Accelerated Slide- and LLL-Reduction

Abstract. Given an LLL-basis B of dimension n = hk we accelerate slide-reduction with blocksize k to run under a reasonable assumption within 1 6 n2 h log1+ε α local SVP-computations of dimension k, where α ≥ 4 3 measures the quality of the given LLL-basis and ε is the quality of slidereduction. If the given basis B is already slide-reduced for blocksize k/2 the 1 6 n2 h log1+ε α bound further decreases to 2 3 h3 (1 + log1+ε γk/2). This bound is polynomial in n for arbitrary bit-length of B, it improves previous bounds considerably. We also accelerate LLL-reduction. Keywords. Block reduction, LLL-reduction, slide reduction.

• Type: Journal
• Year: 2011
• Where: ECCC
• Authors: Claus-Peter Schnorr
• Keywords: Computations, Decreases, ECCC 2011, ECommerce, Polynomial