CMAP-LAP: Configurable Massively Parallel Solver for Lattice Problems

Tateiwa, Nariaki, Shinano, Yuji, Yamamura, Keiichiro, Yoshida, Akihiro, Kaji, Shizuo, Yasuda, Masaya, Fujisawa, Katsuki

Lattice problems are a class of optimization problems that are notably hard. There are no classical or quantum algorithms known to solve these problems efficiently. Their hardness has made lattices a major cryptographic primitive for postquantum cryptography. Several different approaches have been used for lattice problems with different computational profiles; some suffer from super-exponential time, and others require exponential space. This motivated us to develop a novel lattice problem solver, CMAP-LAP, based on the clever coordination of different algorithms that run massively in parallel. With our flexible framework, heterogeneous modules run asynchronously in parallel on a large-scale distributed system while exchanging information, which drastically boosts the overall performance. We also implement full checkpoint-and-restart functionality, which is vital to high-dimensional lattice problems. CMAP-LAP facilitates the implementation of large-scale parallel strategies for lattice problems since all the functions are designed to be customizable and abstract. Through numerical experiments with up to 103,680 cores, we evaluated the performance and stability of our system and demonstrated its high capability for future massive-scale experiments.

CMAP-LAP: Configurable Massively Parallel Solver for Lattice Problems

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