Accelerated Slide- and LLL-Reduction

Given an LLL-basis B of dimension n = hk we accelerate slide-reduction with blocksize k to run under a reasonable assumption in 1 6 nh log1+ε α local SVP-computations in dimension k, where α ≥ 4 3 measures the quality of the given LLL-basis and ε is the quality of slide-reduction. If the given basis B is already slide-reduced for blocksize k/2 then the number of local SVP-computations for slide-reduction with blocksize k reduces to 2 3 h3(1+log1+ε γk/2). This bound is polynomial for arbitrary bit-length of B, it improves previous bounds considerably. We also accelerate LLL-reduction.