Characterizing lattices for cryptography

Resumo

In this document, we aim to introduce a proposal of poster presentation at the XXVII Unicamp’s Scientific Initiation Congress that will deal with the work that has been done on the characterization of lattices for cryptographic purposes. A lattice is a discrete additive subgroup of the n-dimensional real space that has a periodic structure. In other words, a lattice is a set constructed by all the integer combinations of linearly independent vectors defined on the n-dimensional real space.The usage of lattices for construct cryptographic models begins with the breakthrough work of Ajtai in 1996 ¹. Since then, cryptography based on lattices is being developed more and more, aiming to face the growing advance of computing power. In addition, some cryptographic models built on problems of non-polynomial difficulty on lattices are being considered as security solutions for building cryptoschemes that could face attacks from a sufficiently powerful quantum computer that may appear on the coming years. With this in perspective in view, it is interesting to characterize lattice structures and its parameters to create secure and efficient cryptoschemes.