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For cryptanalysis in lattice-based schemes, the performance evaluation of lattice basis reduction using high-performance computers is becoming increasingly important for the determination of the security level. We propose a distributed and asynchronous parallel reduction algorithm based on randomization and DeepBKZ, which is an improved variant of the block Korkine-Zolotarev (BKZ) reduction algorithm. Randomized copies of a lattice basis are distributed to up to 103,680 cores and independently reduced in parallel, while some basis vectors are shared asynchronously among all processes via MPI. There is a trade-off between randomization and information sharing; if a substantial amount of information is shared, all processes will work on the same problem, thereby diminishing the benefit of parallelization. To monitor this balance between randomness and sharing, we propose a metric to quantify the variety of lattice bases. We empirically find an optimal parameter of sharing for high-dimensional lattices. We demonstrate the efficacy of our proposed parallel algorithm and implementation with respect to both performance and scalability through our experiments.
This paper describes how we solved 12 previously unsolved mixed-integer program-
ming (MIP) instances from the MIPLIB benchmark sets. To achieve these results we
used an enhanced version of ParaSCIP, setting a new record for the largest scale MIP
computation: up to 80,000 cores in parallel on the Titan supercomputer. In this paper
we describe the basic parallelization mechanism of ParaSCIP, improvements of the
dynamic load balancing and novel techniques to exploit the power of parallelization
for MIP solving. We give a detailed overview of computing times and statistics for
solving open MIPLIB instances.