Random Sampling Reduction With Precomputation

Given, an integer n-dimensional lattice basis, the random sampling reduction was proven to find a short vector in O(n(2)(k/6)(k/4)) arithmetic steps with an integer k, which is freely chosen by users. This paper introduces new random sampling reduction using precomputation techniques. The computation cost O(k(2) log(2) k(k/6)(k/4) + nk log k) is almost independent of the lattice dimension number. The new method is therefore especially advantageous to find a short lattice vector in higher dimensions. The arithmetic operation number of our new method is about 20% of the random sampling reduction with 200 dimensions, and with 1000 dimensions it is less than 1% (similar or equal to 1/130) of that of the random sampling reduction with representative parameter settings under reasonable assumptions.