Short review of lattice basis reduction types and his applications (Russian)

Abstract

This article presets a review of lattice lattice basis reduction types. Paper contains the main five types of lattice basis reduction: size reduced (weak Hermit), c-reduced, Lovasz condition, Hermit-Korkin-Zolotarev, Minkowski reduced. The article provides references to applications in: information theory (decoding of coding group in MIMO), calculus (minimize of the positive quadratic form), complexity theory and cryptanalysis of Merkle-Hellman cryptography (solving subset sum problems), algebra and control theory(solving system of linear diophantine equation), compiler theory (lattice based memory allocation), synthesize cryptographic and cryptanalysis in lattice based cryptography.