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sections.tex
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\chapter{Introduction} \label{sec:intro}
\input{sections/intro/intro}
\section{Our Results}
\input{sections/intro/our-results}
%\section{Organization}
% \inpute{sections/intro/organization}
\chapter{Preliminaries} \label{sec:prelim}
\section{Notation} \label{sec:notation}
\input{sections/prelim/notation}
\section{Public-Key Cryptography}
\input{sections/prelim/basic}
\section{Bilinear Groups} \label{sec:bil-groups}
\input{sections/prelim/bil-groups}
\section{Matrix Diffie-Hellman Assumptions} \label{sec:mddh}
\input{sections/prelim/assumptions}
\section{Non-Interactive Zero-Knowledge Proofs} \label{sec:zk}
\input{sections/prelim/zk}
\section{Groth-Sahai Proofs}\label{sec:gs-proofs}
\input{sections/prelim/gs-proofs}
\section{QA-NIZK Arguments of Membership in Subspaces of $\GG_1$ or $\GG_2$} \label{sect:QANIZKlinspace}
\input{sections/prelim/QANIZKlinspace}
\chapter{QA-NIZK Arguments of Membership in Subspaces of $\GG_1\times\GG_2$}\label{sec:agg-asym}
\input{sections/linear-subspaces/main}
\section{Argument of Membership in Subspace Concatenation}\label{sec:concat}
\input{sections/linear-subspaces/concat}
\section{Argument of Sum in Subspace}\label{sec:sum}
\input{sections/linear-subspaces/sum}
\section{Argument of Equal Opening in Different Groups} \label{sec:aggcommit}
\input{sections/linear-subspaces/aggcommit}
\section{Aggregation of Groth-Sahai Proofs}\label{sec:agg-gs}
\input{sections/linear-subspaces/agg-gs}
\section{Structure Preserving Linearly Homomorphic Signatures}
\input{sections/linear-subspaces/lhsps}
\chapter {QA-NIZK Arguments for Bit-Strings} \label{sec:bits}
\input{sections/bits/intro}
\section{The Perfectly Binding case} \label{sec:bits-binding}
\input{sections/bits/perfectly-binding}
\subsection{Intuition} \label{sec:bits-intuition}
\input{sections/bits/intuition}
\subsection{Instantiations} \label{sec:bits-instantiations}
\input{sections/bits/instantiations}
\subsection{The Scheme} \label{sec:bits-scheme}
\input{sections/bits/bits-scheme}
\subsection{Extensions} \label{sec:bits-extensions}
\input{sections/bits/extensions}
\subsection{Applications} \label{sec:bits-applications}
\input{sections/bits/applications}
\section{The Computationally Binding Case} \label{sec:bits-non-binding}
\input{sections/bits/bits-non-binding}
\subsection{Extended Multi-Pedersen Commitments} \label{sec:ext-mp}
\input{sections/bits/mp-comm}
\subsubsection{Comparison with other Primitives}
\input{sections/bits/mp-vs-others}
\subsection{The Scheme} \label{sec:bits-scheme-nb}
\input{sections/bits/bits-scheme-nb}
\subsection{Constant-Size Argument for $\Lang_{ck,\sfbits}^n$} \label{sec:matr-bits}
\input{sections/bits/matr-bits}
\subsection{The Perfectly Binding Case from the Computatinally Binding Case}
\input{sections/bits/bits-single-com.tex}
\chapter{New Techniques for Non-Interactive Shuffle and Range Arguments} \label{sec:shuf-rp}
\input{sections/set-membership/intro}
\section{Related Work} \label{sec:set-memb-rel-work}
\input{sections/set-membership/related-work}
\section{Overview} \label{sec:shuf-rp-overview}
\input{sections/set-membership/overview}
\section{Aggregated NIZK Set Membership Arguments} \label{sec:aZKSMP}
\input{sections/set-membership/set-membership}
\subsection{QA-NIZK Argument of Membership in $\Lang_{[\matr{M}]_1,[\matr{N}]_1,\matr{\Lambda},\grkb{\alpha}}^n$} \label{sec:bin-lan-constr}
\input{sections/set-membership/set-membership-construction}
\section{Proof of Correctness of a Shuffle} \label{sec:shuffle}
\input{sections/shuffle/shuffle}
\section{Range Argument} \label{sec:range-proof}
\input{sections/range-proof/range-proof}
%\chapter{Other Contributions} \label{sec:extras}
% \input{sections/extras/intro}
\chapter{Ring Signature of Size $\Theta(\sqrt[3]{n})$ without Random O\-ra\-cles} \label{sec:opt-rs}
\input{sections/ring-signature/ring-signature}
\section{High Level Description}
\input{sections/ring-signature/high-level}
\section{Preliminaries}
\subsection{Groth-Sahai Proofs in the $\lin{2}$ Instantiation}
\input{sections/ring-signature/symm-gs}
\subsection{Flawed or Weaker Ring Signatures}\label{sec:rs-flawed}
\input{sections/ring-signature/flawed}
\subsection{Definition}
\input{sections/ring-signature/definition}
\subsection{Boneh-Boyen Signatures} \label{sec:bbs}
\input{sections/ring-signature/bb-signatures}
\section{Our Construction}
\input{sections/ring-signature/construction}
\chapter{Improved Aggregated Zero-Knowledge Set-Membership Proofs} \label{improved-aZKSMP} \label{sec:improved-aZKSMP}
\input{sections/improved-aZKSMP/improved-aZKSMP}
\section{Intuition} \label{sec:improved-aZKSMP-intuition}
\input{sections/improved-aZKSMP/aZKSMP-intuition}
\section{The Aggregated Case} \label{sec:log-set-memb-Z}
\input{sections/improved-aZKSMP/aZKSMP-scheme}
% \section{Application: Theoretical \(\Theta(\log n)\) Ring Signature} \label{sec:log-ring-signature}
% \input{sections/improved-aZKSMP/logn-ring-signature}
\chapter{Conclusions}
\input{sections/conclusions/conclusions}