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

TL;DR

This paper reviews five main types of lattice basis reduction and discusses their applications across various fields including information theory, cryptography, and algebra.

Contribution

It provides a comprehensive overview of lattice basis reduction types and their diverse applications, highlighting recent developments and references.

Findings

Identifies five main lattice basis reduction types.

Connects lattice reduction to applications in cryptography and information theory.

Summarizes the role of lattice reduction in solving Diophantine equations.

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.