notation.sty

%Copyright 2018, Andrea Proietto
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%
%The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.
%
%THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

%=============================================
% This is a personal undertaking which aims to uniformize and disambiguate mathematical notation between all its branches

\ProvidesPackage{notation}[2018/09/21 v0.3 The Notation]

% binom macro
\RequirePackage{amsmath}
% mathbb command, complement symbol and others
\RequirePackage{amssymb}
% More blackboard symbols
\RequirePackage{bbm}

% Required for crypto games
\RequirePackage{tikz} % duh...
\usetikzlibrary{arrows,shadows} % shadow for the entities, arrow for the messages
\RequirePackage{xparse} % Improved environment definition


% These definiions relate to numerical sets
%
% The prime numbers
\newcommand{\primenum}{\mathbb{P}}
% The natural (non-negative) numbers
% NOTE: \natural is already defined as a musical symbol, hence the \nonneg name
\newcommand{\nonneg}{\mathbb{N}}
% The integers
\newcommand{\integer}{\mathbb{Z}}
% The rationals
\newcommand{\rational}{\mathbb{Q}}
% The real numbers
\newcommand{\real}{\mathbb{R}}
%
% NOTE: Generic n-size sets are represented by their corresponding blackboard number, as the following macros suggest.
% This package implements the first two immediately because of their widespread use, though the logic should remain consistent for all such sets
%
% The generic singleton, to be interpreted as {0}
\newcommand{\singleton}{\mathbbm{1}}
% The generic doubleton, or binary set, to be interpreted as {0, 1}
\newcommand{\binary}{\mathbbm{2}}

% Comfort macros
%
\newcommand{\oneover}[1]{\frac{1}{#1}}
\newcommand{\half}{\frac{1}{2}}

% Some most-used functions
%
% Expected value of a RV [math mode]
\newcommand{\expect}{\mathcal{E}}
% Power set of a set [math mode]
\newcommand{\powerset}{\mathcal{P}}

% Probability distributions
%
% Generic distribution
\newcommand{\probdist}{\mathcal{R}and}
% Uniform distribution
\newcommand{\unifdist}{\mathcal{U}nif}
% Binomial distribution
\newcommand{\binomdist}{\mathcal{B}inom}
% Bernoulli distribution, or coin
\newcommand{\berdist}{\mathcal{B}er}
\newcommand{\coin}{\berdist}
% Independency relation
\newcommand{\indep}{\perp\!\!\!\!\perp}

% Similarities
\newcommand{\jaccsim}{\mathcal{J}\textit{acc}}
\newcommand{\hammsim}{\mathcal{H}\textit{amm}}

% Function classes and relations
%
% Comutational indistinguishability
\newcommand{\compindist}{\approx_\textsc{c}}
% Statistical indistinguishability
\newcommand{\statindist}{\approx_\textsc{s}}
% Polynomial function
\newcommand{\poly}{\mathcal{P}\textit{oly}}
% Negligible function
\newcommand{\negl}{\mathcal{N}\textit{egl}}
% Permutation, or ordering
\newcommand{\permut}{\mathcal{P}\textit{erm}}
\newcommand{\order}{\permut}

% Cryptography
%
% Evaluate UAR [math mode]
\newcommand{\pickUAR}{\mathrel{{\leftarrow}\vcenter{\hbox{\scriptsize\rmfamily\upshape\!\!\textsf{\$}}}}}
% Default challenger
\newcommand{\challenger}{\textsf{C}}
% Default adversary
\newcommand{\adversary}{\textsf{A}}
% Default distinguisher
\newcommand{\distinguisher}{\textsf{D}}
% Cryptogame [math mode]
\NewDocumentCommand{\cryptog}{m O{\Pi} O{\adversary}}{\textsc{Game}^{\textsc{#1}}_{#2, #3}}
% Hybrid game [math mode]
\NewDocumentCommand{\hybridg}{m O{\Pi} O{\adversary}}{\textsc{Hyb}^{\textsc{#1}}_{#2, #3}}

% Acronyms
%
% Independent and Identically Distributed
\newcommand{\iid}{\textsc{iid}}
% Uniformly At Random
\newcommand{\uar}{\textsc{uar}}
% Probabilistic Polynomial time
\newcommand{\ppt}{\textsc{ppt}}
% Universally unforgeable from chosen message attack
\newcommand{\ufcma}{\textsc{uf-cma}}
% Decisional Diffie-Hellman
\newcommand{\ddh}{\textsc{ddh}}
% Computational Diffie-Hellman
\newcommand{\cdh}{\textsc{cdh}}
% Secret Key Encryption
\newcommand{\ske}{\textsc{ske}}
% Public Key Encryption
\newcommand{\pke}{\textsc{pke}}
% Chosen Plaintext Attack
\newcommand{\cpa}{\textsc{cpa}}
% Chosen Ciphertext Attack
\newcommand{\cca}{\textsc{cca}}
% One-Way Function
\newcommand{\owf}{\textsc{owf}}
% PseudoRandom Generator
\newcommand{\prg}{\textsc{prg}}
% PseudoRandom Function
\newcommand{\prf}{\textsc{prf}}
% PseudoRandom Permutation
\newcommand{\prp}{\textsc{prp}}


%%%%%%%%%%%%%%%%%%%%%%%%
% Cryptosequences
%%%%%%%%%%%%%%%%%%%%%%%%

% Define counters
\newcounter{preinstance}
\newcounter{instancecount}
\newcounter{sequencecursor}
\newcounter{intransientfigure}
\setcounter{intransientfigure}{0}
\newcounter{looplabel}

\newcommand{\cseqcraftfloat}{
    \ifnum\@floatpenalty<0\relax
    \else
        \setcounter{intransientfigure}{1}
        \begin{figure}[htbp]
        \centering
    \fi
}

% Styles
\tikzstyle{msgstyle}=[->, >=angle 60]
\tikzstyle{inststyle}=[rectangle, draw, anchor=west, minimum height=0.8cm, minimum width=1.6cm, fill=white, drop shadow={opacity=1,fill=black}]

% Internal commands
%
% Diagram spacing
\newcommand{\cseqdelay}{\stepcounter{sequencecursor}}

% Message: from, fromtext, msgtext, to, totext
\newcommand{\cseqmessager}[5]{
    \stepcounter{sequencecursor}
    \path (#1)+(0, -\thesequencecursor*\unitfactor-0.7*\unitfactor) 
        node (tail) {} node [anchor = east] {#2};
    \path (#4)+(0, -\thesequencecursor*\unitfactor-0.7*\unitfactor)
        node (head) {} node [anchor = west] {#5};
    \draw [msgstyle] (tail) -- (head)
        node [midway, above] {#3};
}

% Message: from, fromtext, msgtext, to, totext
\newcommand{\cseqmessagel}[5]{
    \stepcounter{sequencecursor}
    \path (#1)+(0, -\thesequencecursor*\unitfactor-0.7*\unitfactor) 
        node (tail) {} node [anchor = west] {#2};
    \path (#4)+(0, -\thesequencecursor*\unitfactor-0.7*\unitfactor)
        node (head) {} node [anchor = east] {#5};
    \draw [msgstyle] (tail) -- (head)
        node [midway, above] {#3};
}

% New participant
% \cseqentity[edge distance]{var}{name:class}
\newcommand{\cseqentity}[3][0]{
    \stepcounter{instancecount}
    \path (inst\thepreinstance.east)+(#1,0)
        node[inststyle] (inst\theinstancecount) {#3};
    \path (inst\theinstancecount)+(0,-0.5*\unitfactor)
        node (#2) {};
    \tikzstyle{instcolor#2}=[]
    \stepcounter{preinstance}
}

% Entity computation
\newcommand{\cseqcompute}[3]{
    \stepcounter{sequencecursor}
    \path (#1)+(0,-\thesequencecursor*\unitfactor-0.7*\unitfactor)
        node [anchor = #3] {#2};
}


% API Commands
%
% Challenger computation
\newcommand{\cseqchallenger}[1]{
    \cseqcompute{C}{#1}{west};
}
% Adversary computation - optional orientation as first argument: [east|west]
\newcommand{\cseqadversary}[2][east]{
    \cseqcompute{A}{#2}{#1};
}
% Distinguisher computation
\newcommand{\cseqdistinguisher}[1]{
    \cseqcompute{D}{#1}{east};
}


% Message from adversary to challenger
\newcommand{\send}[3]{
    \cseqmessager{A}{#1}{#2}{C}{#3}
}
% Message from challenger to adversary
\newcommand{\receive}[3]{
    \cseqmessagel{C}{#1}{#2}{A}{#3}
}
% Message from adversary to distinguisher - cryptoredux only
\newcommand{\invoke}[3]{
    \cseqmessagel{A}{#1}{#2}{D}{#3}
}
% Message from distinguisher to adversary - cryptoredux only
\newcommand{\return}[3]{
    \cseqmessager{D}{#1}{#2}{A}{#3}
}


% Arguments: Identifier (used as label) | description | challengername
\NewDocumentEnvironment{cryptogame}{m m m}
{ % Crypto-game BEGIN

    \cseqcraftfloat

    \begin{tikzpicture}

        % Set unit measurements
        \setlength{\unitlength}{1cm}
        \def\unitfactor{0.6}

        % Set counters
        \setcounter{preinstance}{0}
        \setcounter{instancecount}{0}
        \setcounter{sequencecursor}{0}
        \node[coordinate] (inst0) {};
        
        % Loop macros
        \newcommand{\cseqbeginloop}{
            \ifnum\thelooplabel=0
            \setcounter{looplabel}{\thesequencecursor}
            \stepcounter{looplabel}
            \else \PackageError{notation}{Attempting to nest loops in a         cryptosequence. Close the former loop first}
            \fi
        }

        \newcommand{\cseqendloop}{
            \ifnum\thelooplabel=0
                \PackageError{notation}{No loop to close here}
            \fi
            \ifnum\thelooplabel>\thesequencecursor\relax
                \PackageError{notation}{Closing an empty loop}
            \fi
            \draw[->](A)+(-0.2,         -0.15-\thesequencecursor*\unitfactor-0.7*\unitfactor)
            .. controls +(-0.6, -1.3)
            and         +(-0.6, +1.3)
            ..          +(-0.2,         0.15-\thelooplabel*\unitfactor-0.7*\unitfactor);
            \setcounter{looplabel}{0}
        }

        % Add the game's participants
        \cseqentity{A}{$\adversary$}
        \cseqentity[2.5]{C}{$\challenger^{\textsc{#3}}$}

}
{ % Crypto-game END

        \ifnum\value{instancecount}>0
            \foreach \t [evaluate=\t] in {1,...,\theinstancecount}{
                \draw[dotted] (inst\t) -- ++(0,-\thesequencecursor*\unitfactor-2.2*\unitfactor);
            }
        \fi
    \end{tikzpicture}

    \ifnum\value{intransientfigure}=1
        \caption{#2}
        \label{cryptogame:#1}
        \end{figure}
        \setcounter{intransientfigure}{0}
    \fi
}



% Arguments: Identifier (used as label) | description | challengername | Second adversary name
\NewDocumentEnvironment{cryptoredux}{m m m m}
{ % Crypto-game BEGIN

    \cseqcraftfloat

    \begin{tikzpicture}

        % Set unit measurements
        \setlength{\unitlength}{1cm}
        \def\unitfactor{0.6}

        % Set counters
        \setcounter{preinstance}{0}
        \setcounter{instancecount}{0}
        \setcounter{sequencecursor}{0}
        \node[coordinate] (inst0) {};
        
        % Loop macros
        \newcommand{\cseqbeginloop}{
            \ifnum\thelooplabel=0
            \setcounter{looplabel}{\thesequencecursor}
            \stepcounter{looplabel}
            \else \PackageError{notation}{Attempting to nest loops in a       cryptosequence. Close the former loop first}
            \fi
        }

        \newcommand{\cseqendloop}{
            \ifnum\thelooplabel=0
                \PackageError{notation}{No loop to close here}
            \fi
            \ifnum\thelooplabel>\thesequencecursor\relax
                \PackageError{notation}{Closing an empty loop}
            \fi
            \draw[->](D)+(-0.2,         -0.15-\thesequencecursor*\unitfactor-0.7*\unitfactor)
            .. controls +(-0.6, -1.3)
            and         +(-0.6, +1.3)
            ..          +(-0.2,         0.15-\thelooplabel*\unitfactor-0.7*\unitfactor);
            \setcounter{looplabel}{0}
        }

        % Add the reduction's participants
        \cseqentity{D}{$\distinguisher^{\textsc{#4}}$}
        \cseqentity[2.2]{A}{$\adversary$}
        \cseqentity[2.2]{C}{$\challenger^{\textsc{#3}}$}

}
{ % Crypto-game END

        \ifnum\value{instancecount}>0
            \foreach \t [evaluate=\t] in {1,...,\theinstancecount}{
                \draw[dotted] (inst\t) -- ++(0,-\thesequencecursor*\unitfactor-2.2*\unitfactor);
            }
        \fi
    \end{tikzpicture}
    
    \ifnum\value{intransientfigure}=1
        \caption{#2}
        \label{cryptoredux:#1}
        \end{figure}
        \setcounter{intransientfigure}{0}
    \fi
}

% Apply paragraph spacing
%\setlength{\parskip}{1em}
%\usepackage{indentfirst}

% Put all formulae in display style for fractions, binomial coefficients, etc.
%\everymath{\displaystyle}