High performance lattice reduction on heterogeneous computing platform

Abstract

Jozsa, CM.; Domene Oltra, F.; Vidal Maciá, AM.; Piñero Sipán, MG.; González Salvador, A. (2014). High performance lattice reduction on heterogeneous computing platform. Journal of Supercomputing. 70(2):772-785. doi:10.1007/s11227-014-1201-2. Abstract The lattice reduction (LR) technique has become very important in many engineering fields. However, its high complexity makes difficult its use in real-time applications, especially in applications that deal with large matrices. As a solution, the Modified Block LLL (MB-LLL) algorithm was introduced in [10], where several levels of parallelism were exploited: (i.) coarse-grained parallelism was achieved by applying the block-reduction concept presented in [15] and (ii.) fine-grained parallelism was achieved through the Cost Reduced All-Swap LLL (CR-AS-LLL) algorithm introduced in [10].In this paper, we present the Cost Reduced MB-LLL (CR-MB-LLL) algorithm, which allows to significantly reduce the computational complexity of the MB-LLL by allowing the relaxation of the first LLL condition while executing the LR of submatrices, resulting in the delay of the GS coefficients update and by using less costly procedures during the boundary checks. The effects of complexity reduction and implementation details are analyzed and discussed for several architectures. A mapping of the CR-MB-LLL on a heterogenenous platform is proposed and it is compared with implementations running on a dynamic parallelism enabled GPU and a multi-core CPU. The mapping on the architecture proposed allows a dynamic scheduling of kernels where the overhead introduced is hidden by the use of several CUDA streams. Results show that the execution time of the CR-MB-LLL algorithm on the heterogeneous platform outperforms the multi-core CPU and it is more efficient than the CR-AS-LLL algorithm in case of large matrices.

Heterogeneous Implementation of a Voronoi Cell-Based SVP Solver

“…Up until now, there is substantial work on computing platforms with tens of CPU cores e.g. [9], [13], [30], or, alternatively, solely on GPUs, but there is no work on CPU+GPU platforms, except for building blocks for attacks rather than attacks themselves [23] or attacks that can be broken down into many instances of the same attack [25], which is typically not the case with most attacks.…”

“…The second paper, published in 2014, implements a relaxed version of LLL, called ''cost-reduced MB-LLL'' or CR-MB-LLL, a lattice reduction algorithm, on heterogeneous systems [23]. The authors showed that the heterogeneous implementation of the CR-MB-LLL algorithm performs better than the multi-threaded version for CPUs, if large matrices (i.e.…”