Lattice Problems and Their Reductions(Russian)

TL;DR

This paper reviews key lattice problems, their reductions, and applications in cryptography, highlighting the connection between SVP and CVP, and discussing Ajtai's theorem's significance.

Contribution

It provides a comprehensive overview of lattice problems, their reductions, and cryptographic relevance, including detailed analysis of the SVP-CVP connection and Ajtai's theorem.

Findings

Detailed analysis of the connection between SVP and CVP

Presentation of Ajtai's theorem and its cryptographic role

Comprehensive review of 18 lattice problems and their reductions

Abstract

This article presets a review of lattice problems. Paper contains the main eighteen problems with their reductions and referents to his cryptography application. As an example of reduction, we detail analyze connection between SVP and CVP. Moreover, we give an Ajtai theorem and demonstrate its role in lattice based cryptography.