Random Sampling for Short Lattice Vectors on Graphics Cards
نویسندگان
چکیده
We present a GPU implementation of the Simple Sampling Reduction (SSR) algorithm that searches for short vectors in lattices. SSR makes use of the famous BKZ algorithm. It complements an exhaustive search in a suitable search region to insert random, short vectors to the lattice basis. The sampling of short vectors can be executed in parallel. Our GPU implementation increases the number of sampled vectors per second from 5200 to more than 120, 000. With this we are the first to present a parallel implementation of SSR and we make use of the computing capability of modern graphics cards to enhance the search for short vectors even more.
منابع مشابه
Parallel Shortest Lattice Vector Enumeration on Graphics Cards
In this paper we present an algorithm for parallel exhaustive search for short vectors in lattices. This algorithm can be applied to a wide range of parallel computing systems. To illustrate the algorithm, it was implemented on graphics cards using CUDA, a programming framework for NVIDIA graphics cards. We gain large speedups compared to previous serial CPU implementations. Our implementation ...
متن کاملRandom Sampling Revisited: Lattice Enumeration with Discrete Pruning
In 2003, Schnorr introduced Random sampling to find very short lattice vectors, as an alternative to enumeration. An improved variant has been used in the past few years by Kashiwabara et al. to solve the largest Darmstadt SVP challenges. However, the behaviour of random sampling and its variants is not well-understood: all analyses so far rely on a questionable heuristic assumption, namely tha...
متن کاملShortest Lattice Vector Enumeration on Graphics Cards
In this paper we make a first feasibility analysis for implementing lattice reduction algorithms on GPU using CUDA, a programming framework for NVIDIA graphics cards. The enumeration phase of the BKZ lattice reduction algorithm is chosen as a good candidate for massive parallelization on GPU. Given the nature of the problem we gain large speedups compared to previous CPU implementations. Our im...
متن کاملImproved Lattice Basis Reduction Algorithms and their Efficient Implementation on Parallel Systems
Zusammenfassung We present the rst implementation of a full lattice basis reduction for graphics cards. Existing algorithms for lattice basis reduction on CPUs o er reasonable results concerning runtime or reduction quality but unfortunately not both at the same time. In this work, we show that the powerful architecture of graphics cards is well suited to apply alternative algorithms that were ...
متن کاملOn the Distribution of Lengths of Short Vectors in a Random Lattice
We use an idea from sieve theory to estimate the distribution of the lengths of kth shortest vectors in a random lattice of covolume 1 in dimension n. This is an improvement of the results of Rogers [3] and Södergren [5] in that it allows k to increase with n.
متن کامل