On the distribution of lengths of short vectors in a random lattice

2014/10/08 by Kim, Seungki
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1410.2005

Abstract

We use an idea from sieve theory to estimate the distribution of the lengths of kth shortest vectors in a random lattice of covolume 1 in dimension n. This is an improvement of the results of Rogers and Södergren in that it allows k to increase with n.

Related

• Random lattice vectors in a set of size O(n)
• Module lattices and their shortest vectors
• Improved algorithms for the Shortest Vector Problem and the Closest Vector Problem in the infinity norm
• Long shortest vectors in low dimensional lattices
• Upper and lower bound on the cardinality containing shortest vectors in a lattice reduced by block Korkin-Zolotarev method (Russian)