TY - JOUR
A1 - Schnorr, Claus Peter
T1 - A hierarchy of polynomial time lattice basis reduction algorithms
T2 - Theoretical Computer Science
N2 - We present a hierarchy of polynomial time lattice basis reduction algorithms that stretch from Lenstra, Lenstra, Lovász reduction to Korkine–Zolotareff reduction. Let λ(L) be the length of a shortest nonzero element of a lattice L. We present an algorithm which for k∈N finds a nonzero lattice vector b so that |b|2⩽(6k2)nkλ(L)2. This algorithm uses O(n2(kk+o(k))+n2)log B) arithmetic operations on O(n log B)-bit integers. This holds provided that the given basis vectors b1,…,bn∈Zn are integral and have the length bound B. This algorithm successively applies Korkine–Zolotareff reduction to blocks of length k of the lattice basis. We also improve Kannan's algorithm for Korkine-Zolotareff reduction.
Y1 - 2023
UR - http://publikationen.ub.uni-frankfurt.de/frontdoor/index/index/docId/75886
UR - https://nbn-resolving.org/urn:nbn:de:hebis:30:3-758869
SN - 0304-3975
VL - 53
IS - 2-3
SP - 201
EP - 224
PB - Elsevier
CY - Amsterdam [u.a.]
ER -