Lower bounds of shortest vector lengths in random NTRU lattices

Lower Bounds of Shortest Vector Lengths in Random NTRU Lattices

Finding the shortest vector of a lattice is one of the most important problems in computational lattice theory. For a random lattice, one can estimate the length of the shortest vector using the Gaussian heuristic. However, no rigorous proof can be provided for some classes of lattices, as the Gaussian heuristic may not hold for them. In this paper, we propose a general method to estimate lower...

Lower bounds of shortest vector lengths in random knapsack lattices and random NTRU lattices

Finding the shortest vector of a lattice is one of the most important problems in computational lattice theory. For a random lattice, one can estimate the length of the shortest vector using the Gaussian heuristic. However, no rigorous proof can be provided for some classes of lattices, as the Gaussian heuristic may not hold for them. In the paper we study two types of random lattices in crypto...

Lower Bounds on Sequence Lengths

In this paper we study the sequence length requirements of distance-based evolutionary tree building algorithms in the Jukes-Cantor model of evolution. By deriving lower bounds on sequence lengths required to recover the evolutionary tree topology correctly , we show that two algorithms, the Short Quartet Method and the Harmonic Greedy Triplets algorithms have optimal sequence length requirements.

An equivalence functor between local vector lattices and vector lattices

We call a local vector lattice any vector lattice with a distinguished positive strong unit and having exactly one maximal ideal (its radical). We provide a short study of local vector lattices. In this regards, some characterizations of local vector lattices are given. For instance, we prove that a vector lattice with a distinguished strong unit is local if and only if it is clean with non no-...

Ideal Lattices and NTRU