gold fix (TBD).
|
|
\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 does not use $\CoinCommitS$, and $\cm$ can be computed
|
|
from the other fields.
|
|
\end{itemize}
|
|
}
|
|
|
|
|
|
\section{References}
|
|
|
|
\begingroup
|
|
\renewcommand{\section}[2]{}
|
|
\bibliographystyle{plain}
|
|
\bibliography{zcash}
|
|
\endgroup
|
|
|
|
\end{document}
|