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Fabrice Mouhartem
2018-04-13 15:41:25 +02:00
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sec-lattices.tex
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@ -60,7 +60,7 @@ This problem reduces to the \textit{Learning With Errors}~($\LWE$) problems and
These links are important as those are ``worst-case to average-case'' reductions.
In other words, the $\SIVP$ assumption by itself is not very handy to manipulate in order to construct new cryptographic designs.
On the other hand, the $\LWE$ and $\SIS$ assumptions ---\,which are ``average-case'' assumptions\,--- are more suitable to design cryptographic schemes.
On the other hand, the $\LWE$ and $\SIS$ assumptions --\,which are ``average-case'' assumptions\,-- are more suitable to design cryptographic schemes.
In order to define the $\SIVP$ problem and assumption, let us first define the successive minima of a lattice, a generalization of the minimum of a lattice (the length of a shortest non-zero vector in a lattice).