\newcommand{\blue}[1]{{\color{blue}#1}}
\newcommand{\red}[1]{{\color{red}#1}}
\newcommand{\Guardian}{\mathcal{G}}
\newcommand{\Child}{\mathcal{C}}
\newcommand{\Customer}{\mathcal{C}}
\newcommand{\Merchant}{\mathcal{M}}
\newcommand{\Exchange}{\mathcal{E}}

\newcommand{\Commit}{\mathsf{Commit}}
\newcommand{\Attest}{\mathsf{Attest}}
\newcommand{\Verify}{\mathsf{Verify}}
\newcommand{\Derive}{\mathsf{Derive}}
\newcommand{\DeriveCompare}{\mathsf{DeriveCompare_\kappa}}
\newcommand{\Compare}{\mathsf{Compare}}
\newcommand{\AgeVer}{\mathsf{AgeVer}}

\newcommand{\HashF}{\mathsf{H}}
\newcommand{\Hash}{\mathsf{H}}
\newcommand{\Block}{\mathbb{B}}
\newcommand{\Pub}{\mathsf{Pub}}
\newcommand{\Sign}{\mathsf{Sig}}
\newcommand{\Ver}{\mathsf{Ver}}
\newcommand{\Encoding}{\mathsf{Encoding}}
\newcommand{\ECDSA}{\mathsf{ECDSA}}
\newcommand{\Null}{\mathcal{O}}
\newcommand{\EC}{\mathrm{ec}}
\newcommand{\Curve}{\mathsf{Curve25519}}
\newcommand{\SHA}{\mathsf{SHA256}}
\newcommand{\SHAF}{\mathsf{SHA252}}
\newcommand{\FDH}{\mathsf{FDH}}

\newcommand{\negl}{\epsilon}

\newcommand{\rand}{\mathsf{rand}}
\newcommand{\age}{\mathsf{a}}
\newcommand{\Age}{\mathsf{M}}
\newcommand{\bage}{\mathsf{b}}
\newcommand{\minage}{\mathsf{m}}
\newcommand{\attest}{\mathsf{T}}
\newcommand{\commitment}{\mathsf{Q}}
\newcommand{\pruf}{\mathsf{P}}
\newcommand{\Vcommitment}{\vec{\mathsf{Q}}}
\newcommand{\Vpruf}{\vec{\mathsf{P}}}
\newcommand{\blinding}{\beta}

\newcommand{\ZN}{\mathbb{Z}_N}
\newcommand{\Z}{\mathbb{Z}}
\newcommand{\N}{\mathbb{N}}
\newcommand{\A}{\mathbb{A}}
\newcommand{\E}{\mathbb{E}}
\newcommand{\F}{\mathbb{F}}
\newcommand{\seck}{\mathsf{s}}
\newcommand{\pubk}{\mathsf{P}}
\renewcommand{\H}{\mathbb{H}}
\newcommand{\K}{\mathbb{K}}
\newcommand{\Proofs}{\mathbb{P}}
\newcommand{\Commitments}{\mathbb{O}}
\newcommand{\Attests}{\mathbb{T}}
\newcommand{\Blindings}{\mathbb{B}}
\newcommand{\Nil}{\perp}

\newcommand{\p}{\mathsf{p}}
\newcommand{\com}{\mathsf{com}}
\newcommand{\prf}{\mathsf{prf}}

\newcommand{\Adv}{\mathcal{A}}
\newcommand{\PPT}{\mathfrak{A}}
\newcommand{\Probability}{\mathrm{Pr}}
\newcommand{\Algorithm}{f}
\renewcommand{\Game}[1]{G_\Adv^\mathsf{#1}}

\DeclareMathOperator{\Image}{Im}
\DeclareMathOperator{\Mod}{mod}

\newcommand{\Encode}[1]{\overbracket[0.5pt][2pt]{\,#1\,}}
\newcommand{\Decode}[1]{\underbracket[0.5pt][3pt]{\,#1\,}}
\newcommand{\FDHg}[1]{[#1]_g\,}
\newcommand{\logg}{{\breve{g}}}


\newcommand{\drawfrom}{\xleftarrow{\$}}
\newcommand\Exists{%
	  \mathop{\lower0.75ex\hbox{\ensuremath{%
		  \mathlarger{\mathlarger{\mathlarger{\mathlarger{\exists}}}}}}}%
	  \limits}

\newcommand\Forall{%
	  \mathop{\lower0.75ex\hbox{\ensuremath{%
		  \mathlarger{\mathlarger{\mathlarger{\mathlarger{\forall}}}}}}}%
	  \limits}
