35 lines
1.9 KiB
TeX
35 lines
1.9 KiB
TeX
\begin{comment}
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\section %hack for vim-latexsuite
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\end{comment}
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In this thesis, we presented new cryptographic schemes that relies on lattice or pairing assumptions.
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These contributions focus on the design and analysis of new cryptographic schemes that target privacy-preserving applications.
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In pairing-related cryptography, we propose a practical dynamic group signature scheme, for which security is well understood.
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It relies on broadly used assumptions with simple statements that exists for more than ten years.
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This work is also supported by a practical implementation in C.
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Our work in the lattice work give rise of three fundamental schemes that were missing in the landscape of lattice-based privacy-preserving primitives.
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Even if these schemes suffer from some efficiency issues due to their novelty, we do believe that it's one step toward a quantum-secure privacy-friendly world.
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In the way of doing it, improvements have been made in the state of zero-knowledge proofs in the lattice setting as well as providing building blocks that, we believe, are of independent interest.
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As of our signature with efficient protocols, which have been used to provide a lattice-based e-cash system~\cite{LLNW17}.
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All these works are proven under strong security model within simple assumptions.
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This made a breeding ground for new theoretical constructions, as well as going toward practicality.
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\section*{Open Problems}
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The path of providing new cryptographic primitives and proving them is sometimes uneven.
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The most obvious questions that stem from this work are about how to tackle the compromises we made in the design of those primitives.
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\begin{question}
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Is it possible to build an adaptive oblivious transfer with access control with polynomially-large approximation factor?
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\end{question}
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In other words, is it possible to avoid smudging to keep message-privacy in the oblivious transfer scheme of~\cref{ch:ot-lwe}.
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\begin{question}
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\end{question}
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