% Games
\newcommand{\game}{\textbf{Game}\xspace}
\newcommand{\oracle}{\textbf{Oracle}\xspace}
\newcommand{\inp}{\cdot}
\newcommand{\field}[1]{\mathbb{Z}_{#1}}
\newcommand{\secparamter}{\lambda}
\newcommand{\randomsample}{\leftarrow}
\newcommand{\randomassign}{\leftarrow}
\newcommand{\assign}{\coloneqq}
\newcommand{\encoded}[1]{\underline{#1}}
\newcommand{\m}{m}
\newcommand{\signature}{\sigma}
\newcommand{\pubkey}{pk}
\newcommand{\privkey}{sk}
\newcommand{\groupelement}[1]{#1}
\newcommand{\agmgroupelement}[2]{[\groupelement{#1}]_{\overset{\rightharpoonup}{#2}}}
\newcommand{\group}[1]{\mathbb{#1}}
\newcommand{\oraclequeries}{q_o}
\newcommand{\groupqueries}{q_g}
\newcommand{\hashqueries}{q_h}
\newcommand{\test}{\overset{?}{=}}
\newcommand{\ch}{\textbf{ch}}
\newcommand{\messagespace}{\mathcal{M}}
\newcommand{\pset}[1]{\mathbf{#1}}
\newcommand{\context}{\textit{context}}

% Special Dlog
\newcommand{\sdlog}{\text{Ed-DLog}\xspace}
\newcommand{\somdl}{\text{Ed-OMDL}\xspace}

% SIM algotithm
\newcommand{\simalg}{\textit{Sim}\xspace}

% Intermediate Game
\newcommand{\igame}{\text{Ed-IDLOG}\xspace}
\newcommand{\ioracle}{\textit{Chall}\xspace}

% EdDSA procedures
\newcommand{\keygen}{\textsf{KeyGen}\xspace}
\newcommand{\sign}{\textsf{Sign}\xspace}
\newcommand{\verify}{\textsf{Verify}\xspace}

% Security Notions
\newcommand{\cma}{\text{SUF-CMA}\xspace}
\newcommand{\adversary}[1]{\mathcal{#1}}
\newcommand{\advantage}[2]{\text{Adv}_{#1}^{#2}}
\newcommand{\prone}[1]{\Pr[#1 \Rightarrow 1]}

% Oracle
\newcommand{\Osign}{\textit{Sign}\xspace}
\newcommand{\Odl}{\textif{DL}\xspace}

% Structrues
\newcommand{\curve}{E}