mirror of https://github.com/zcash/zips.git
804 lines
32 KiB
TeX
804 lines
32 KiB
TeX
\documentclass[8pt]{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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\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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% 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{\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{\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{\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{\publicAddress}{\term{confidential address}}
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% Let's rename ``privateAddress'' to something else, since it sounds like an oxymoron to me. (This is related to a code naming issue #602 and we might want to update both at the same time.)
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\newcommand{\privateAddress}{\term{confidential private key}}
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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{\transmitPublicAlgorithm}{\term{key-private encryption}}
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\newcommand{\transmitPrivateAlgorithm}{\term{key-private decryption}}
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\newcommand{\spendAuthority}{\term{spend authority}}
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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{\PublicAddress}{\mathsf{addr_{pk}}}
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\newcommand{\PrivateAddress}{\mathsf{addr_{sk}}}
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\newcommand{\PublicAddressLeadByte}{\mathbf{0x92}}
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\newcommand{\PrivateAddressLeadByte}{\mathbf{0x93}}
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\newcommand{\SpendAuthorityPublic}{\mathsf{a_{pk}}}
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\newcommand{\SpendAuthorityPrivate}{\mathsf{a_{sk}}}
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\newcommand{\SpendAuthorityPublicOld}[1]{\mathsf{a^{old}_{pk,\mathnormal{#1}}}}
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\newcommand{\SpendAuthorityPrivateOld}[1]{\mathsf{a^{old}_{sk,\mathnormal{#1}}}}
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\newcommand{\SpendAuthorityPublicNew}[1]{\mathsf{a^{new}_{pk,\mathnormal{#1}}}}
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\newcommand{\SpendAuthorityPrivateNew}[1]{\mathsf{a^{new}_{sk,\mathnormal{#1}}}}
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\newcommand{\TransmitPublic}{\mathsf{pk_{enc}}}
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\newcommand{\TransmitPublicNew}[1]{\mathsf{pk_{enc,\mathnormal{#1}}}}
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\newcommand{\TransmitPrivate}{\mathsf{sk_{enc}}}
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\newcommand{\TransmitPrivateNew}[1]{\mathsf{sk_{enc,\mathnormal{#1}}}}
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\newcommand{\EphemeralPublic}{\mathsf{pk_{eph}}}
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\newcommand{\EphemeralPrivate}{\mathsf{sk_{eph}}}
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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{\CoinCommitS}{\mathsf{s}}
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\newcommand{\TransmitPlaintextVersionByte}{\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}_{#1}}
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\newcommand{\Ciphertext}[1]{\mathbf{C}_{#1}}
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\newcommand{\Nonce}{\mathsf{nonce}}
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\newcommand{\TransmitEncrypt}[1]{\mathsf{Encrypt}_{#1}}
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\newcommand{\TransmitDecrypt}[1]{\mathsf{Decrypt}_{#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{\CryptoBoxSealHash}{\mathsf{blake2b}}
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\newcommand{\CryptoBoxSealHashbox}[1]{\CryptoBoxSealHash\left(\;\raisebox{-1.3ex}{\usebox{#1}}\;\right)}
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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{\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{\Trailing}[1]{\mathtt{Trailing}_{#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{\ephemeralKey}{\mathtt{ephemeralKey}}
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\newcommand{\ciphertexts}{\mathtt{ciphertexts}}
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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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\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{magenta}\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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\begin{document}
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\title{Zcash Protocol Specification}
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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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\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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\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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$\PRF{x}{}$ is a pseudo-random function seeded by $x$. Three \emph{independent}
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$\PRF{x}{}$ are needed in our scheme: $\PRFaddr{x}$, $\PRFsn{x}$, and $\PRFpk{x}$.
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It is required that $\PRFsn{x}$ be collision-resistant across all $x$ --- i.e. it
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should not be feasible to find $(x, y) \neq (x', y')$ such that
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$\PRFsn{x}(y) = \PRFsn{x'}(y')$.
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In \Zcash, the $\SHAName$ function is used to construct all three of these
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functions. The bits $\mathtt{00}$, $\mathtt{01}$ and $\mathtt{10}$ are included
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(respectively) within the blocks that are hashed, ensuring that the functions are
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independent.
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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 $\SpendAuthorityPrivate$} &
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\bitbox{14}{0} &
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\bitbox{14}{0} &
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\bitbox{242}{$0^{254}$} &
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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 $\SpendAuthorityPrivate$} &
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\bitbox{14}{0} &
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\bitbox{14}{1} &
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\bitbox{242}{$\Leading{254}(\CoinAddressRand)$} &
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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 $\SpendAuthorityPrivate$} &
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\bitbox{14}{1} &
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\bitbox{14}{0} &
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\bitbox{14}{$i$} &
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\bitbox{228}{$\Leading{253}(\hSig)$}
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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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\SpendAuthorityPublic &:= \PRFaddr{\SpendAuthorityPrivate}(0) &= \CRHbox{\addrbox} \\
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\sn &:= \PRFsn{\SpendAuthorityPrivate}(\CoinAddressRand) &= \CRHbox{\snbox} \\
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\h{i} &:= \PRFpk{\SpendAuthorityPrivate}(i, \hSig) &= \CRHbox{\pkbox}
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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{Confidential Addresses and Private Keys}
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\nathan{This term, \publicAddress, may be confusing by comparison to
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a ``private key''. In the latter case the adjective is reminding a
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user of their responsibility to protect its privacy, but in the case
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of \publicAddress we want users to know ``transfers to this address
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are confidential, but the address itself *may* be published or kept
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confidential depending on your needs. Two different people can compare
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addresses to know they have the same \publicAddress.''}
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A key pair $(\PublicAddress, \PrivateAddress)$ is generated by
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users who wish to receive coins under this scheme. The tuple parts
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embody two distinct keypairs used for different purposes called
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the \spendAuthority and the \transmitPublicAlgorithm keypair. The
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\publicAddress $\PublicAddress$ is a tuple $(\SpendAuthorityPublic,
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\TransmitPublic)$, containing the public components of the \spendAuthority
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and \transmitPublicAlgorithm respectively. The $\PrivateAddress$ is
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a tuple $(\SpendAuthorityPrivate, \TransmitPrivate)$, containing the
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secret components respectively.
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\nathan{A diagram could really help here.}
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Users can accept payment from multiple parties with a single
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$\PublicAddress$ and the fact that these payments are destined to
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the same payee is not revealed on the blockchain, even to the
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paying parties. \emph{However} if two parties collude to compare a
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$\PublicAddress$ they can trivially determine they are the same. In the
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case that a payee wishes to prevent this they should create a distinct
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\publicAddress for each payer.
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\subsection{Coins}
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A \coin (denoted $\Coin$) is a tuple $(\SpendAuthorityPublic, \Value,
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\CoinAddressRand, \CoinCommitRand)$ which represents that a value $\Value$ is
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spendable by the recipient who holds the $\spendAuthority$ key pair
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$(\SpendAuthorityPublic, \SpendAuthorityPrivate)$ such that
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$\SpendAuthorityPublic = \PRFaddr{\SpendAuthorityPrivate}(0)$. $\CoinAddressRand$ and
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$\CoinCommitRand$ are tokens randomly generated by the sender. Only a hash of
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these values is disclosed publicly, which allows these random tokens to blind the
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value and recipient \emph{except} to those who possess these tokens.
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\subparagraph{In-band secret distribution}
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In order to transmit the secret $\Value$, $\CoinAddressRand$, and $\CoinCommitRand$
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(necessary for the recipient to later spend) and also a \memo to the recipient
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\emph{without} requiring an out-of-band communication channel, the
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$\transmitPublicAlgorithm$ public key $\TransmitPublic$ is used to encrypt these
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secrets to form a \coinsCiphertext. The recipient's possession of the associated
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$(\PublicAddress, \PrivateAddress)$ (which contains both $\SpendAuthorityPublic$ and
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$\TransmitPrivate$) is used to reconstruct the original \coin and \memo.
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The encryption algorithm is defined in terms of $\CryptoBox$ (i.e.
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$\CryptoBoxSpecific$) \cite{cryptobox} as follows.
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\newsavebox{\noncebox}
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\begin{lrbox}{\noncebox}
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\begin{bytefield}[bitwidth=0.05em]{520}
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\bitbox{120}{1 byte $i-1$} &
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\bitbox{256}{32 byte $\EphemeralPublic$}
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\bitbox{256}{32 byte $\TransmitPublicNew{i}$}
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\end{bytefield}
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\end{lrbox}
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Define $\Nonce(i, \EphemeralPublic, \TransmitPublicNew{i}) =
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\CryptoBoxSealHashbox{\noncebox}$.
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Let $\TransmitPublicNew{1..\NNew}$ be the Curve25519 public keys for the intended
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recipient addresses of each new \coin, and let $\Plaintext{1..\NNew}$ be their
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\coinPlaintexts.
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Then to encrypt:
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\begin{itemize}
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\item Generate a new Curve25519 (public, private) key pair $(\EphemeralPublic, \EphemeralPrivate)$.
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\item For $i$ in $\{1..\NNew\}$, let $\Ciphertext{i} = \CryptoBox(\Plaintext{i}, \TransmitPublicNew{i}, \EphemeralPrivate,
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\Nonce(i, \EphemeralPublic, \TransmitPublicNew{i}))$.
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\item Let $\TransmitEncrypt{\TransmitPublicNew{1..\NNew}}(\Plaintext{1..\NNew}) =
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(\EphemeralPublic, \Ciphertext{1..\NNew})$.
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\end{itemize}
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Let $(\TransmitPublic, \TransmitPrivate)$ be the recipient's Curve25519
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(public, private) key pair, and let $(\EphemeralPublic, \Ciphertext{1..\NNew})$
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be the \coinsCiphertext.
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Then for each $i$ in $\{1..\NNew\}$, the recipient will attempt to decrypt that
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ciphertext component as follows:
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\begin{itemize}
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\item $\TransmitDecrypt{\TransmitPrivate}(i, \EphemeralPublic, \Ciphertext{i}) =
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\CryptoBoxOpen(\Ciphertext{i}, \EphemeralPublic, \TransmitPrivate,
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\Nonce(i, \EphemeralPublic, \TransmitPublic))$
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\end{itemize}
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Any ciphertext components that fail to decrypt with a given recipient's private key
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will be ignored.
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(This is a variation on the $\CryptoBoxSeal$ algorithm defined in libsodium
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\cite{cryptoboxseal}, but with a single ephemeral key used for all encryptions in a
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given \PourDescription, and with the nonce for each ciphertext component depending
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on the index $i$.)
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\subparagraph{Coin Commitments}
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The underlying $\Value$ and $\SpendAuthorityPublic$ are blinded with $\CoinAddressRand$
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and $\CoinCommitRand$ using the collision-resistant hash function $\CRH$ in a
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multi-layered process. The resulting hash $\cm = \CoinCommitment{\Coin}$.
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\newsavebox{\ihbox}
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\begin{lrbox}{\ihbox}
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\begin{bytefield}[bitwidth=0.08em]{512}
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\bitbox{256}{256 bit $\SpendAuthorityPublic$} &
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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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\newsavebox{\ihkbox}
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\begin{lrbox}{\ihkbox}
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\begin{bytefield}[bitwidth=0.08em]{512}
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\bitbox{384}{384 bit $\CoinCommitRand$} &
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\bitbox{128}{$\Leading{128}(\InternalHash)$}
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\end{bytefield}
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\end{lrbox}
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\newsavebox{\cmbox}
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\begin{lrbox}{\cmbox}
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\begin{bytefield}[bitwidth=0.08em]{512}
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\bitbox{64}{64 bit $\Value$} &
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\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*}
|
|
|
|
\subparagraph{Serials}
|
|
|
|
A \serialNumber (denoted $\sn$) equals
|
|
$\PRFsn{\SpendAuthorityPrivate}(\CoinAddressRand)$. A \coin is spent by proving
|
|
knowledge of $\CoinAddressRand$ and $\SpendAuthorityPrivate$ 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 sequence of \PourDescriptions. TODO They also have
|
|
a transparent value flow that interacts with the Pour $\vpubOld$ 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 first \PourDescription in a \transaction must refer to some
|
|
earlier \block's final \treestate.
|
|
|
|
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
|
|
sequence of \PourDescriptions.
|
|
|
|
Each \PourDescription consists of:
|
|
|
|
\begin{list}{}{}
|
|
|
|
\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. The $\SHA$ hash of this value is $\hSig$.
|
|
|
|
\daira{Why $\SHA$ and not $\SHAOrig$? The script is variable-length.}
|
|
|
|
\item $\scriptPubKey$ which is a \script used to satisfy the conditions of the
|
|
$\scriptSig$.
|
|
|
|
\item $\serials$ which is an $\NOld$ size sequence of serials $\snOld{1..\NOld}$.
|
|
|
|
\item $\commitments$ which is a $\NNew$ size sequence of \coinCommitments
|
|
$\cmNew{1..\NNew}$.
|
|
|
|
\item $\ephemeralKey$ which is a Curve25519 public key $\EphemeralPublic$.
|
|
|
|
\item $\ciphertexts$ which is a $\NNew$ size sequence of ciphertext components.
|
|
($\ephemeralKey$ and $\ciphertexts$ together form the \coinsCiphertext.)
|
|
|
|
\item $\vmacs$ which is a $\NOld$ size sequence of message authentication tags
|
|
$\h{1..\NOld}$ that bind $\hSig$ to each $\SpendAuthorityPrivate$ of the
|
|
$\PourDescription$.
|
|
|
|
\item $\zkproof$ which is the zero-knowledge proof $\PourProof$.
|
|
|
|
\end{list}
|
|
|
|
\subparagraph{Merkle root validity}
|
|
|
|
A $\PourDescription$ is valid if $\rt$ is a Coin commitment tree root found in
|
|
either the blockchain or a merkle root produced by inserting the Coin commitments
|
|
of a previous $\PourDescription$ in the transaction to the Coin commitment tree
|
|
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 and an output simultaneously. $\vpubOld$ takes value from the value pool and
|
|
$\vpubNew$ adds value to the value pool. As a result, $\vpubOld$ is treated like an
|
|
\emph{output} value, whereas $\vpubNew$ is treated like an \emph{input} value.
|
|
|
|
\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}
|
|
$(\rt, \snOld{1..\NOld}, \cmNew{1..\NNew}, \vpubOld, \vpubNew, \hSig, \h{1..\NOld})$,
|
|
a witness of \term{auxiliary input}
|
|
$(\treepath{1..\NOld}, \cOld{1..\NOld}, \SpendAuthorityPrivateOld{1..\NOld}, \cNew{1..\NNew})$
|
|
exists, where:
|
|
|
|
\begin{list}{}{}
|
|
|
|
\item for each $i \in \{1..\NOld\}$: $\cOld{i}$ = $(\SpendAuthorityPublicOld{i},
|
|
\vOld{i}, \CoinAddressRandOld{i}, \CoinCommitRandOld{i})$
|
|
|
|
\item for each $i \in \{1..\NNew\}$: $\cNew{i}$ = $(\SpendAuthorityPublicNew{i},
|
|
\vNew{i}, \CoinAddressRandNew{i}, \CoinCommitRandNew{i})$
|
|
|
|
\item The following conditions hold:
|
|
|
|
\end{list}
|
|
|
|
\subparagraph{Merkle path validity}
|
|
|
|
for each $i \in \{1..\NOld\}$ $\mid$ $\vOld{i} \neq 0$: $\treepath{i}$ must be a valid path
|
|
of depth $\MerkleDepth$ from \linebreak $\CoinCommitment{\cOld{i}}$ to Coin
|
|
commitment merkle tree root $\rt$.
|
|
|
|
\subparagraph{Balance}
|
|
|
|
$\vpubOld + \vsum{i=1}{\NOld} \vOld{i} = \vpubNew + \vsum{i=1}{\NNew} \vNew{i}$.
|
|
|
|
\subparagraph{Serial integrity}
|
|
|
|
for each $i \in \{1..\NNew\}$:
|
|
$\snOld{i} = \PRFsn{\SpendAuthorityPrivateOld{i}}(\CoinAddressRandOld{i})$.
|
|
|
|
\subparagraph{Spend authority}
|
|
|
|
for each $i \in \{1..\NOld\}$:
|
|
$\SpendAuthorityPublicOld{i} = \PRFaddr{\SpendAuthorityPrivateOld{i}}(0)$.
|
|
|
|
\subparagraph{Non-malleability}
|
|
|
|
for each $i \in \{1..\NOld\}$: $\h{i}$ = $\PRFpk{\SpendAuthorityPrivateOld{i}}(i, \hSig)$
|
|
|
|
\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 \publicAddress consists of $\SpendAuthorityPublic$ and $\TransmitPublic$.
|
|
$\SpendAuthorityPublic$ is a SHA-256 compression function output.
|
|
$\TransmitPublic$ is a 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]{528}
|
|
\bitbox{48}{$\PublicAddressLeadByte$} &
|
|
\bitbox{256}{$\SpendAuthorityPublic$ (32 bytes)} &
|
|
\bitbox{264}{A 33-byte encoding of $\TransmitPublic$}
|
|
\end{bytefield}
|
|
\end{equation*}
|
|
|
|
\begin{itemize}
|
|
\item A byte, $\PublicAddressLeadByte$, indicating this version of the
|
|
raw encoding of a \Zcash public address.
|
|
\item 32 bytes specifying $\SpendAuthorityPublic$.
|
|
\item 32 bytes specifying $\TransmitPublic$, 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 $\SpendAuthorityPrivate$ and
|
|
$\TransmitPrivate$. $\SpendAuthorityPrivate$ is a SHA-256 compression function
|
|
output. $\TransmitPrivate$ is a 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}
|
|
\bitbox{48}{$\PrivateAddressLeadByte$} &
|
|
\bitbox{256}{$\SpendAuthorityPrivate$ (32 bytes)} &
|
|
\bitbox{256}{$\TransmitPrivate$ (32 bytes)}
|
|
\end{bytefield}
|
|
\end{equation*}
|
|
|
|
\begin{itemize}
|
|
\item A byte $\PrivateAddressLeadByte$ indicating this version of the
|
|
raw encoding of a \Zcash private key.
|
|
\item 32 bytes specifying $\SpendAuthorityPrivate$.
|
|
\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 $\cm$.
|
|
|
|
A \coinsCiphertext is an encryption of a \coinPlaintext to a
|
|
\transmitPublicAlgorithm key $\TransmitPublic$.
|
|
|
|
A \coinPlaintext consists of $(\Value, \CoinAddressRand, \CoinCommitRand, \Memo)$,
|
|
where:
|
|
|
|
\begin{itemize}
|
|
\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 $\PRFsn{\SpendAuthorityPrivate}$ preimage.
|
|
\item $\CoinCommitRand$ is a 48-byte \COMMtrapdoor.
|
|
\item $\Memo$ is a 64-byte \memo associated with this \coin.
|
|
\end{itemize}
|
|
|
|
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.
|
|
|
|
\subsection{Raw Encoding}
|
|
|
|
The raw encoding of a \coinPlaintext consists of, in order:
|
|
|
|
\begin{equation*}
|
|
\begin{bytefield}[bitwidth=0.05em]{712}
|
|
\bitbox{64}{$\TransmitPlaintextVersionByte$} &
|
|
\bitbox{120}{$\Value$ (8 bytes)} &
|
|
\bitbox{256}{$\CoinAddressRand$ (32 bytes)} &
|
|
\bitbox{384}{$\CoinCommitRand$ (48 bytes)} &
|
|
\end{bytefield}
|
|
\end{equation*}
|
|
|
|
\begin{itemize}
|
|
\item A byte $\TransmitPlaintextVersionByte$ indicating this version of the raw
|
|
encoding of a \coinPlaintext.
|
|
\item 8 bytes specifying a big-endian encoding of $\Value$.
|
|
\item 32 bytes specifying $\CoinAddressRand$.
|
|
\item 48 bytes specifying $\CoinCommitRand$.
|
|
\end{itemize}
|
|
|
|
\section{Pours (within a transaction on the blockchain)}
|
|
|
|
TBD.
|
|
|
|
\section{Transactions}
|
|
|
|
TBD.
|
|
|
|
|
|
\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 $(\SpendAuthorityPublic, \Value,
|
|
\CoinAddressRand, \CoinCommitRand, \CoinCommitS, \cm)$, whereas this specification
|
|
defines it as $(\SpendAuthorityPublic, \Value, \CoinAddressRand, \CoinCommitRand)$.
|
|
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}
|