Algorithms to construct minkowski reduced and hermite reduced lattice bases
نویسندگان
چکیده
منابع مشابه
Worst-Case Hermite-Korkine-Zolotarev Reduced Lattice Bases
The Hermite-Korkine-Zolotarev reduction plays a central role in strong lattice reduction algorithms. By building upon a technique introduced by Ajtai, we show the existence of Hermite-Korkine-Zolotarev reduced bases that are arguably least reduced. We prove that for such bases, Kannan’s algorithm solving the shortest lattice vector problem requires d d 2e (1+o(1)) bit operations in dimension d....
متن کاملPractical algorithms for constructing HKZ and Minkowski reduced bases
In this paper, three practical lattice basis reduction algorithms are presented. The first algorithm constructs a Hermite, Korkine and Zolotareff (HKZ) reduced lattice basis, in which a unimodular transformation is used for basis expansion. Our complexity analysis shows that our algorithm is significantly more efficient than the existing HKZ reduction algorithms. The second algorithm computes a...
متن کاملLattice Point Enumeration on Block Reduced Bases
When analyzing lattice-based cryptosystems, we often need to solve the Shortest Vector Problem (SVP) in some lattice associated to the system under scrutiny. The go-to algorithms in practice to solve SVP are enumeration algorithms, which usually consist of a preprocessing step, followed by an exhaustive search. Obviously, the two steps offer a trade-off and should be balanced in their running t...
متن کاملOn the Structure of Reduced Kernel Lattice Bases
Lattice-based reformulation techniques have been used successfully both theoretically and computationally. One such reformulation is obtained from the lattice kerZ(A) = {x ∈ Z | Ax = 0}. Some of the hard instances in the literature that have been successfully tackled by lattice-based techniques, such as market split and certain classes of knapsack instances, have randomly generated input A. The...
متن کاملPractical HKZ and Minkowski Lattice Reduction Algorithms
Recently, lattice reduction has been widely used for signal detection in multiinput multioutput (MIMO) communications. In this paper, we present three novel lattice reduction algorithms. First, using a unimodular transformation, a significant improvement on an existing Hermite-Korkine-Zolotareff-reduction algorithm is proposed. Then, we present two practical algorithms for constructing Minkowsk...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 1985
ISSN: 0304-3975
DOI: 10.1016/0304-3975(85)90067-2