Isodual Reduction of Lattices.
Nicholas Howgrave-Graham · 2007
Abstract We define a new notion of a reduced lattice, based on a quantity introduced in the LLL paper. We show that lattices reduced in this sense are simultaneously reduced in both their primal and dual. We show that the definition applies naturally to blocks, and therefore gives a new hierarchy of polynomial time algorithms for lattice reduction with fixed blocksize. We compare this hierarchy of algorithms to previous ones. We then explore algorithms to provably minimize the associated measure, and also some more efficient heuristics. Finally we comment on the initial investigations of applying our technique to the NTRU family of lattices. 1 Introduction Although not emphasized in the original LLL paper [14], one can view the LLL algorithm in the followingway: given an input basis B = { b1, b2,..., bn} it monotonically reduces the quantity1