Dev Blog
| ./dev |
|
Original theme by orderedlist (CC-BY-SA)
Where applicable, all content is licensed under a CC-BY-SA.
|
Lattice Reduction
There seem to be two main methods of using lattice reduction techniques for other norms. The first looks to be to use a linear programming step in place of the 'weak reduction' step (the Gram-Schmidt reduction step). The second is embedding the base in a higher dimension with extra structure and giving bounds on how far it is from the different norm.
References
- Other norms for Lattice reduction techniques (LLL, PSLQ)?
- Other norms for Lattice reduction techniques (LLL, PSLQ)?
- "The generalized basis reduction algorithm" by Laszlo Lovasz and Herbert Scarf
- "Lattice Problems and Norm Embeddings" by Oded Regev and Ricky Rosen
- "Limits on the Hardness of Lattice Problems in lp Norms" by Chris Peikert
- "Lattice Basis Reduction in Infinity Norm" by Vanya Ivanova (Bachelor Thesis)