Parallel Lattice Basis Reduction

Abstract. Lattice basis reduction is an important problem in geometry of numbers with applications in combinatorial optimization, computer algebra, and cryptography. The well-known sequential LLL algorithm finds a short vector in O(n4 log B) arithmetic operations on integers having binary length O(n log B), where n denotes the dimension of the lattice and B denotes the maximum L2 norm of the initial basis vectors. In this paper a new analysis of the parallel algorithm of Roch and Villard is presented. It is shown that on an n

• Type: Conference
• Year: 1992
• Where: ISSAC
• Authors: Gilles Villard
• Keywords: Binary Length, ISSAC 1992, Lattice Basis Reduction, Log B, Mathematics