macros.tex

\newcommand{\mc}{\mathcal}
\newcommand{\msf}{\mathsf}
\newcommand{\mbb}{\mathbb}
\newcommand{\defn}{\stackrel{\textrm{\scriptsize def}}{=}}

%%% TEXT
\newcommand{\eg}{e.g., }
\newcommand{\ie}{i.e., }
\newcommand{\wrt}{w.r.t. }
\newcommand{\st}{s.t. }
\newcommand{\etc}{\textit{etc.} }
\newcommand{\etal}{\textit{et al.}}

%%% PARAMETERS
\newcommand{\secparam}{\kappa}
\newcommand{\persistenceParam}{k}
\newcommand{\livenessParam}{u}

%%% PARTIES
\newcommand{\adversary}{\mc{A}}
\newcommand{\simulator}{\mc{S}}
\newcommand{\Iadv}{\simulator}
\newcommand{\party}{\mc{P}}
\newcommand{\partyset}{\mbb{P}}
\newcommand{\env}{\mc{Z}}

%%% PRIMITIVES
\newcommand{\hash}{\msf{H}}
\newcommand{\sigscheme}{\Sigma}
\newcommand{\eufcma}{\ensuremath{\textsf{EUF-CMA}}}
\newcommand{\algokeygen}{\msf{KeyGen}}
\newcommand{\algoverify}{\msf{Verify} }
\newcommand{\algover}{\msf{Verify} }
\newcommand{\algosign}{\msf{Sign}}
\newcommand{\pubkey}{\msf{vk}}
\newcommand{\privkey}{\msf{sk}}
\newcommand{\keypair}{(\pubkey, \privkey)}
\newcommand{\signature}{\sigma}
\newcommand{\sig}{\signature}

%%% BLOCKCHAIN OBJECTS
\newcommand{\ledger}{\mc{L}}
\newcommand{\chain}{\mc{C}}
\newcommand{\block}{\mc{B}}
\newcommand{\transaction}{\tau}
\newcommand{\tx}{\transaction}
\newcommand{\txSet}{\mbb{T}}
\newcommand{\utxo}{\msf{UTxO}}
\newcommand{\inp}{\msf{Input}}
\newcommand{\addr}{\alpha}
\newcommand{\addrlen}{\ell}

\newcommand{\head}{\msf{head}}

\newcommand{\algovalidate}{\msf{Validate}}

\newcommand{\keyset}{\mbb{K}}
\newcommand{\masterpubkey}{\msf{mvk}}
\newcommand{\masterprivkey}{\msf{msk}}
\newcommand{\masterkeypair}{(\masterpubkey, \masterprivkey)}


%%% UC
\newcommand{\func}{\mc{F}}
\newcommand{\protocol}{\pi}
\newcommand{\globalfunc}{\mc{G}}


%%%%%%%%%%%%%%%%%%%%%%%%%
% HARDWARE WALLETS
%%%%%%%%%%%%%%%%%%%%%%%%%

\newcommand{\user}{\mc{U}}
\newcommand{\client}{\mc{D}}
\newcommand{\hardware}{\mc{H}}

\newcommand{\msg}[2]{
    \ifthenelse{\isempty{#1}}{\ensuremath{(\msf{sid}, #2)}}{
        \ifthenelse{\isempty{#2}}{\ensuremath{(\textsc{#1}, \msf{sid})}}{
            \ensuremath{(\textsc{#1}, \msf{sid}, #2)}
        }
    }
}

\newcommand{\clId}{\msf{pass}_{\client}}

\newcommand{\Fw}{\func_{\mathrm{w}}}
\newcommand{\Fsig}{\func_\msf{SIG}}
\newcommand{\Gledg}{\globalfunc_\msf{LEDGER}}
\newcommand{\Goracle}{\globalfunc_\msf{RO}}
\newcommand{\pclient}{\protocol_{client}}
\newcommand{\ph}{\protocol_{human}}
\newcommand{\pw}{\protocol_{w}}
\newcommand{\Fhw}{\protocol_{hw}}
\newcommand{\phybrid}{\protocol_{hybrid}}

\newcommand{\Hprob}{R_{h}}


%%%%%%%%%%%%%%%%%%%%%%%%%
% UTXO GROWTH
%%%%%%%%%%%%%%%%%%%%%%%%%

\newcommand{\utxoSize}{\omega}
\newcommand{\txInputSize}{\iota}
\newcommand{\sizeByteFee}{\beta}
\newcommand{\utxoFee}{\psi}

\newcommand{\utxoCost}{c}
\newcommand{\feeFunction}{F}
\newcommand{\costFunc}{\msf{costTx}}
\newcommand{\stateCost}{C}

\newcommand{\fee}{f}
\newcommand{\ledgerState}{\mc{S}}
\newcommand{\ledgerStateSet}{\mbb{S}}
\newcommand{\txCostFeeRate}{r}

\newcommand{\infixOperator}{\langle \tau \rangle}


%%%%%%%%%%%%%%%%%%%%%%%%%
% DELEGATION
%%%%%%%%%%%%%%%%%%%%%%%%%

\def\cF{\func}

\newcommand{\accPay}{\mc{I}_p}
\newcommand{\accSta}{\mc{I}_s}
\newcommand{\sid}{\msf{sid}}
\newcommand{\asset}{\theta}
\newcommand{\assetset}{\Theta}
\newcommand{\addresset}{\mbb{A}}
\newcommand{\addresslist}{l_{\addr}}
\newcommand{\addresslistindexed}{l_{\addr}}
\newcommand{\addressgenlist}{l_{\addr, Gen}}
\newcommand{\addresstuple}{(\delta_1, \ldots, \delta_\addrgenlength )}
\newcommand{\addresstupleprime}{(\delta^\prime_1, \ldots, \delta^\prime_\addrgenlength )}
\newcommand{\attributedistribution}{\mc{L}}
\newcommand{\attribute}{\delta}
\newcommand{\attributeset}{\Delta}
\newcommand{\addrgenlength}{g}
\newcommand{\addrgendomain}{\attributeset_1 \times \ldots \times \attributeset_\addrgenlength}
\newcommand{\paymentkeyverify}{\msf{vkp}}
\newcommand{\paymentkeysign}{\msf{skp}}
\newcommand{\paymentkeypair}{(\paymentkeyverify, \paymentkeysign)}
\newcommand{\stakingkeyverify}{\msf{vks}}
\newcommand{\stakingkeysign}{\msf{sks}}
\newcommand{\stakingkeypair}{(\stakingkeyverify, \stakingkeysign)}
\newcommand{\sign}{\sigma}

\newcommand{\FuncW}{\cF_\mathrm{CoreWallet}}
\newcommand{\ProtoW}{\protocol_\mathrm{CoreWallet}}
\newcommand{\p}{\mc{P}}

%Template for boxfigure
\newenvironment{boxfig}[2]{% {#1}{#2} = {Figure Caption}{Box caption}{label}
   \begin{figure}[ht!]
     \newcommand{\FigCaption}{#1}
     \newcommand{\FigLabel}{#2}
     \begin{center}
       \begin{small}
       \setlist{nosep}
         \begin{tabular}{@{}|@{~~}l@{~~}|@{}}
           \hline
           \rule[-1.5ex]{0pt}{1ex}\begin{minipage}[b]{0.96\linewidth}
             \smallskip
             }{%
           \end{minipage}\\
           \hline
         \end{tabular}
       \end{small}
       \vspace{-0.3cm}
       \caption{\FigCaption}
       \label{\FigLabel}
     \end{center}
   \end{figure}
}

\def\bits{\{0,1\}}

\newcommand{\keyverify}{\msf{vk}}
\newcommand{\keysign}{\msf{sk}}
\newcommand{\negl}{\mathsf{negl}}
\newcommand{\algohierarchicalkeygen}{\msf{HKeyGen}}
\newcommand{\algorecoverytaggen}{\msf{RTagGen}}

\newcommand{\N}{{{\mbb N}}}

\newcommand{\ideal}{{\msf{IDEAL}_{\Fuc, \Iadv, \env}}}
\newcommand{\idealprimesim}{{\msf{IDEAL}_{\Fuc, \Iadv^\prime, \env}}}
\newcommand{\idealwalletfunc}{{\msf{IDEAL}_{\FuncW, \Iadv, \env}}}

\newcommand{\real}{{\msf{REAL}_{\protocol, \adv, \env}}}
\newcommand{\realpiw}{{\msf{REAL}_{\piw, \adv, \env}}}

\newcommand{\piw}{\protocol_{\wallet}}

\newcommand{\enseideal}{{\{\msf{IDEAL}_{\Fuc, \Iadv, \env}(\secparam,z,r)\}_{\secparam \in \N, z \in \bits^{*}}}}
\newcommand{\ensereal}{{\{\msf{REAL}_{\protocol, \adv, \env}(\secparam,z,r)\}_{\secparam \in \N,z \in \bits^{*}}}}

\newcommand{\payTx}{\ensuremath{\tau_{p}\xspace}}
\newcommand{\regTx}{\ensuremath{\tau_{register}\xspace}}
\newcommand{\delegTx}{\ensuremath{\tau_{delegate}\xspace}}
\newcommand{\stakeTx}{\ensuremath{\tau_{stake}\xspace}}

\newcommand{\wallet}{\ensuremath{\mc{WC}\xspace}}

\newcommand{\Fuc}{\ensuremath{\func\xspace}}
\newcommand{\adv}{\mc{A}}
\newcommand{\sind}{\approx_s}
\newcommand{\cind}{\approx_c}

\newcommand{\ignore}[1]{\relax}

\newcommand{\cmark}{\large \color{OliveGreen} \ding{51}}
\newcommand{\xmark}{\large \color{red} \ding{55}}

\DeclarePairedDelimiter{\ceil}{\lceil}{\rceil}

\algnewcommand\algorithmicassert{\texttt{assert}}
\algnewcommand\Assert[1]{\State \algorithmicassert(#1)}

\algnewcommand\algorithmicfinally{\textbf{finally}}
\algnewcommand\Finally[1]{\State \algorithmicfinally #1}

\algnewcommand\algorithmicswitch{\textbf{switch}}
\algnewcommand\algorithmiccase{\textbf{case}}
\algdef{SE}[SWITCH]{Switch}{EndSwitch}[1]{\algorithmicswitch\ #1\ \algorithmicdo}{\algorithmicend\ \algorithmicswitch}
\algdef{SE}[CASE]{Case}{EndCase}[1]{\algorithmiccase\ #1}{\algorithmicend\ \algorithmiccase}
\algtext*{EndSwitch}
\algtext*{EndCase}

\newcommand{\indexSet}{\mbb{I}}


%%%%%%%%%%%%%%%%%%%%%%%%%
% COLLECTIVE POOLS
%%%%%%%%%%%%%%%%%%%%%%%%%

\newcommand{\outs}{\rightarrow}
\newcommand{\fail}{\bot}
\newcommand{\rand}{r}
\newcommand{\randompick}{\stackrel{\$}{\leftarrow}}
\def\bits{\{0,1\}}

\newcommand{\Z}{{{\mbb Z}}}
\newcommand{\znn}{{\mbb{Z}_{N^2}}}
\newcommand{\zntil}{{\mbb{Z}_{\widetilde{N}}}}

\newcommand{\Ppool}{\protocol_{pool}}

\newcommand{\globalmodel}{\overline{\globalfunc}}

\newcommand{\Fpool}{{\func}_{pool}}
\newcommand{\Fbroad}{{\func}_{BC}}
\newcommand{\Fcore}{{\func}_{corewallet}}

\newcommand{\Gledger}{{\globalmodel}_{simpleLedger}}

\newcommand{\Pconsensus}{\protocol_{consensus}}

\newcommand{\iadv}{\mc{S}}

\newcommand{\hybmodel}{{\msf{HYBRID}_{\protocol^{\fauxmodel}, \adv, \env}}}
\newcommand{\hyb}{{\msf{HYBRID}_{\protocol^{\script}, \adv, \env}}}
\newcommand{\hybpool}{{\msf{HYBRID}^{pool}_{\Ppool, \adv, \env}}}

\newcommand{\idealmodel}{{\msf{IDEAL}_{\func, \iadv, \env}}}

\newcommand{\envinput}{z}

\newcommand{\ensideal}{{\{\msf{IDEAL}_{\func, \iadv, \env}(\secparam,\envinput,\rand)\}_{\secparam \in \N, \envinput \in \bits^{*}}}}
\newcommand{\enshyb}{{\{\msf{HYBRID}_{{\protocolauxmodel}, \adv, \env}(\secparam,\envinput,\rand)\}_{\secparam \in \N,\envinput \in \bits^{*}}}}

\newcommand{\idealvar}{{\msf{IDEAL}_{\func, \iadv, \env}}}
\newcommand{\hybvar}{{\msf{HYBRID}_{{\protocolauxmodel}, \adv, \env}}}

\newcommand{\blockify}{\msf{blockify}}

\newcommand{\contractstate}{\Omega}

\newcommand{\m}{\msf{m}}

\newcommand{\parse}{\stackrel{p}{\leftarrow}}

\newcommand{\digsign}{(\algokeygen,\algosign,\algover)}

\newcommand{\parties}{\mc{P}}
\newcommand{\totalParties}{n}
\newcommand{\totalShares}{m}
\newcommand{\adversarialParties}{t}
\newcommand{\adversarialWeights}{t}

\newcommand{\addEncScheme}{\mc{E}}
\newcommand{\addModule}{N}
\newcommand{\addEnc}{E}
\newcommand{\addDec}{D}
\newcommand{\addPK}{PK}
\newcommand{\addPlus}{+_{\addEncScheme}}
\newcommand{\addTimes}{\times_{\addEncScheme}}
\newcommand{\addc}{c}

\newcommand{\mybox}[5]{
    \begin{figure*}[htpb]
        \centering
    \begin{tikzpicture}
        \node[anchor=text,text width=2*\columnwidth-0.5cm, draw, rounded corners, line width=1pt, fill=#3, inner sep=5mm] (big) {\\#4};
        \node[draw, rounded corners, line width=.5pt, fill=#2, anchor=west, xshift=5mm] (small) at (big.north west) {#1};
    \end{tikzpicture}
    \caption{#5}
    \end{figure*}
}

\newcommand{\myhalfbox}[5]{
    \begin{figure}[htpb]
        \centering
    \begin{tikzpicture}
        \node[anchor=text,text width=\columnwidth-1.2cm, draw, rounded corners, line width=1pt, fill=#3, inner sep=5mm, align=justify] (big) {\\#4};
        \node[draw, rounded corners, line width=.5pt, fill=#2, anchor=west, xshift=5mm] (small) at (big.north west) {#1};
    \end{tikzpicture}
    \caption{#5}
    \end{figure}
}

\newcommand{\threshver}{\msf{ThreshVerify}}
\newcommand{\threshsigscheme}{\sigscheme_{\msf{thresh}}}
\newcommand{\threshkeygen}{\msf{ThreshKeyGen}}
\newcommand{\threshsign}{\msf{ThreshSign}}
\newcommand{\threshpubkey}{\msf{vk}}
\newcommand{\threshprivkey}{\msf{tsk}}
\newcommand{\threshsig}{\signature}

\newcommand{\wfunc}{\omega}

\newcommand{\totalweight}{W}
\newcommand{\weight}{w}
\newcommand{\thold}{T}
\newcommand{\baseg}{g}
\newcommand{\gorder}{p}
\newcommand{\tholdset}{B}
\newcommand{\tholdsetweight}{W_{\tholdset}}

\newcommand{\zp}{\mbb{Z}_{\gorder}}
\newcommand{\Gr}{\mbb{G}}
\newcommand{\RO}{\mc{O}}

\newcommand{\addone}{\alpha}
\newcommand{\addtwo}{\beta}

\newcommand{\addwone}{\mu}
\newcommand{\addtwwo}{\nu}

\newcommand{\enc}{E}
\newcommand{\encN}{N}

\newcommand{\localvalues}{u}
\newcommand{\dshare}{y}

\newcommand{\keyshare}{x}

\newcommand{\com}{\msf{com}}
\newcommand{\cvalue}{C}
\newcommand{\copen}{D}
\newcommand{\cgen}{\msf{gen}}
\newcommand{\cver}{\msf{ver}}
\newcommand{\cequiv}{\msf{equiv}}

\newcommand{\ckey}{\msf{pk}}
\newcommand{\ctrap}{\msf{tk}}
\newcommand{\ctoss}{\rand}

\newcommand{\cvalueh}{\widehat{\cvalue}}
\newcommand{\copenh}{\widehat{\copen}}

\newcommand{\cvaluet}{\widetilde{\cvalue}}
\newcommand{\copent}{\widetilde{\copen}}

\newcommand{\mempool}{\mc{M}}
\newcommand{\blockProductionFunction}{f}

\newcommand{\permutationAlgo}{a_{perm}}
\newcommand{\partylist}{L}
\newcommand{\keylist}{K}
\newcommand{\weightkeylist}{\hat{K}}
\newcommand{\permutedList}{\hat{L}}
\newcommand{\broadcastAlgo}{a_{broadcast}}
\newcommand{\subselectionParam}{\theta}
\newcommand{\indexfunc}{\mc{I}}
\newcommand{\keysharelambda}{\mathbf{x}}

\newcommand{\sysparam}{\mc{S}}
\newcommand{\bulletinboard}{\mc{BB}}
\newcommand{\cvtmsBits}{b_P}
\newcommand{\bbIdentifier}{ID_\bulletinboard}
\newcommand{\ddhVer}{\mc{V}_{DDH}}

\newcommand{\Fweight}{{\func}_{wtss}}

\newcommand{\prob}{\Pi}
\newcommand{\cert}{\msf{cert}}
\newcommand{\reward}{R}

\newcommand{\rewardFunc}{\Gamma_{reward}}

\newcommand{\cost}{C}

\newcommand{\distinguisher}{\mc{D}}

\newcommand{\members}{W}


%%%%%%%%%%%%%%%%%%%%%%%%%
% COMPLIANCE
%%%%%%%%%%%%%%%%%%%%%%%%%

\newcommand{\poly}{p}
\newcommand{\honest}{\mc{H}}
\newcommand{\partySet}{\mathbb{P}}
\newcommand{\observer}{\Omega}

\newcommand{\miningpower}{\mu}

\newcommand{\genesis}{\block_G}
\newcommand{\oracle}{\mc{O}}

\newcommand{\mesg}{m}
\newcommand{\msgSet}{\mathbb{M}}
\newcommand{\msgOutputSet}{M}

\newcommand{\execution}{\mc{E}}
\newcommand{\executionSet}{\mathbb{E}}
\newcommand{\executionTrace}{\Im}
\newcommand{\proto}{\Pi}
\newcommand{\strategy}{S}
\newcommand{\strategySet}{\mathbb{S}}
\newcommand{\profile}{\sigma}
\newcommand{\point}{L}

\newcommand{\messageValidityPredicate}{\mc{V}}
\newcommand{\infractionPredicate}{\mc{X}}

\newcommand{\compliant}{\infractionPredicate\mathsf{-compliant}}

\newcommand{\slot}{r}
\newcommand{\round}{\slot}
\newcommand{\epoch}{e}
\newcommand{\epochLength}{l_\epoch}

\newcommand{\utility}{U}
\newcommand{\totalReward}{\mc{R}}
\newcommand{\rewardVal}{\rho}
\newcommand{\proportionalRewardFunc}{\varrho}
\newcommand{\universalRewardFunc}{\xi}
\newcommand{\costVal}{c}

\newcommand{\maxDelay}{D}
\newcommand{\networkLossProb}{d}

\newcommand{\difficulty}{\delta}
\newcommand{\powQueryNum}{q}
\newcommand{\queryCost}{\lambda}

\newcommand{\networkTieProb}{p_n}

\newcommand{\voterSet}{\mathbb{T}}
\newcommand{\attestation}{\alpha}
\newcommand{\validator}{V}

\newcommand{\exchangeRate}{X}
\newcommand{\utilityBoost}{B}

\newcommand{\exchangeRateVal}{x}
\newcommand{\utilityBoostVal}{b}
\newcommand{\deposit}{g}


%%%%%%%%%%%%%%%%%%%%%%%%%
% TAXATION
%%%%%%%%%%%%%%%%%%%%%%%%%

\newcommand{\exchange}{\mc{E}}
\newcommand{\taxAuth}{\mc{T}}

\newcommand{\assets}{\Theta}
\newcommand{\taxationProto}{\mc{P}_{asset}}
\newcommand{\taxationAddressProto}{\mc{P}_{address}}
\newcommand{\balance}{\mathsf{bal}}

\newcommand{\taxBtc}{\ledger^{t}}