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

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.