A fast variant of the Gaussian reduction algorithm

We propose a fast variant of the Gaussian algorithm for the reduction of two{ dimensional lattices for the l1; l2; and l1;norm. The algorithm runs in at most O(n M(B) logB) bit operations for the l1;norm and in O(n logn M(B) logB) bit operations for the l1; and l2;norm on input vectors a b 2 ZZ n with norm at most 2B where M(B) is a time bound for B-bit integer multiplication. This generalizes Schonhages monotone Algorithm Sch91] to the centered case and to various norms.

• Type: Conference
• Year: 1994
• Where: ANTS
• Authors: Michael Kaib
• Keywords: Algorithms, ANTS 1994, Bit Operations, Gaussian Algorithm, Schonhages Monotone Algorithm