defs-aad.tex

\newcommand{\upperbound}{\ensuremath{B}\xspace}

%
% Scheme names
%
\newcommand{\biaas}{\ensuremath{\mathsf{AAS}_\mathsf{bilinear}}\xspace}
\newcommand{\biaad}{\ensuremath{\mathsf{AAD}_\mathsf{bilinear}^{\mathsf{tall}}}\xspace}
\newcommand{\biaadset}{\ensuremath{\mathsf{AAD}_\mathsf{bilinear}^{\mathsf{short}}}\xspace}

\newcommand{\rsaaas}{\ensuremath{\mathsf{AAS}_\mathsf{rsa}}\xspace}
\newcommand{\rsaaad}{\ensuremath{\mathsf{AAD}_\mathsf{rsa}^{\mathsf{tall}}}\xspace}
\newcommand{\rsaaadset}{\ensuremath{\mathsf{AAD}_\mathsf{rsa}^{\mathsf{short}}}\xspace}

%
% Helpful terminology that might change later
%
\newcommand{\communionTree}{Communion Tree\xspace}
\newcommand{\communionTrees}{Communion Trees\xspace}
\newcommand{\prefixCommunionTree}{Prefix Communion Tree\xspace}
\newcommand{\prefixCommunionTrees}{Prefix Communion Trees\xspace}
\newcommand{\frontierCommunionTree}{Frontier Communion Tree\xspace}
\newcommand{\frontierCommunionTrees}{Frontier Communion Trees\xspace}

%
% Append-only Auth. Set/Dictionary API
%
\newcommand{\setup}{\ensuremath{\mathsf{Setup}}\xspace}

\newcommand{\append}{\ensuremath{\mathsf{Append}}\xspace}
\newcommand{\multiappend}{\append^{+}}

\newcommand{\proveappendonly}{\ensuremath{\mathsf{ProveAppendOnly}}\xspace}
\newcommand{\verappendonly}{\ensuremath{\mathsf{VerAppendOnly}}\xspace}

% AAS-specific
\newcommand{\provememb}{\ensuremath{\mathsf{ProveMemb}}\xspace}
\newcommand{\vermemb}{\ensuremath{\mathsf{VerMemb}}\xspace}

% AAD-specific
\newcommand{\provelookup}{\ensuremath{\mathsf{ProveLookup}}\xspace}
\newcommand{\verlookup}{\ensuremath{\mathsf{VerLookup}}\xspace}

%
% Algorithms
%
\newcommand{\verpath}{\ensuremath{\mathsf{VerPath}}\xspace}
\newcommand{\provepath}{\ensuremath{\mathsf{ProvePath}}\xspace}
\newcommand{\proverootaccs}{\ensuremath{\mathsf{ProveRootAccs}}\xspace}
\newcommand{\provefrontier}{\ensuremath{\mathsf{ProveFrontier}}\xspace}
\newcommand{\verfrontier}{\ensuremath{\mathsf{VerFrontier}}\xspace}
\newcommand{\accumulate}{\ensuremath{\mathsf{Accum}}\xspace}
\newcommand{\createfrontier}{\ensuremath{\mathsf{CreateFrontier}}\xspace}

%
% Variables used in AAS algorithms
%
\newcommand{\elems}{\myblue{\mathbf{S}}}                     % notation for the set of elements at a certain node in the forest
\newcommand{\hash}{\myblue{\mathbf{h}}}                      % notation for Merkle hash in the forest
\newcommand{\acc}{\myblue{\mathbf{a}}}                       % notation for node accumulator commitment: \acc = g^{\accpoly(s)}
\newcommand{\eacc}{\myblue{\hat{\mathbf{a}}}}                % for extractable counterpart of \eacc
\newcommand{\subsetProof}{\myblue{\boldsymbol{\pi}}}
\newcommand{\bft}{\myblue{\boldsymbol{\sigma}}}              % notation for frontier accumulator commitment (on the server side): \fac = g^{\fropoly(s)}
\newcommand{\disj}{\myblue{\boldsymbol{\psi}}}               % notation for disjointness witness between a node accumulator and a frontier accumulator

% Not global variables
\newcommand{\charpoly}{\mathcal{C}}                 % characteristic polynomial of a set
\newcommand{\accpoly}{\alpha}                       % notation for node accumulator polynomial
\newcommand{\fropoly}{\phi}                         % notation for frontier accumulator 
\newcommand{\fac}{o}                                % notation for frontier accumulator commitment (on the verifier side): \fac = g^{\fropoly(s)}
\newcommand{\efac}{\hat{o}}                         % for extractabile counterpart of \fac
\newcommand{\CP}{\chi}                              % completeness proof w.r.t. frontier accumulator

%
% Notation for AAS/AAD
%
\newcommand{\AS}{\mathcal{S}}       % authenticated set
\newcommand{\AD}{\mathcal{D}}       % authenticated dictionary