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

2012/10/24 by Vasiliy Usatyuk, Usatyuk, Vasiliy
Computer Science · #Coding theory and cryptography #Cryptographic Implementations and Security #Cryptography and Data Security #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.1210.6494

openalex publication_date 2012/10/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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