International Association for Cryptologic Research

International Association
for Cryptologic Research


Paper: Isodual Reduction of Lattices

Nicholas A. Howgrave-Graham
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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.
  title={Isodual Reduction of Lattices},
  booktitle={IACR Eprint archive},
  keywords={foundations / Lattice reduction},
  note={ 13752 received 22 Mar 2007, last revised 26 Aug 2007},
  author={Nicholas A. Howgrave-Graham},