|
|
|
@ -0,0 +1,998 @@ |
|
|
|
\documentclass{article} |
|
|
|
\RequirePackage{amsmath} |
|
|
|
\RequirePackage{bytefield} |
|
|
|
\RequirePackage{graphicx} |
|
|
|
\RequirePackage{newtxmath} |
|
|
|
\RequirePackage{mathtools} |
|
|
|
\RequirePackage{xspace} |
|
|
|
\RequirePackage{url} |
|
|
|
\RequirePackage{changepage} |
|
|
|
\RequirePackage{enumitem} |
|
|
|
\RequirePackage{tabularx} |
|
|
|
\RequirePackage{hhline} |
|
|
|
\RequirePackage[usestackEOL]{stackengine} |
|
|
|
\RequirePackage{comment} |
|
|
|
\RequirePackage{needspace} |
|
|
|
\RequirePackage[nobottomtitles]{titlesec} |
|
|
|
\RequirePackage[hang]{footmisc} |
|
|
|
\RequirePackage{xstring} |
|
|
|
\RequirePackage[unicode,bookmarksnumbered,bookmarksopen,pdfview=Fit]{hyperref} |
|
|
|
\RequirePackage{cleveref} |
|
|
|
\RequirePackage{nameref} |
|
|
|
|
|
|
|
\RequirePackage[style=alphabetic,maxbibnames=99,dateabbrev=false,urldate=iso8601,backref=true,backrefstyle=none,backend=biber]{biblatex} |
|
|
|
\addbibresource{hush.bib} |
|
|
|
|
|
|
|
% Fonts |
|
|
|
\RequirePackage{lmodern} |
|
|
|
\RequirePackage{quattrocento} |
|
|
|
\RequirePackage[bb=ams]{mathalfa} |
|
|
|
|
|
|
|
% Quattrocento is beautiful but doesn't have an italic face. So we scale |
|
|
|
% New Century Schoolbook italic to fit in with slanted Quattrocento and |
|
|
|
% match its x height. |
|
|
|
\renewcommand{\emph}[1]{\hspace{0.15em}{\fontfamily{pnc}\selectfont\scalebox{1.02}[0.999]{\textit{#1}}}\hspace{0.02em}} |
|
|
|
|
|
|
|
% While we're at it, let's match the tt x height to Quattrocento as well. |
|
|
|
\let\oldtexttt\texttt |
|
|
|
\let\oldmathtt\mathtt |
|
|
|
\renewcommand{\texttt}[1]{\scalebox{1.02}[1.07]{\oldtexttt{#1}}} |
|
|
|
\renewcommand{\mathtt}[1]{\scalebox{1.02}[1.07]{$\oldmathtt{#1}$}} |
|
|
|
|
|
|
|
% bold but not extended |
|
|
|
\newcommand{\textbnx}[1]{{\fontseries{b}\selectfont #1}} |
|
|
|
|
|
|
|
|
|
|
|
\crefformat{footnote}{#2\footnotemark[#1]#3} |
|
|
|
|
|
|
|
\DeclareLabelalphaTemplate{ |
|
|
|
\labelelement{\field{citekey}} |
|
|
|
} |
|
|
|
|
|
|
|
\DefineBibliographyStrings{english}{ |
|
|
|
page = {page}, |
|
|
|
pages = {pages}, |
|
|
|
backrefpage = {\mbox{$\uparrow$ p\!}}, |
|
|
|
backrefpages = {\mbox{$\uparrow$ p\!}} |
|
|
|
} |
|
|
|
|
|
|
|
\setlength{\oddsidemargin}{-0.25in} |
|
|
|
\setlength{\textwidth}{7in} |
|
|
|
\setlength{\topmargin}{-0.75in} |
|
|
|
\setlength{\textheight}{9.2in} |
|
|
|
\setlength{\parindent}{0ex} |
|
|
|
\renewcommand{\arraystretch}{1.4} |
|
|
|
\overfullrule=2cm |
|
|
|
|
|
|
|
\setlength{\footnotemargin}{0.6em} |
|
|
|
\setlength{\footnotesep}{2ex} |
|
|
|
\addtolength{\skip\footins}{3ex} |
|
|
|
|
|
|
|
\renewcommand{\bottomtitlespace}{8ex} |
|
|
|
|
|
|
|
% Use rubber lengths between paragraphs to improve default pagination. |
|
|
|
% https://tex.stackexchange.com/questions/17178/vertical-spacing-pagination-and-ideal-results |
|
|
|
\setlength{\parskip}{1.5ex plus 1pt minus 1pt} |
|
|
|
|
|
|
|
\setlist[enumerate]{before=\vspace{-1ex}} |
|
|
|
\setlist[itemize]{itemsep=0.5ex,topsep=0.2ex,before=\vspace{-1ex},after=\vspace{1.5ex}} |
|
|
|
|
|
|
|
\newlist{formulae}{itemize}{3} |
|
|
|
\setlist[formulae]{itemsep=0.2ex,topsep=0ex,leftmargin=1.5em,label=,after=\vspace{1.5ex}} |
|
|
|
|
|
|
|
\newcommand{\docversion}{Version unavailable (check protocol.ver)} |
|
|
|
\InputIfFileExists{protocol.ver}{}{} |
|
|
|
|
|
|
|
\newcommand{\doctitle}{Hushlist Protocol Specification} |
|
|
|
\newcommand{\leadauthor}{David Mercer} |
|
|
|
\newcommand{\coauthora}{Duke Leto} |
|
|
|
|
|
|
|
\newcommand{\keywords}{anonymity, freedom of speech, cryptographic protocols,\ |
|
|
|
electronic commerce and payment, financial privacy, proof of work, zero knowledge} |
|
|
|
|
|
|
|
\hypersetup{ |
|
|
|
pdfborderstyle={/S/U/W 0.7}, |
|
|
|
pdfinfo={ |
|
|
|
Title={\doctitle, \docversion}, |
|
|
|
Author={\leadauthor, \coauthora}, |
|
|
|
Keywords={\keywords} |
|
|
|
} |
|
|
|
} |
|
|
|
|
|
|
|
\makeatletter |
|
|
|
\renewcommand*{\@fnsymbol}[1]{\ensuremath{\ifcase#1\or \dagger\or \ddagger\or |
|
|
|
\mathsection\or \mathparagraph\else\@ctrerr\fi}} |
|
|
|
\makeatother |
|
|
|
|
|
|
|
\renewcommand{\sectionautorefname}{\S\!} |
|
|
|
\renewcommand{\subsectionautorefname}{\S\!} |
|
|
|
\renewcommand{\subsubsectionautorefname}{\S\!} |
|
|
|
\renewcommand{\subparagraphautorefname}{\S\!} |
|
|
|
\newcommand{\crossref}[1]{\autoref{#1}\, \emph{`\nameref*{#1}\kern -0.05em'} on p.\,\pageref*{#1}} |
|
|
|
|
|
|
|
\newcommand{\nstrut}[1]{\texorpdfstring{#1\rule[-.2\baselineskip]{0pt}{\baselineskip}}{#1}} |
|
|
|
\newcommand{\nsection}[1]{\section{\nstrut{#1}}} |
|
|
|
\newcommand{\nsubsection}[1]{\subsection{\nstrut{#1}}} |
|
|
|
\newcommand{\nsubsubsection}[1]{\subsubsection{\nstrut{#1}}} |
|
|
|
|
|
|
|
\newcommand{\introlist}{\needspace{15ex}} |
|
|
|
\newcommand{\introsection}{\needspace{30ex}} |
|
|
|
|
|
|
|
\mathchardef\mhyphen="2D |
|
|
|
|
|
|
|
% http://tex.stackexchange.com/a/309445/78411 |
|
|
|
\DeclareFontFamily{U}{FdSymbolA}{} |
|
|
|
\DeclareFontShape{U}{FdSymbolA}{m}{n}{ |
|
|
|
<-> s*[.4] FdSymbolA-Regular |
|
|
|
}{} |
|
|
|
\DeclareSymbolFont{fdsymbol}{U}{FdSymbolA}{m}{n} |
|
|
|
\DeclareMathSymbol{\smallcirc}{\mathord}{fdsymbol}{"60} |
|
|
|
|
|
|
|
\makeatletter |
|
|
|
\newcommand{\hollowcolon}{\mathpalette\hollow@colon\relax} |
|
|
|
\newcommand{\hollow@colon}[2]{ |
|
|
|
\mspace{0.7mu} |
|
|
|
\vbox{\hbox{$\m@th#1\smallcirc$}\nointerlineskip\kern.45ex \hbox{$\m@th#1\smallcirc$}\kern-.06ex} |
|
|
|
\mspace{1mu} |
|
|
|
} |
|
|
|
\makeatother |
|
|
|
\newcommand{\typecolon}{\;\hollowcolon\;} |
|
|
|
|
|
|
|
% We just want one ampersand symbol from boisik. |
|
|
|
\DeclareSymbolFont{bskadd}{U}{bskma}{m}{n} |
|
|
|
\DeclareFontFamily{U}{bskma}{\skewchar\font130 } |
|
|
|
\DeclareFontShape{U}{bskma}{m}{n}{<->bskma10}{} |
|
|
|
\DeclareMathSymbol{\binampersand}{\mathbin}{bskadd}{"EE} |
|
|
|
|
|
|
|
\newcommand{\hairspace}{~\!} |
|
|
|
\newcommand{\hparen}{\hphantom{(}} |
|
|
|
|
|
|
|
\newcommand{\hfrac}[2]{\scalebox{0.8}{$\genfrac{}{}{0.5pt}{0}{#1}{#2}$}} |
|
|
|
|
|
|
|
|
|
|
|
\RequirePackage[usenames,dvipsnames]{xcolor} |
|
|
|
% https://en.wikibooks.org/wiki/LaTeX/Colors#The_68_standard_colors_known_to_dvips |
|
|
|
\newcommand{\todo}[1]{{\color{Sepia}\sf{TODO: #1}}} |
|
|
|
|
|
|
|
\newcommand{\changedcolor}{magenta} |
|
|
|
\newcommand{\setchanged}{\color{\changedcolor}} |
|
|
|
\newcommand{\changed}[1]{\texorpdfstring{{\setchanged{#1}}}{#1}} |
|
|
|
|
|
|
|
% terminology |
|
|
|
|
|
|
|
\newcommand{\term}[1]{\textsl{#1}\kern 0.05em\xspace} |
|
|
|
\newcommand{\titleterm}[1]{#1} |
|
|
|
\newcommand{\termbf}[1]{\textbf{#1}\xspace} |
|
|
|
\newcommand{\quotedterm}[1]{``~\!\!\term{#1}''} |
|
|
|
\newcommand{\conformance}[1]{\textbnx{#1}\xspace} |
|
|
|
|
|
|
|
\newcommand{\Zcash}{\termbf{Zcash}} |
|
|
|
\newcommand{\Hush}{\termbf{Hush}} |
|
|
|
\newcommand{\Hushlist}{\termbf{HushList}} |
|
|
|
\newcommand{\Zerocash}{\termbf{Zerocash}} |
|
|
|
\newcommand{\Bitcoin}{\termbf{Bitcoin}} |
|
|
|
\newcommand{\CryptoNote}{\termbf{CryptoNote}} |
|
|
|
\newcommand{\ZEC}{\termbf{ZEC}} |
|
|
|
\newcommand{\HUSH}{\termbf{HUSH}} |
|
|
|
\newcommand{\zatoshi}{\term{zatoshi}} |
|
|
|
\newcommand{\zcashd}{\textsf{zcashd}\,} |
|
|
|
|
|
|
|
\newcommand{\MUST}{\conformance{MUST}} |
|
|
|
\newcommand{\MUSTNOT}{\conformance{MUST NOT}} |
|
|
|
\newcommand{\SHOULD}{\conformance{SHOULD}} |
|
|
|
\newcommand{\SHOULDNOT}{\conformance{SHOULD NOT}} |
|
|
|
\newcommand{\ALLCAPS}{\conformance{ALL CAPS}} |
|
|
|
|
|
|
|
\newcommand{\note}{\term{note}} |
|
|
|
\newcommand{\notes}{\term{notes}} |
|
|
|
\newcommand{\Note}{\titleterm{Note}} |
|
|
|
\newcommand{\Notes}{\titleterm{Notes}} |
|
|
|
\newcommand{\dummy}{\term{dummy}} |
|
|
|
\newcommand{\dummyNotes}{\term{dummy notes}} |
|
|
|
\newcommand{\DummyNotes}{\titleterm{Dummy Notes}} |
|
|
|
\newcommand{\commitmentScheme}{\term{commitment scheme}} |
|
|
|
\newcommand{\commitmentTrapdoor}{\term{commitment trapdoor}} |
|
|
|
\newcommand{\commitmentTrapdoors}{\term{commitment trapdoors}} |
|
|
|
\newcommand{\trapdoor}{\term{trapdoor}} |
|
|
|
\newcommand{\noteCommitment}{\term{note commitment}} |
|
|
|
\newcommand{\noteCommitments}{\term{note commitments}} |
|
|
|
\newcommand{\NoteCommitment}{\titleterm{Note Commitment}} |
|
|
|
\newcommand{\NoteCommitments}{\titleterm{Note Commitments}} |
|
|
|
\newcommand{\noteCommitmentTree}{\term{note commitment tree}} |
|
|
|
\newcommand{\NoteCommitmentTree}{\titleterm{Note Commitment Tree}} |
|
|
|
\newcommand{\noteTraceabilitySet}{\term{note traceability set}} |
|
|
|
\newcommand{\noteTraceabilitySets}{\term{note traceability sets}} |
|
|
|
\newcommand{\joinSplitDescription}{\term{JoinSplit description}} |
|
|
|
\newcommand{\joinSplitDescriptions}{\term{JoinSplit descriptions}} |
|
|
|
\newcommand{\JoinSplitDescriptions}{\titleterm{JoinSplit Descriptions}} |
|
|
|
\newcommand{\sequenceOfJoinSplitDescriptions}{\changed{sequence of} \joinSplitDescription\changed{\term{s}}\xspace} |
|
|
|
\newcommand{\joinSplitTransfer}{\term{JoinSplit transfer}} |
|
|
|
\newcommand{\joinSplitTransfers}{\term{JoinSplit transfers}} |
|
|
|
\newcommand{\JoinSplitTransfer}{\titleterm{JoinSplit Transfer}} |
|
|
|
\newcommand{\JoinSplitTransfers}{\titleterm{JoinSplit Transfers}} |
|
|
|
\newcommand{\joinSplitSignature}{\term{JoinSplit signature}} |
|
|
|
\newcommand{\joinSplitSignatures}{\term{JoinSplit signatures}} |
|
|
|
\newcommand{\joinSplitSigningKey}{\term{JoinSplit signing key}} |
|
|
|
\newcommand{\joinSplitVerifyingKey}{\term{JoinSplit verifying key}} |
|
|
|
\newcommand{\joinSplitStatement}{\term{JoinSplit statement}} |
|
|
|
\newcommand{\joinSplitStatements}{\term{JoinSplit statements}} |
|
|
|
\newcommand{\JoinSplitStatement}{\titleterm{JoinSplit Statement}} |
|
|
|
\newcommand{\joinSplitProof}{\term{JoinSplit proof}} |
|
|
|
\newcommand{\statement}{\term{statement}} |
|
|
|
\newcommand{\zeroKnowledgeProof}{\term{zero-knowledge proof}} |
|
|
|
\newcommand{\ZeroKnowledgeProofs}{\titleterm{Zero-Knowledge Proofs}} |
|
|
|
\newcommand{\provingSystem}{\term{proving system}} |
|
|
|
\newcommand{\zeroKnowledgeProvingSystem}{\term{zero-knowledge proving system}} |
|
|
|
\newcommand{\ZeroKnowledgeProvingSystem}{\titleterm{Zero-Knowledge Proving System}} |
|
|
|
\newcommand{\ppzkSNARK}{\term{preprocessing zk-SNARK}} |
|
|
|
\newcommand{\provingKey}{\term{proving key}} |
|
|
|
\newcommand{\zkProvingKeys}{\term{zero-knowledge proving keys}} |
|
|
|
\newcommand{\verifyingKey}{\term{verifying key}} |
|
|
|
\newcommand{\zkVerifyingKeys}{\term{zero-knowledge verifying keys}} |
|
|
|
\newcommand{\joinSplitParameters}{\term{JoinSplit parameters}} |
|
|
|
\newcommand{\JoinSplitParameters}{\titleterm{JoinSplit Parameters}} |
|
|
|
\newcommand{\arithmeticCircuit}{\term{arithmetic circuit}} |
|
|
|
\newcommand{\rankOneConstraintSystem}{\term{Rank 1 Constraint System}} |
|
|
|
\newcommand{\primary}{\term{primary}} |
|
|
|
\newcommand{\primaryInput}{\term{primary input}} |
|
|
|
\newcommand{\primaryInputs}{\term{primary inputs}} |
|
|
|
\newcommand{\auxiliaryInput}{\term{auxiliary input}} |
|
|
|
\newcommand{\auxiliaryInputs}{\term{auxiliary inputs}} |
|
|
|
\newcommand{\fullnode}{\term{full node}} |
|
|
|
\newcommand{\fullnodes}{\term{full nodes}} |
|
|
|
\newcommand{\anchor}{\term{anchor}} |
|
|
|
\newcommand{\anchors}{\term{anchors}} |
|
|
|
\newcommand{\block}{\term{block}} |
|
|
|
\newcommand{\blocks}{\term{blocks}} |
|
|
|
\newcommand{\header}{\term{header}} |
|
|
|
\newcommand{\headers}{\term{headers}} |
|
|
|
\newcommand{\blockHeader}{\term{block header}} |
|
|
|
\newcommand{\blockHeaders}{\term{block headers}} |
|
|
|
\newcommand{\Blockheader}{\term{Block header}} |
|
|
|
\newcommand{\BlockHeader}{\titleterm{Block Header}} |
|
|
|
\newcommand{\blockVersionNumber}{\term{block version number}} |
|
|
|
\newcommand{\blockVersionNumbers}{\term{block version numbers}} |
|
|
|
\newcommand{\Blockversions}{\term{Block versions}} |
|
|
|
\newcommand{\blockTime}{\term{block time}} |
|
|
|
\newcommand{\blockHeight}{\term{block height}} |
|
|
|
\newcommand{\blockHeights}{\term{block heights}} |
|
|
|
\newcommand{\genesisBlock}{\term{genesis block}} |
|
|
|
\newcommand{\transaction}{\term{transaction}} |
|
|
|
\newcommand{\transactions}{\term{transactions}} |
|
|
|
\newcommand{\Transactions}{\titleterm{Transactions}} |
|
|
|
\newcommand{\transactionFee}{\term{transaction fee}} |
|
|
|
\newcommand{\transactionFees}{\term{transaction fees}} |
|
|
|
\newcommand{\transactionVersionNumber}{\term{transaction version number}} |
|
|
|
\newcommand{\transactionVersionNumbers}{\term{transaction version numbers}} |
|
|
|
\newcommand{\Transactionversion}{\term{Transaction version}} |
|
|
|
\newcommand{\coinbaseTransaction}{\term{coinbase transaction}} |
|
|
|
\newcommand{\coinbaseTransactions}{\term{coinbase transactions}} |
|
|
|
\newcommand{\CoinbaseTransactions}{\titleterm{Coinbase Transactions}} |
|
|
|
\newcommand{\transparent}{\term{transparent}} |
|
|
|
\newcommand{\xTransparent}{\term{Transparent}} |
|
|
|
\newcommand{\Transparent}{\titleterm{Transparent}} |
|
|
|
\newcommand{\transparentValuePool}{\term{transparent value pool}} |
|
|
|
\newcommand{\shielded}{\term{shielded}} |
|
|
|
\newcommand{\shieldedNote}{\term{shielded note}} |
|
|
|
\newcommand{\shieldedNotes}{\term{shielded notes}} |
|
|
|
\newcommand{\xShielded}{\term{Shielded}} |
|
|
|
\newcommand{\Shielded}{\titleterm{Shielded}} |
|
|
|
\newcommand{\blockchain}{\term{block chain}} |
|
|
|
\newcommand{\blockchains}{\term{block chains}} |
|
|
|
\newcommand{\mempool}{\term{mempool}} |
|
|
|
\newcommand{\treestate}{\term{treestate}} |
|
|
|
\newcommand{\treestates}{\term{treestates}} |
|
|
|
\newcommand{\nullifier}{\term{nullifier}} |
|
|
|
\newcommand{\nullifiers}{\term{nullifiers}} |
|
|
|
\newcommand{\xNullifiers}{\term{Nullifiers}} |
|
|
|
\newcommand{\Nullifier}{\titleterm{Nullifier}} |
|
|
|
\newcommand{\Nullifiers}{\titleterm{Nullifiers}} |
|
|
|
\newcommand{\nullifierSet}{\term{nullifier set}} |
|
|
|
\newcommand{\NullifierSet}{\titleterm{Nullifier Set}} |
|
|
|
% Daira: This doesn't adequately distinguish between zk stuff and transparent stuff |
|
|
|
\newcommand{\paymentAddress}{\term{payment address}} |
|
|
|
\newcommand{\paymentAddresses}{\term{payment addresses}} |
|
|
|
\newcommand{\viewingKey}{\term{viewing key}} |
|
|
|
\newcommand{\viewingKeys}{\term{viewing keys}} |
|
|
|
\newcommand{\spendingKey}{\term{spending key}} |
|
|
|
\newcommand{\spendingKeys}{\term{spending keys}} |
|
|
|
\newcommand{\payingKey}{\term{paying key}} |
|
|
|
\newcommand{\transmissionKey}{\term{transmission key}} |
|
|
|
\newcommand{\transmissionKeys}{\term{transmission keys}} |
|
|
|
\newcommand{\keyTuple}{\term{key tuple}} |
|
|
|
\newcommand{\notePlaintext}{\term{note plaintext}} |
|
|
|
\newcommand{\notePlaintexts}{\term{note plaintexts}} |
|
|
|
\newcommand{\NotePlaintexts}{\titleterm{Note Plaintexts}} |
|
|
|
\newcommand{\notesCiphertext}{\term{transmitted notes ciphertext}} |
|
|
|
\newcommand{\incrementalMerkleTree}{\term{incremental Merkle tree}} |
|
|
|
\newcommand{\merkleRoot}{\term{root}} |
|
|
|
\newcommand{\merkleNode}{\term{node}} |
|
|
|
\newcommand{\merkleNodes}{\term{nodes}} |
|
|
|
\newcommand{\merkleHash}{\term{hash value}} |
|
|
|
\newcommand{\merkleHashes}{\term{hash values}} |
|
|
|
\newcommand{\merkleLeafNode}{\term{leaf node}} |
|
|
|
\newcommand{\merkleLeafNodes}{\term{leaf nodes}} |
|
|
|
\newcommand{\merkleInternalNode}{\term{internal node}} |
|
|
|
\newcommand{\merkleInternalNodes}{\term{internal nodes}} |
|
|
|
\newcommand{\MerkleInternalNodes}{\term{Internal nodes}} |
|
|
|
\newcommand{\merklePath}{\term{path}} |
|
|
|
\newcommand{\merkleLayer}{\term{layer}} |
|
|
|
\newcommand{\merkleLayers}{\term{layers}} |
|
|
|
\newcommand{\merkleIndex}{\term{index}} |
|
|
|
\newcommand{\merkleIndices}{\term{indices}} |
|
|
|
\newcommand{\zkSNARK}{\term{zk-SNARK}} |
|
|
|
\newcommand{\zkSNARKs}{\term{zk-SNARKs}} |
|
|
|
\newcommand{\libsnark}{\term{libsnark}} |
|
|
|
\newcommand{\memo}{\term{memo field}} |
|
|
|
\newcommand{\memos}{\term{memo fields}} |
|
|
|
\newcommand{\Memos}{\titleterm{Memo Fields}} |
|
|
|
\newcommand{\keyAgreementScheme}{\term{key agreement scheme}} |
|
|
|
\newcommand{\KeyAgreement}{\titleterm{Key Agreement}} |
|
|
|
\newcommand{\keyDerivationFunction}{\term{Key Derivation Function}} |
|
|
|
\newcommand{\KeyDerivation}{\titleterm{Key Derivation}} |
|
|
|
\newcommand{\encryptionScheme}{\term{encryption scheme}} |
|
|
|
\newcommand{\symmetricEncryptionScheme}{\term{authenticated one-time symmetric encryption scheme}} |
|
|
|
\newcommand{\SymmetricEncryption}{\titleterm{Authenticated One-Time Symmetric Encryption}} |
|
|
|
\newcommand{\signatureScheme}{\term{signature scheme}} |
|
|
|
\newcommand{\pseudoRandomFunction}{\term{Pseudo Random Function}} |
|
|
|
\newcommand{\pseudoRandomFunctions}{\term{Pseudo Random Functions}} |
|
|
|
\newcommand{\PseudoRandomFunctions}{\titleterm{Pseudo Random Functions}} |
|
|
|
|
|
|
|
% conventions |
|
|
|
\newcommand{\bytes}[1]{\underline{\raisebox{-0.22ex}{}\smash{#1}}} |
|
|
|
\newcommand{\zeros}[1]{[0]^{#1}} |
|
|
|
\newcommand{\bit}{\mathbb{B}} |
|
|
|
\newcommand{\Nat}{\mathbb{N}} |
|
|
|
\newcommand{\PosInt}{\mathbb{N}^+} |
|
|
|
\newcommand{\Rat}{\mathbb{Q}} |
|
|
|
\newcommand{\typeexp}[2]{{#1}\vphantom{)}^{[{#2}]}} |
|
|
|
\newcommand{\bitseq}[1]{\typeexp{\bit}{#1}} |
|
|
|
\newcommand{\byteseqs}{\typeexp{\bit}{8\mult\Nat}} |
|
|
|
\newcommand{\concatbits}{\mathsf{concat}_\bit} |
|
|
|
\newcommand{\listcomp}[1]{[~{#1}~]} |
|
|
|
\newcommand{\for}{\text{ for }} |
|
|
|
\newcommand{\from}{\text{ from }} |
|
|
|
\newcommand{\upto}{\text{ up to }} |
|
|
|
\newcommand{\downto}{\text{ down to }} |
|
|
|
\newcommand{\squash}{\!\!\!} |
|
|
|
\newcommand{\caseif}{\squash\text{if }} |
|
|
|
\newcommand{\caseotherwise}{\squash\text{otherwise}} |
|
|
|
\newcommand{\sorted}{\mathsf{sorted}} |
|
|
|
\newcommand{\length}{\mathsf{length}} |
|
|
|
\newcommand{\mean}{\mathsf{mean}} |
|
|
|
\newcommand{\median}{\mathsf{median}} |
|
|
|
\newcommand{\clamp}[2]{\mathsf{clamp\,}_{#1}^{#2}} |
|
|
|
\newcommand{\Lower}{\mathsf{lower}} |
|
|
|
\newcommand{\Upper}{\mathsf{upper}} |
|
|
|
\newcommand{\bitlength}{\mathsf{bitlength}} |
|
|
|
\newcommand{\size}{\mathsf{size}} |
|
|
|
\newcommand{\mantissa}{\mathsf{mantissa}} |
|
|
|
\newcommand{\ToCompact}{\mathsf{ToCompact}} |
|
|
|
\newcommand{\ToTarget}{\mathsf{ToTarget}} |
|
|
|
\newcommand{\hexint}[1]{\mathbf{0x{#1}}} |
|
|
|
\newcommand{\dontcare}{\kern -0.06em\raisebox{0.1ex}{\footnotesize{$\times$}}} |
|
|
|
\newcommand{\ascii}[1]{\textbf{``\texttt{#1}"}} |
|
|
|
\newcommand{\Justthebox}[2][-1.3ex]{\;\raisebox{#1}{\usebox{#2}}\;} |
|
|
|
\newcommand{\hSigCRH}{\mathsf{hSigCRH}} |
|
|
|
\newcommand{\hSigLength}{\mathsf{\ell_{hSig}}} |
|
|
|
\newcommand{\hSigType}{\bitseq{\hSigLength}} |
|
|
|
\newcommand{\EquihashGen}[1]{\mathsf{EquihashGen}_{#1}} |
|
|
|
\newcommand{\CRH}{\mathsf{CRH}} |
|
|
|
\newcommand{\CRHbox}[1]{\SHA\left(\Justthebox{#1}\right)} |
|
|
|
\newcommand{\SHA}{\mathtt{SHA256Compress}} |
|
|
|
\newcommand{\SHAName}{\term{SHA-256 compression}} |
|
|
|
\newcommand{\FullHash}{\mathtt{SHA256}} |
|
|
|
\newcommand{\FullHashName}{\mathsf{SHA\mhyphen256}} |
|
|
|
\newcommand{\Blake}[1]{\mathsf{BLAKE2b\kern 0.05em\mhyphen{#1}}} |
|
|
|
\newcommand{\BlakeGeneric}{\mathsf{BLAKE2b}} |
|
|
|
\newcommand{\FullHashbox}[1]{\FullHash\left(\Justthebox{#1}\right)} |
|
|
|
\newcommand{\setof}[1]{\{{#1}\}} |
|
|
|
\newcommand{\range}[2]{\{{#1}\,..\,{#2}\}} |
|
|
|
\newcommand{\minimum}{\mathsf{min}} |
|
|
|
\newcommand{\maximum}{\mathsf{max}} |
|
|
|
\newcommand{\floor}[1]{\mathsf{floor}\!\left({#1}\right)} |
|
|
|
\newcommand{\trunc}[1]{\mathsf{trunc}\!\left({#1}\right)} |
|
|
|
\newcommand{\ceiling}[1]{\mathsf{ceiling}\left({#1}\right)} |
|
|
|
\newcommand{\vsum}[2]{\smashoperator[r]{\sum_{#1}^{#2}}} |
|
|
|
\newcommand{\vxor}[2]{\smashoperator[r]{\bigoplus_{#1}^{#2}}} |
|
|
|
\newcommand{\xor}{\oplus} |
|
|
|
\newcommand{\band}{\binampersand} |
|
|
|
\newcommand{\mult}{\cdot} |
|
|
|
\newcommand{\rightarrowR}{\buildrel{\scriptstyle\mathrm{R}}\over\rightarrow} |
|
|
|
\newcommand{\leftarrowR}{\buildrel{\scriptstyle\mathrm{R}}\over\leftarrow} |
|
|
|
|
|
|
|
% key pairs: |
|
|
|
\newcommand{\PaymentAddress}{\mathsf{addr_{pk}}} |
|
|
|
\newcommand{\PaymentAddressLeadByte}{\hexint{16}} |
|
|
|
\newcommand{\PaymentAddressSecondByte}{\hexint{9A}} |
|
|
|
\newcommand{\SpendingKeyLeadByte}{\hexint{AB}} |
|
|
|
\newcommand{\SpendingKeySecondByte}{\hexint{36}} |
|
|
|
\newcommand{\PtoSHAddressLeadByte}{\hexint{1C}} |
|
|
|
\newcommand{\PtoSHAddressSecondByte}{\hexint{BD}} |
|
|
|
\newcommand{\PtoPKHAddressLeadByte}{\hexint{1C}} |
|
|
|
\newcommand{\PtoPKHAddressSecondByte}{\hexint{B8}} |
|
|
|
\newcommand{\PaymentAddressTestnetLeadByte}{\hexint{16}} |
|
|
|
\newcommand{\PaymentAddressTestnetSecondByte}{\hexint{B6}} |
|
|
|
\newcommand{\SpendingKeyTestnetLeadByte}{\hexint{AC}} |
|
|
|
\newcommand{\SpendingKeyTestnetSecondByte}{\hexint{08}} |
|
|
|
\newcommand{\PtoSHAddressTestnetLeadByte}{\hexint{1C}} |
|
|
|
\newcommand{\PtoSHAddressTestnetSecondByte}{\hexint{BA}} |
|
|
|
\newcommand{\PtoPKHAddressTestnetLeadByte}{\hexint{1D}} |
|
|
|
\newcommand{\PtoPKHAddressTestnetSecondByte}{\hexint{25}} |
|
|
|
\newcommand{\NotePlaintextLeadByte}{\hexint{00}} |
|
|
|
\newcommand{\AuthPublic}{\mathsf{a_{pk}}} |
|
|
|
\newcommand{\AuthPrivate}{\mathsf{a_{sk}}} |
|
|
|
\newcommand{\AuthPublicX}[1]{\mathsf{a^\mathrm{#1}_{pk}}} |
|
|
|
\newcommand{\AuthPrivateX}[1]{\mathsf{a^\mathrm{#1}_{sk}}} |
|
|
|
\newcommand{\AuthPrivateLength}{\mathsf{\ell_{\AuthPrivate}}} |
|
|
|
\newcommand{\AuthPublicOld}[1]{\mathsf{a^{old}_{pk,\mathnormal{#1}}}} |
|
|
|
\newcommand{\AuthPrivateOld}[1]{\mathsf{a^{old}_{sk,\mathnormal{#1}}}} |
|
|
|
\newcommand{\AuthEmphPublicOld}[1]{\mathsf{a^{old}_{\textsf{\textbf{pk}},\mathnormal{#1}}}} |
|
|
|
\newcommand{\AuthPublicOldX}[1]{\mathsf{a^{old}_{pk,\mathrm{#1}}}} |
|
|
|
\newcommand{\AuthPrivateOldX}[1]{\mathsf{a^{old}_{sk,\mathrm{#1}}}} |
|
|
|
\newcommand{\AuthPublicNew}[1]{\mathsf{a^{new}_{pk,\mathnormal{#1}}}} |
|
|
|
\newcommand{\AuthPrivateNew}[1]{\mathsf{a^{new}_{sk,\mathnormal{#1}}}} |
|
|
|
\newcommand{\AddressPublicNew}[1]{\mathsf{addr^{new}_{pk,\mathnormal{#1}}}} |
|
|
|
\newcommand{\enc}{\mathsf{enc}} |
|
|
|
\newcommand{\DHSecret}[1]{\mathsf{sharedSecret}_{#1}} |
|
|
|
\newcommand{\EphemeralPublic}{\mathsf{epk}} |
|
|
|
\newcommand{\EphemeralPrivate}{\mathsf{esk}} |
|
|
|
\newcommand{\TransmitPublic}{\mathsf{pk_{enc}}} |
|
|
|
\newcommand{\TransmitPublicSup}[1]{\mathsf{pk}^{#1}_\mathsf{enc}} |
|
|
|
\newcommand{\TransmitPublicNew}[1]{\mathsf{pk^{new}_{\enc,\mathnormal{#1}}}} |
|
|
|
\newcommand{\TransmitPrivate}{\mathsf{sk_{enc}}} |
|
|
|
\newcommand{\TransmitPrivateSup}[1]{\mathsf{sk}^{#1}_\mathsf{enc}} |
|
|
|
|
|
|
|
% PRFs |
|
|
|
\newcommand{\PRF}[2]{\mathsf{{PRF}^{#2}_\mathnormal{#1}}} |
|
|
|
\newcommand{\PRFaddr}[1]{\PRF{#1}{addr}} |
|
|
|
\newcommand{\PRFnf}[1]{\PRF{#1}{\nf}} |
|
|
|
\newcommand{\PRFsn}[1]{\PRF{#1}{sn}} |
|
|
|
\newcommand{\PRFpk}[1]{\PRF{#1}{pk}} |
|
|
|
\newcommand{\PRFrho}[1]{\PRF{#1}{\NoteAddressRand}} |
|
|
|
\newcommand{\PRFOutputLength}{\mathsf{\ell_{PRF}}} |
|
|
|
\newcommand{\PRFOutput}{\bitseq{\PRFOutputLength}} |
|
|
|
|
|
|
|
% Commitments |
|
|
|
\newcommand{\Commit}[1]{\mathsf{COMM}_{#1}} |
|
|
|
\newcommand{\CommitTrapdoor}{\mathsf{COMM.Trapdoor}} |
|
|
|
\newcommand{\CommitInput}{\mathsf{COMM.Input}} |
|
|
|
\newcommand{\CommitOutput}{\mathsf{COMM.Output}} |
|
|
|
\newcommand{\NoteCommit}{\mathtt{NoteCommitment}} |
|
|
|
\newcommand{\Uncommitted}{\mathsf{Uncommitted}} |
|
|
|
|
|
|
|
% Symmetric encryption |
|
|
|
\newcommand{\Sym}{\mathsf{Sym}} |
|
|
|
\newcommand{\SymEncrypt}[1]{\mathsf{Sym.}\mathtt{Encrypt}_{#1}} |
|
|
|
\newcommand{\SymDecrypt}[1]{\mathsf{Sym.}\mathtt{Decrypt}_{#1}} |
|
|
|
\newcommand{\SymSpecific}{\mathsf{AEAD\_CHACHA20\_POLY1305}} |
|
|
|
\newcommand{\SymCipher}{\mathsf{ChaCha20}} |
|
|
|
\newcommand{\SymAuth}{\mathsf{Poly1305}} |
|
|
|
\newcommand{\Ptext}{\mathsf{P}} |
|
|
|
\newcommand{\Plaintext}{\mathsf{Sym.}\mathbf{P}} |
|
|
|
\newcommand{\Ctext}{\mathsf{C}} |
|
|
|
\newcommand{\Ciphertext}{\mathsf{Sym.}\mathbf{C}} |
|
|
|
\newcommand{\Key}{\mathsf{K}} |
|
|
|
\newcommand{\Keyspace}{\mathsf{Sym.}\mathbf{K}} |
|
|
|
\newcommand{\TransmitPlaintext}[1]{\Ptext^\enc_{#1}} |
|
|
|
\newcommand{\TransmitCiphertext}[1]{\Ctext^\enc_{#1}} |
|
|
|
\newcommand{\TransmitKey}[1]{\Key^\enc_{#1}} |
|
|
|
\newcommand{\Adversary}{\mathcal{A}} |
|
|
|
\newcommand{\CryptoBoxSeal}{\mathsf{crypto\_box\_seal}} |
|
|
|
|
|
|
|
% Key agreement |
|
|
|
\newcommand{\KA}{\mathsf{KA}} |
|
|
|
\newcommand{\KAPublic}{\mathsf{KA.Public}} |
|
|
|
\newcommand{\KAPrivate}{\mathsf{KA.Private}} |
|
|
|
\newcommand{\KASharedSecret}{\mathsf{KA.SharedSecret}} |
|
|
|
\newcommand{\KAFormatPrivate}{\mathsf{KA.}\mathtt{FormatPrivate}} |
|
|
|
\newcommand{\KADerivePublic}{\mathsf{KA.}\mathtt{DerivePublic}} |
|
|
|
\newcommand{\KAAgree}{\mathsf{KA.}\mathtt{Agree}} |
|
|
|
\newcommand{\CurveMultiply}{\mathsf{Curve25519}} |
|
|
|
\newcommand{\CurveBase}{\bytes{9}} |
|
|
|
\newcommand{\Clamp}{\mathsf{clamp_{Curve25519}}} |
|
|
|
|
|
|
|
% KDF |
|
|
|
\newcommand{\KDF}{\mathsf{KDF}} |
|
|
|
\newcommand{\kdftag}{\mathsf{kdftag}} |
|
|
|
\newcommand{\kdfinput}{\mathsf{kdfinput}} |
|
|
|
|
|
|
|
% Notes |
|
|
|
\newcommand{\Value}{\mathsf{v}} |
|
|
|
\newcommand{\ValueNew}[1]{\mathsf{v^{new}_\mathnormal{#1}}} |
|
|
|
\newcommand{\ValueOld}[1]{\mathsf{v^{old}_\mathnormal{#1}}} |
|
|
|
\newcommand{\NoteTuple}[1]{\mathbf{n}_{#1}} |
|
|
|
\newcommand{\NoteType}{\mathsf{Note}} |
|
|
|
\newcommand{\NotePlaintext}[1]{\mathbf{np}_{#1}} |
|
|
|
\newcommand{\NoteCommitRand}{\mathsf{r}} |
|
|
|
\newcommand{\NoteCommitRandLength}{\mathsf{\ell_{\NoteCommitRand}}} |
|
|
|
\newcommand{\NoteCommitRandOld}[1]{\mathsf{r^{old}_\mathnormal{#1}}} |
|
|
|
\newcommand{\NoteCommitRandNew}[1]{\mathsf{r^{new}_\mathnormal{#1}}} |
|
|
|
\newcommand{\NoteAddressRand}{\mathsf{\uprho}} |
|
|
|
\newcommand{\NoteAddressRandOld}[1]{\mathsf{\uprho^{old}_\mathnormal{#1}}} |
|
|
|
\newcommand{\NoteAddressRandOldX}[1]{\mathsf{\uprho^{old}_\mathrm{#1}}} |
|
|
|
\newcommand{\NoteAddressRandNew}[1]{\mathsf{\uprho^{new}_\mathnormal{#1}}} |
|
|
|
\newcommand{\NoteAddressPreRand}{\mathsf{\upvarphi}} |
|
|
|
\newcommand{\NoteAddressPreRandLength}{\mathsf{\ell_{\NoteAddressPreRand}}} |
|
|
|
\newcommand{\NoteCommitS}{\mathsf{s}} |
|
|
|
\newcommand{\cm}{\mathsf{cm}} |
|
|
|
\newcommand{\cmOld}[1]{\mathsf{{cm}^{old}_\mathnormal{#1}}} |
|
|
|
\newcommand{\cmOldX}[1]{\mathsf{{cm}^{old}_\mathrm{#1}}} |
|
|
|
\newcommand{\cmNew}[1]{\mathsf{{cm}^{new}_\mathnormal{#1}}} |
|
|
|
\newcommand{\snOldX}[1]{\mathsf{{sn}^{old}_\mathrm{#1}}} |
|
|
|
\newcommand{\nf}{\mathsf{nf}} |
|
|
|
\newcommand{\nfOld}[1]{\nf^\mathsf{old}_\mathnormal{#1}} |
|
|
|
\newcommand{\Memo}{\mathsf{memo}} |
|
|
|
\newcommand{\DecryptNote}{\mathtt{DecryptNote}} |
|
|
|
\newcommand{\ReplacementCharacter}{\textsf{U+FFFD}} |
|
|
|
|
|
|
|
% Money supply |
|
|
|
\newcommand{\MAXMONEY}{\mathsf{MAX\_MONEY}} |
|
|
|
\newcommand{\BlockSubsidy}{\mathsf{BlockSubsidy}} |
|
|
|
\newcommand{\MinerSubsidy}{\mathsf{MinerSubsidy}} |
|
|
|
\newcommand{\FoundersReward}{\mathsf{FoundersReward}} |
|
|
|
\newcommand{\SlowStartInterval}{\mathsf{SlowStartInterval}} |
|
|
|
\newcommand{\SlowStartShift}{\mathsf{SlowStartShift}} |
|
|
|
\newcommand{\SlowStartRate}{\mathsf{SlowStartRate}} |
|
|
|
\newcommand{\HalvingInterval}{\mathsf{HalvingInterval}} |
|
|
|
\newcommand{\MaxBlockSubsidy}{\mathsf{MaxBlockSubsidy}} |
|
|
|
\newcommand{\NumFounderAddresses}{\mathsf{NumFounderAddresses}} |
|
|
|
\newcommand{\FounderAddressChangeInterval}{\mathsf{FounderAddressChangeInterval}} |
|
|
|
\newcommand{\FoundersFraction}{\mathsf{FoundersFraction}} |
|
|
|
\newcommand{\BlockHeight}{\mathsf{height}} |
|
|
|
\newcommand{\Halving}{\mathsf{Halving}} |
|
|
|
\newcommand{\FounderAddress}{\mathsf{FounderAddress}} |
|
|
|
\newcommand{\FounderAddressList}{\mathsf{FounderAddressList}} |
|
|
|
\newcommand{\FounderAddressIndex}{\mathsf{FounderAddressIndex}} |
|
|
|
\newcommand{\RedeemScriptHash}{\mathsf{RedeemScriptHash}} |
|
|
|
|
|
|
|
\newcommand{\blockSubsidy}{\term{block subsidy}} |
|
|
|
\newcommand{\minerSubsidy}{\term{miner subsidy}} |
|
|
|
\newcommand{\foundersReward}{\term{Founders' Reward}} |
|
|
|
\newcommand{\slowStartPeriod}{\term{slow-start period}} |
|
|
|
\newcommand{\halvingInterval}{\term{halving interval}} |
|
|
|
|
|
|
|
\newcommand{\PoWLimit}{\mathsf{PoWLimit}} |
|
|
|
\newcommand{\PoWAveragingWindow}{\mathsf{PoWAveragingWindow}} |
|
|
|
\newcommand{\PoWMedianBlockSpan}{\mathsf{PoWMedianBlockSpan}} |
|
|
|
\newcommand{\PoWMaxAdjustDown}{\mathsf{PoWMaxAdjustDown}} |
|
|
|
\newcommand{\PoWMaxAdjustUp}{\mathsf{PoWMaxAdjustUp}} |
|
|
|
\newcommand{\PoWDampingFactor}{\mathsf{PoWDampingFactor}} |
|
|
|
\newcommand{\PoWTargetSpacing}{\mathsf{PoWTargetSpacing}} |
|
|
|
\newcommand{\MeanTarget}{\mathsf{MeanTarget}} |
|
|
|
\newcommand{\MedianTime}{\mathsf{MedianTime}} |
|
|
|
\newcommand{\AveragingWindowTimespan}{\mathsf{AveragingWindowTimespan}} |
|
|
|
\newcommand{\MinActualTimespan}{\mathsf{MinActualTimespan}} |
|
|
|
\newcommand{\MaxActualTimespan}{\mathsf{MaxActualTimespan}} |
|
|
|
\newcommand{\ActualTimespan}{\mathsf{ActualTimespan}} |
|
|
|
\newcommand{\ActualTimespanDamped}{\mathsf{ActualTimespanDamped}} |
|
|
|
\newcommand{\ActualTimespanClamped}{\mathsf{ActualTimespanClamped}} |
|
|
|
\newcommand{\Threshold}{\mathsf{Threshold}} |
|
|
|
\newcommand{\ThresholdBits}{\mathsf{ThresholdBits}} |
|
|
|
|
|
|
|
\newcommand{\targetThreshold}{\term{target threshold}} |
|
|
|
\newcommand{\targetThresholds}{\term{target thresholds}} |
|
|
|
|
|
|
|
% Signatures |
|
|
|
\newcommand{\Sig}{\mathsf{Sig}} |
|
|
|
\newcommand{\SigPublic}{\mathsf{Sig.Public}} |
|
|
|
\newcommand{\SigPrivate}{\mathsf{Sig.Private}} |
|
|
|
\newcommand{\SigMessage}{\mathsf{Sig.Message}} |
|
|
|
\newcommand{\SigSignature}{\mathsf{Sig.Signature}} |
|
|
|
\newcommand{\SigGen}{\mathsf{Sig.Gen}} |
|
|
|
\newcommand{\SigSign}[1]{\mathsf{Sig.Sign}_{#1}} |
|
|
|
\newcommand{\SigVerify}[1]{\mathsf{Sig.Verify}_{#1}} |
|
|
|
\newcommand{\JoinSplitSig}{\mathsf{JoinSplitSig}} |
|
|
|
\newcommand{\JoinSplitSigPublic}{\mathsf{JoinSplitSig.Public}} |
|
|
|
\newcommand{\JoinSplitSigPrivate}{\mathsf{JoinSplitSig.Private}} |
|
|
|
\newcommand{\JoinSplitSigMessage}{\mathsf{JoinSplitSig.Message}} |
|
|
|
\newcommand{\JoinSplitSigSignature}{\mathsf{JoinSplitSig.Signature}} |
|
|
|
\newcommand{\JoinSplitSigGen}{\mathsf{JoinSplitSig.Gen}} |
|
|
|
\newcommand{\JoinSplitSigSign}[1]{\mathsf{JoinSplitSig.Sign}_{#1}} |
|
|
|
\newcommand{\JoinSplitSigVerify}[1]{\mathsf{JoinSplitSig.Verify}_{#1}} |
|
|
|
\newcommand{\JoinSplitSigSpecific}{\mathsf{Ed25519}} |
|
|
|
\newcommand{\JoinSplitSigHashName}{\mathsf{SHA\mhyphen512}} |
|
|
|
\newcommand{\EdDSAr}{R} |
|
|
|
\newcommand{\EdDSAs}{S} |
|
|
|
\newcommand{\EdDSAR}{\bytes{R}} |
|
|
|
\newcommand{\EdDSAS}{\bytes{S}} |
|
|
|
\newcommand{\RandomSeedLength}{\mathsf{\ell_{Seed}}} |
|
|
|
\newcommand{\RandomSeedType}{\bitseq{\mathsf{\ell_{Seed}}}} |
|
|
|
\newcommand{\pksig}{\mathsf{pk_{sig}}} |
|
|
|
\newcommand{\sk}{\mathsf{sk}} |
|
|
|
\newcommand{\hSigInput}{\mathsf{hSigInput}} |
|
|
|
\newcommand{\dataToBeSigned}{\mathsf{dataToBeSigned}} |
|
|
|
|
|
|
|
% Merkle tree |
|
|
|
\newcommand{\MerkleDepth}{\mathsf{d_{Merkle}}} |
|
|
|
\newcommand{\MerkleNode}[2]{\mathsf{M}^{#1}_{#2}} |
|
|
|
\newcommand{\MerkleSibling}{\mathsf{sibling}} |
|
|
|
\newcommand{\MerkleCRH}{\mathsf{MerkleCRH}} |
|
|
|
\newcommand{\MerkleHashLength}{\mathsf{\ell_{Merkle}}} |
|
|
|
\newcommand{\MerkleHash}{\bitseq{\MerkleHashLength}} |
|
|
|
|
|
|
|
% Transactions |
|
|
|
\newcommand{\versionField}{\mathtt{version}} |
|
|
|
\newcommand{\txInCount}{\mathtt{tx\_in\_count}} |
|
|
|
\newcommand{\txIn}{\mathtt{tx\_in}} |
|
|
|
\newcommand{\txOutCount}{\mathtt{tx\_out\_count}} |
|
|
|
\newcommand{\txOut}{\mathtt{tx\_out}} |
|
|
|
\newcommand{\lockTime}{\mathtt{lock\_time}} |
|
|
|
\newcommand{\nJoinSplit}{\mathtt{nJoinSplit}} |
|
|
|
\newcommand{\vJoinSplit}{\mathtt{vJoinSplit}} |
|
|
|
\newcommand{\vpubOldField}{\mathtt{vpub\_old}} |
|
|
|
\newcommand{\vpubNewField}{\mathtt{vpub\_new}} |
|
|
|
\newcommand{\anchorField}{\mathtt{anchor}} |
|
|
|
\newcommand{\joinSplitSig}{\mathtt{joinSplitSig}} |
|
|
|
\newcommand{\joinSplitPrivKey}{\mathtt{joinSplitPrivKey}} |
|
|
|
\newcommand{\joinSplitPubKey}{\mathtt{joinSplitPubKey}} |
|
|
|
\newcommand{\nullifiersField}{\mathtt{nullifiers}} |
|
|
|
\newcommand{\commitments}{\mathtt{commitments}} |
|
|
|
\newcommand{\ephemeralKey}{\mathtt{ephemeralKey}} |
|
|
|
\newcommand{\encCiphertexts}{\mathtt{encCiphertexts}} |
|
|
|
\newcommand{\randomSeed}{\mathtt{randomSeed}} |
|
|
|
\newcommand{\Varies}{\textit{Varies}} |
|
|
|
\newcommand{\heading}[1]{\multicolumn{1}{c|}{#1}} |
|
|
|
\newcommand{\type}[1]{\texttt{#1}} |
|
|
|
\newcommand{\compactSize}{\type{compactSize uint}} |
|
|
|
|
|
|
|
\newcommand{\sighashType}{\term{SIGHASH type}} |
|
|
|
\newcommand{\sighashTypes}{\term{SIGHASH types}} |
|
|
|
\newcommand{\SIGHASHALL}{\mathsf{SIGHASH\_ALL}} |
|
|
|
\newcommand{\scriptSig}{\mathtt{scriptSig}} |
|
|
|
\newcommand{\scriptPubKey}{\mathtt{scriptPubKey}} |
|
|
|
\newcommand{\ScriptOP}[1]{\texttt{OP\_{#1}}} |
|
|
|
|
|
|
|
% Equihash and block headers |
|
|
|
\newcommand{\validEquihashSolution}{\term{valid Equihash solution}} |
|
|
|
\newcommand{\powtag}{\mathsf{powtag}} |
|
|
|
\newcommand{\powheader}{\mathsf{powheader}} |
|
|
|
\newcommand{\powcount}{\mathsf{powcount}} |
|
|
|
\newcommand{\nVersion}{\mathtt{nVersion}} |
|
|
|
\newcommand{\hashPrevBlock}{\mathtt{hashPrevBlock}} |
|
|
|
\newcommand{\hashMerkleRoot}{\mathtt{hashMerkleRoot}} |
|
|
|
\newcommand{\hashReserved}{\mathtt{hashReserved}} |
|
|
|
\newcommand{\nTimeField}{\mathtt{nTime}} |
|
|
|
\newcommand{\nTime}{\mathsf{nTime}} |
|
|
|
\newcommand{\nBitsField}{\mathtt{nBits}} |
|
|
|
\newcommand{\nBits}{\mathsf{nBits}} |
|
|
|
\newcommand{\nNonce}{\mathtt{nNonce}} |
|
|
|
\newcommand{\solutionSize}{\mathtt{solutionSize}} |
|
|
|
\newcommand{\solution}{\mathtt{solution}} |
|
|
|
\newcommand{\SHAd}{\term{SHA-256d}} |
|
|
|
|
|
|
|
% Proving system |
|
|
|
\newcommand{\ZK}{\mathsf{ZK}} |
|
|
|
\newcommand{\ZKProvingKey}{\mathsf{ZK.ProvingKey}} |
|
|
|
\newcommand{\ZKVerifyingKey}{\mathsf{ZK.VerifyingKey}} |
|
|
|
\newcommand{\pk}{\mathsf{pk}} |
|
|
|
\newcommand{\vk}{\mathsf{vk}} |
|
|
|
\newcommand{\ZKGen}{\mathsf{ZK.Gen}} |
|
|
|
\newcommand{\ZKProof}{\mathsf{ZK.Proof}} |
|
|
|
\newcommand{\ZKPrimary}{\mathsf{ZK.PrimaryInput}} |
|
|
|
\newcommand{\ZKAuxiliary}{\mathsf{ZK.AuxiliaryInput}} |
|
|
|
\newcommand{\ZKSatisfying}{\mathsf{ZK.SatisfyingInputs}} |
|
|
|
\newcommand{\ZKProve}[1]{\mathsf{ZK.}\mathtt{Prove}_{#1}} |
|
|
|
\newcommand{\ZKVerify}[1]{\mathsf{ZK.}\mathtt{Verify}_{#1}} |
|
|
|
\newcommand{\Simulator}{\mathcal{S}} |
|
|
|
\newcommand{\Distinguisher}{\mathcal{D}} |
|
|
|
\newcommand{\JoinSplit}{\text{\footnotesize\texttt{JoinSplit}}} |
|
|
|
\newcommand{\ZKJoinSplit}{\mathsf{ZK}_{\JoinSplit}} |
|
|
|
\newcommand{\ZKJoinSplitVerify}{\ZKJoinSplit\mathsf{.Verify}} |
|
|
|
\newcommand{\ZKJoinSplitProve}{\ZKJoinSplit\mathsf{.Prove}} |
|
|
|
\newcommand{\ZKJoinSplitProof}{\ZKJoinSplit\mathsf{.Proof}} |
|
|
|
\newcommand{\Proof}{\pi} |
|
|
|
\newcommand{\JoinSplitProof}{\Proof_{\JoinSplit}} |
|
|
|
\newcommand{\zkproof}{\mathtt{zkproof}} |
|
|
|
\newcommand{\POUR}{\texttt{POUR}} |
|
|
|
\newcommand{\Prob}[2]{\mathrm{Pr}\scalebox{0.88}{\ensuremath{ |
|
|
|
\left[\!\!\begin{array}{c}#1\end{array} \middle| \begin{array}{l}#2\end{array}\!\!\right] |
|
|
|
}}} |
|
|
|
|
|
|
|
% JoinSplit |
|
|
|
\newcommand{\hSig}{\mathsf{h_{Sig}}} |
|
|
|
\newcommand{\hSigText}{\texorpdfstring{$\hSig$}{hSig}} |
|
|
|
\newcommand{\h}[1]{\mathsf{h_{\mathnormal{#1}}}} |
|
|
|
\newcommand{\NOld}{\mathrm{N}^\mathsf{old}} |
|
|
|
\newcommand{\NNew}{\mathrm{N}^\mathsf{new}} |
|
|
|
\newcommand{\allN}[1]{\mathrm{1}..\mathrm{N}^\mathsf{#1}} |
|
|
|
\newcommand{\allOld}{\allN{old}} |
|
|
|
\newcommand{\allNew}{\allN{new}} |
|
|
|
\newcommand{\setofOld}{\setof{\allOld}} |
|
|
|
\newcommand{\setofNew}{\setof{\allNew}} |
|
|
|
\newcommand{\vmacs}{\mathtt{vmacs}} |
|
|
|
\newcommand{\GroupG}[1]{\mathbb{G}_{#1}} |
|
|
|
\newcommand{\GroupGstar}[1]{\mathbb{G}^\ast_{#1}} |
|
|
|
\newcommand{\PointP}[1]{\mathcal{P}_{#1}} |
|
|
|
\newcommand{\xP}{{x_{\hspace{-0.12em}P}}} |
|
|
|
\newcommand{\yP}{{y_{\hspace{-0.03em}P}}} |
|
|
|
\newcommand{\AtInfinity}[1]{\mathcal{O}_{#1}} |
|
|
|
\newcommand{\GF}[1]{\mathbb{F}_{#1}} |
|
|
|
\newcommand{\GFstar}[1]{\mathbb{F}^\ast_{#1}} |
|
|
|
\newcommand{\ECtoOSP}{\mathsf{EC2OSP}} |
|
|
|
\newcommand{\ECtoOSPXL}{\mathsf{EC2OSP\mhyphen{}XL}} |
|
|
|
\newcommand{\ECtoOSPXS}{\mathsf{EC2OSP\mhyphen{}XS}} |
|
|
|
\newcommand{\ItoOSP}[1]{\mathsf{I2OSP}_{#1}} |
|
|
|
\newcommand{\ItoBSP}[1]{\mathsf{I2BSP}_{#1}} |
|
|
|
\newcommand{\FEtoIP}{\mathsf{FE2IP}} |
|
|
|
\newcommand{\BNImpl}{\mathtt{ALT\_BN128}} |
|
|
|
\newcommand{\vpubOld}{\mathsf{v_{pub}^{old}}} |
|
|
|
\newcommand{\vpubNew}{\mathsf{v_{pub}^{new}}} |
|
|
|
\newcommand{\nOld}[1]{\NoteTuple{#1}^\mathsf{old}} |
|
|
|
\newcommand{\nNew}[1]{\NoteTuple{#1}^\mathsf{new}} |
|
|
|
\newcommand{\vOld}[1]{\mathsf{v}_{#1}^\mathsf{old}} |
|
|
|
\newcommand{\vNew}[1]{\mathsf{v}_{#1}^\mathsf{new}} |
|
|
|
\newcommand{\RandomSeed}{\mathsf{randomSeed}} |
|
|
|
\newcommand{\rt}{\mathsf{rt}} |
|
|
|
\newcommand{\treepath}[1]{\mathsf{path}_{#1}} |
|
|
|
\newcommand{\Receive}{\mathsf{Receive}} |
|
|
|
\newcommand{\EnforceMerklePath}[1]{\mathsf{enforceMerklePath}_{~\!\!#1}} |
|
|
|
|
|
|
|
|
|
|
|
\newcommand{\consensusrule}[1]{\needspace{3ex}\subparagraph{Consensus rule:}{#1}} |
|
|
|
\newenvironment{consensusrules}{\introlist\subparagraph{Consensus rules:}\begin{itemize}}{\end{itemize}} |
|
|
|
\newcommand{\securityrequirement}[1]{\needspace{3ex}\subparagraph{Security requirement:}{#1}} |
|
|
|
\newenvironment{securityrequirements}{\introlist\subparagraph{Security requirements:}\begin{itemize}}{\end{itemize}} |
|
|
|
\newcommand{\pnote}[1]{\subparagraph{Note:}{#1}} |
|
|
|
\newenvironment{pnotes}{\introlist\subparagraph{Notes:}\begin{itemize}}{\end{itemize}} |
|
|
|
|
|
|
|
\newcommand{\affiliation}{\hairspace$^\dagger$\;} |
|
|
|
|
|
|
|
\begin{document} |
|
|
|
|
|
|
|
\title{\doctitle \\ |
|
|
|
\Large \docversion} |
|
|
|
\author{ |
|
|
|
\Large \leadauthor\hairspace\thanks{\;Hush Core, Zcash Core, Bitcoin Core} \\ |
|
|
|
\Large \coauthora\affiliation } |
|
|
|
\date{\today} |
|
|
|
\maketitle |
|
|
|
|
|
|
|
\renewcommand{\abstractname}{} |
|
|
|
\vspace{-8ex} |
|
|
|
\begin{abstract} |
|
|
|
\normalsize \noindent \textbf{Abstract.} |
|
|
|
|
|
|
|
HushList is a protocol for anonymous mailing lists using the encrypted memo |
|
|
|
field of the \Zcash protocol. |
|
|
|
|
|
|
|
It supports anonymous and pseudonymous senders, receivers and Hushlist creators, as |
|
|
|
well as public and private lists. |
|
|
|
|
|
|
|
The HushList protocol can run on any fork of \Zcash that has a compatible 512 |
|
|
|
byte memo field, though certain advanced features might not be fully supported |
|
|
|
on all chains. |
|
|
|
|
|
|
|
HushList is developed and tested on the Hush and Zcash mainnets as well as |
|
|
|
testnets (TUSH and TAZ), next to be tested is Komodo (KMD). |
|
|
|
|
|
|
|
\Zcash is an implementation of the \term{Decentralized Anonymous Payment} |
|
|
|
scheme \Zerocash, with security fixes and adjustments |
|
|
|
to terminology, functionality and performance. It bridges the existing |
|
|
|
\emph{transparent} payment scheme used by \Bitcoin with a |
|
|
|
\emph{shielded} payment scheme secured by zero-knowledge succinct |
|
|
|
non-interactive arguments of knowledge (\zkSNARKs). |
|
|
|
|
|
|
|
\Hush is a fork of the \Zcash codebase (1.0.9) which generated it's own |
|
|
|
genesis block and uses the Zcash Sprout proving key. |
|
|
|
|
|
|
|
|
|
|
|
\vspace{1.5ex} |
|
|
|
\noindent This specification defines the \Hushlist communication protocol and explains |
|
|
|
how it builds on the foundatio of \Zcash and \Bitcoin. |
|
|
|
|
|
|
|
\vspace{2.5ex} |
|
|
|
\noindent \textbf{Keywords:}~ \StrSubstitute[0]{\keywords}{,}{, }. |
|
|
|
\end{abstract} |
|
|
|
|
|
|
|
\vspace{-10ex} |
|
|
|
\phantomsection |
|
|
|
\addcontentsline{toc}{section}{\Large\nstrut{Contents}} |
|
|
|
|
|
|
|
\renewcommand{\contentsname}{} |
|
|
|
% http://tex.stackexchange.com/a/182744/78411 |
|
|
|
\renewcommand{\baselinestretch}{0.85}\normalsize |
|
|
|
\tableofcontents |
|
|
|
\renewcommand{\baselinestretch}{1.0}\normalsize |
|
|
|
\newpage |
|
|
|
|
|
|
|
|
|
|
|
\nsection{Introduction} |
|
|
|
|
|
|
|
HushList is a protocol for anonymous mailing lists using the encrypted memo |
|
|
|
field of the zcash protocol. |
|
|
|
|
|
|
|
Technical terms for concepts that play an important role in \Hushlist are |
|
|
|
written in \term{slanted text}. \emph{Italics} are used for emphasis and |
|
|
|
for references between sections of the document. |
|
|
|
|
|
|
|
The key words \MUST, \MUSTNOT, \SHOULD, and \SHOULDNOT in this |
|
|
|
document are to be interpreted as described in \cite{RFC-2119} when they |
|
|
|
appear in \ALLCAPS. These words may also appear in this document in |
|
|
|
lower case as plain English words, absent their normative meanings. |
|
|
|
|
|
|
|
\vspace{2ex} |
|
|
|
\introlist |
|
|
|
This specification is structured as follows: |
|
|
|
|
|
|
|
\begin{itemize} |
|
|
|
\item Notation | definitions of notation used throughout the document; |
|
|
|
\item Concepts | the principal abstractions needed to understand the protocol; |
|
|
|
\item Abstract Protocol | a high-level description of the protocol in terms |
|
|
|
of ideal cryptographic components; |
|
|
|
\item Concrete Protocol | how the functions and encodings of the abstract |
|
|
|
protocol are instantiated; |
|
|
|
\item Implications |
|
|
|
\end{itemize} |
|
|
|
|
|
|
|
\nsubsection{High-level Overview} |
|
|
|
|
|
|
|
The following overview is intended to give a concise summary of the ideas behind |
|
|
|
the protocol, for an audience already familiar with \blockchain-based |
|
|
|
cryptocurrencies such as \Bitcoin or \Zcash. |
|
|
|
|
|
|
|
XXX |
|
|
|
|
|
|
|
Value in \Hush is either \transparent or \shielded. Transfers of \transparent |
|
|
|
value work essentially as in \Bitcoin and have the same privacy properties. |
|
|
|
\xShielded value is carried by \notes, which specify an amount and a \payingKey. |
|
|
|
The \payingKey is part of a \paymentAddress, which is a destination to which |
|
|
|
\notes can be sent. As in \Bitcoin, this is associated with a private key that |
|
|
|
can be used to spend \notes sent to the address; in \Hush this is called a |
|
|
|
\spendingKey. |
|
|
|
|
|
|
|
\introlist |
|
|
|
A \transaction can contain \transparent inputs, outputs, and scripts, which all |
|
|
|
work as in \Bitcoin \cite{Bitcoin-Protocol}. It also contains a sequence of zero or |
|
|
|
more \joinSplitDescriptions. Each of these describes a \joinSplitTransfer |
|
|
|
which takes in a \transparent value and up to two input \notes, and produces a |
|
|
|
\transparent value and up to two output \notes. |
|
|
|
|
|
|
|
\nsection{Notation} |
|
|
|
|
|
|
|
$\bit$ means the type of bit values, i.e.\ $\setof{0, 1}$. |
|
|
|
|
|
|
|
$\Nat$ means the type of nonnegative integers. $\PosInt$ |
|
|
|
means the type of positive integers. $\Rat$ means the type of rationals. |
|
|
|
|
|
|
|
$x \typecolon T$ is used to specify that $x$ has type $T$. |
|
|
|
A cartesian product type is denoted by $S \times T$, and a function type |
|
|
|
by $S \rightarrow T$. An argument to a function can determine other argument |
|
|
|
or result types. |
|
|
|
|
|
|
|
The type of a randomized algorithm is denoted by $S \rightarrowR T$. |
|
|
|
The domain of a randomized algorithm may be $()$, indicating that it requires |
|
|
|
no arguments. Given $f \typecolon S \rightarrowR T$ and $s \typecolon S$, |
|
|
|
sampling a variable $x \typecolon T$ from the output of $f$ applied to $s$ |
|
|
|
is denoted by $x \leftarrowR f(s)$. |
|
|
|
|
|
|
|
Initial arguments to a function or randomized algorithm may be |
|
|
|
written as subscripts, e.g.\ if $x \typecolon X$, $y \typecolon Y$, and |
|
|
|
$f \typecolon X \times Y \rightarrow Z$, then an invocation of |
|
|
|
$f(x, y)$ can also be written $f_x(y)$. |
|
|
|
|
|
|
|
$\typeexp{T}{\ell}$, where $T$ is a type and $\ell$ is an integer, |
|
|
|
means the type of sequences of length $\ell$ with elements in $T$. For example, |
|
|
|
$\bitseq{\ell}$ means the set of sequences of $\ell$ bits. |
|
|
|
|
|
|
|
$\length(S)$ means the length of (number of elements in) $S$. |
|
|
|
|
|
|
|
$T \subseteq U$ indicates that $T$ is an inclusive subset or subtype of $U$. |
|
|
|
|
|
|
|
$\byteseqs$ means the set of bit sequences constrained to be of length |
|
|
|
a multiple of 8 bits. |
|
|
|
|
|
|
|
$\hexint{}$ followed by a string of \textbf{boldface} hexadecimal |
|
|
|
digits means the corresponding integer converted from hexadecimal. |
|
|
|
|
|
|
|
$\ascii{...}$ means the given string represented as a |
|
|
|
sequence of bytes in US-ASCII. For example, $\ascii{abc}$ represents the |
|
|
|
byte sequence $[\hexint{61}, \hexint{62}, \hexint{63}]$. |
|
|
|
|
|
|
|
$\zeros{\ell}$ means the sequence of $\ell$ zero bits. |
|
|
|
|
|
|
|
$a..b$, used as a subscript, means the sequence of values |
|
|
|
with indices $a$ through $b$ inclusive. For example, |
|
|
|
$\AuthPublicNew{\allNew}$ means the sequence $[\AuthPublicNew{\mathrm{1}}, |
|
|
|
\AuthPublicNew{\mathrm{2}}, ...\,\AuthPublicNew{\NNew}]$. |
|
|
|
(For consistency with the notation in \cite{BCG+2014} and in \cite{BK2016}, |
|
|
|
this specification uses 1-based indexing and inclusive ranges, |
|
|
|
notwithstanding the compelling arguments to the contrary made in |
|
|
|
\cite{EWD-831}.) |
|
|
|
|
|
|
|
$\range{a}{b}$ means the set or type of integers from $a$ through |
|
|
|
$b$ inclusive. |
|
|
|
|
|
|
|
$\listcomp{f(x) \for x \from a \upto b}$ means the sequence |
|
|
|
formed by evaluating $f$ on each integer from $a$ to $b$ inclusive, in |
|
|
|
ascending order. Similarly, $\listcomp{f(x) \for x \from a \downto b}$ means |
|
|
|
the sequence formed by evaluating $f$ on each integer from $a$ to $b$ |
|
|
|
inclusive, in descending order. |
|
|
|
|
|
|
|
$a\,||\,b$ means the concatenation of sequences $a$ then $b$. |
|
|
|
|
|
|
|
$\concatbits(S)$ means the sequence of bits obtained by |
|
|
|
concatenating the elements of $S$ viewed as bit sequences. If the |
|
|
|
elements of $S$ are byte sequences, they are converted to bit sequences |
|
|
|
with the \emph{most significant} bit of each byte first. |
|
|
|
|
|
|
|
$\sorted(S)$ means the sequence formed by sorting the elements |
|
|
|
of $S$. |
|
|
|
|
|
|
|
$\GF{n}$ means the finite field with $n$ elements, and |
|
|
|
$\GFstar{n}$ means its group under multiplication. |
|
|
|
$\GF{n}[z]$ means the ring of polynomials over $z$ with coefficients |
|
|
|
in $\GF{n}$. |
|
|
|
|
|
|
|
$a \mult b$ means the result of multiplying $a$ and $b$. |
|
|
|
This may refer to multiplication of integers, rationals, or |
|
|
|
finite field elements according to context. |
|
|
|
|
|
|
|
$a^b$, for $a$ an integer or finite field element and |
|
|
|
$b$ an integer, means the result of raising $a$ to the exponent $b$. |
|
|
|
|
|
|
|
$a \bmod q$, for $a \typecolon \Nat$ and $q \typecolon \PosInt$, |
|
|
|
means the remainder on dividing $a$ by $q$. |
|
|
|
|
|
|
|
$a \xor b$ means the bitwise-exclusive-or of $a$ and $b$, |
|
|
|
and $a \band b$ means the bitwise-and of $a$ and $b$. These are |
|
|
|
defined either on integers or bit sequences according to context. |
|
|
|
|
|
|
|
$\vsum{i=1}{\mathrm{N}} a_i$ means the sum of $a_{\allN{}}$.\; |
|
|
|
$\vxor{i=1}{\mathrm{N}} a_i$ means the bitwise exclusive-or of $a_{\allN{}}$. |
|
|
|
|
|
|
|
The binary relations $<$, $\leq$, $=$, $\geq$, and $>$ have their conventional |
|
|
|
meanings on integers and rationals, and are defined lexicographically on |
|
|
|
sequences of integers. |
|
|
|
|
|
|
|
$\floor{x}$ means the largest integer $\leq x$. |
|
|
|
$\ceiling{x}$ means the smallest integer $\geq x$. |
|
|
|
|
|
|
|
$\bitlength(x)$, for $x \typecolon \Nat$, means the smallest integer |
|
|
|
$\ell$ such that $2^\ell > x$. |
|
|
|
|
|
|
|
The symbol $\bot$ is used to indicate unavailable information or a failed decryption. |
|
|
|
|
|
|
|
\nsection{Account Funding} |
|
|
|
|
|
|
|
On first run, \HushList creates a new shielded zaddress for use by the user for |
|
|
|
anonymous sending and to fund transparent addresses for pseudonymous sending. |
|
|
|
It may be funded by the user from any taddr or zaddr with no loss of privacy. |
|
|
|
For each pseudonym the user sends from (may be globally used or per-list), a |
|
|
|
taddr is created and funded from the primary zaddr for the user. |
|
|
|
|
|
|
|
\nsection{List Creation} |
|
|
|
\nsection{Sending To A List} |
|
|
|
|
|
|
|
One may send to a \HushList from a taddr (pen name, psedonym) or zaddr |
|
|
|
(anonymous shielded address) which is implemented in the client via |
|
|
|
the z\_sendmany RPC command. Up to 54 recepients may be in a single shielded |
|
|
|
transaction. v1 of HushList only supports HushLists of this size, but v2 |
|
|
|
may implement larger HushLists. |
|
|
|
|
|
|
|
\nsection{Receiving Messages} |
|
|
|
|
|
|
|
At any time later, after the transaction has entered the blockchain, memos |
|
|
|
sent to a given address can be downloaded and viewed by those parties who |
|
|
|
have valid private keys. |
|
|
|
|
|
|
|
The client will poll the local full node periodically at a user specifiable |
|
|
|
default interval the same as the average block time for the chain in question. |
|
|
|
|
|
|
|
\nsection{Costs} |
|
|
|
|
|
|
|
Sending \HushList memos requires making a financial transaction and by default, |
|
|
|
\HushList sends the recipient a transaction for 0.0 \HUSH (or \ZEC etc) with |
|
|
|
the default network fee (currently 0.0001 for \ZEC+\HUSH). The fee amount can |
|
|
|
be changed via the HUSHLIST\_FEE environment variable. |
|
|
|
|
|
|
|
\nsection{References} |
|
|
|
|
|
|
|
\begingroup |
|
|
|
\hfuzz=2pt |
|
|
|
\renewcommand{\section}[2]{} |
|
|
|
\renewcommand{\emph}[1]{\textit{#1}} |
|
|
|
\printbibliography |
|
|
|
\endgroup |
|
|
|
|
|
|
|
\end{document} |
Jonathan "Duke" Leto
6 years ago