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Fabrice Mouhartem
2018-04-10 17:11:38 +02:00
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sec-lattices.tex
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@ -7,8 +7,8 @@ For example, on the first round of the NIST post-quantum competition, there are
Lattice-based cryptography takes advantage of a simple mathematical structure, the so-called lattices, in order to provide beyond encryption and signature cryptography.
For instance, fully homomorphic encryption~\cite{Gen09,GSW13} are only possible in the lattice-based world for now.
In the context of provable security, lattice assumptions benefits from a worst-case to average-case reduction~\cite{Reg05,GPV08,MP12,AFG14}.
Concurrently, worst-case lattice problems have been extensively analysed in the last decade~\cite{ADS15,ADRS15,HK17}, both classically and quantumly.
In the context of provable security, lattice assumptions benefit from a worst-case to average-case reduction~\cite{Reg05,GPV08,MP12,AFG14}.
Concurrently, worst-case lattice problems have been extensively analyzed in the last decade~\cite{ADS15,ADRS15,HK17}, both classically and quantumly.
This gives us a good confidence in the lattice-based assumptions (given the \emph{caveats} of Chapter~\ref{ch:proofs}) such as Learning with Errors ($\LWE$) and Short Integer Solutions ($\SIS$) that are defined in Section~\ref{sse:lattice-problems}. The rest of this section will describe some useful algorithms that relies on \emph{lattice trapdoors}.