Upper and lower bound on the cardinality containing shortest vectors in a lattice reduced by block Korkin-Zolotarev method (Russian)

TL;DR

This paper provides bounds on the number of shortest vectors in lattices reduced by the BKZ method, analyzing how lattice density and specific lattice types influence this cardinality.

Contribution

It offers new upper and lower bounds on shortest vector cardinality in BKZ-reduced lattices, including for critical and Goldstein-Mayer types, considering density effects.

Findings

Derived bounds depend on block size and density.

Density ratio influences shortest vector cardinality.

Upper estimates provided for specific lattice classes.

Abstract

This article present a concise estimate of upper and lower bound on the cardinality containing shortest vector in a lattice reduced by block Korkin-Zolotarev method (BKZ) for different value of the block size. Paper show how density affect to this cardinality, in form of the ratio of shortest vector size and sucessive minimal. Moreover we give upper estimate of cardinality for critical and Goldstein-Mayer lattices.