Extreme Enumeration on GPU and in Clouds

The complexity of the Shortest Vector Problem (SVP) in lattices is directly related to the security of NTRU and the provable level of security of many recently proposed lattice-based cryptosystems. We integrate several recent algorithmic improvements for solving SVP and take rst place at dimension 120 in the SVP Challenge Hall of Fame. Our implementation allows us to nd a short vector at dimension 114 using 8 NVIDIA video cards in less than two days. Speci cally, our improvements to the recent Extreme Pruning in enumeration approach include: (1) a more exible bounding function in polynomial form; (2) code to take advantage of Clouds of commodity PCs (via the MapReduce framework); and (3) the use of NVIDIA's Graphics Processing Units (GPUs). We may now reasonably estimate the cost of a wide range of SVP instances in U.S. dollars, as rent paid to cloudcomputing service providers, which is arguably a simpler and more practical measure of complexity.