In this paper, we present a GPU-based parallel algorithm for the Learning With Errors (LWE) problem using a lattice-based Bounded Distance Decoding (BDD) approach. To the best of our knowledge, this is the first GPU-based implementation for the LWE problem. Compared to the sequential BDD implementation of Lindner-Peikert and pruned-enumeration strategies by Kirshanova [1], our GPU-based implementation is almost faster by a factor 6 and 9 respectively. The used GPU is NVIDIA GeForce GTX 1060 6G. We also provided a parallel implementation using two GPUs. The results showed that our algorithm is scalable and faster than the sequential version (Lindner-Peikert and pruned-enumeration) by a factor of almost 13 and 16 respectively. Moreover, the results showed that our parallel implementation using two GPUs is more efficient than Kirshanova et al.'s parallel implementation using 20 CPU-cores. INDEX TERMS Learning with error, lattice-based cryptography, LLL algorithm, shortest vector problem, closest vector problem, bounded distance decoding, GPU, cryptanalysis. NOMENCLATURE , Inner product |S| Number of elements of a set S Euclidean norm Z p Set of nonnegative integers less than p O(f) Soft O notation v Row vector (usually in Z m) a mod q Remainder after division of a by q poly(n) Polynomial function of degree n span{b 1 ,. .. , b n } Span of a set of vectors over Z