Accelerating subset sum and lattice based public-key cryptosystems with multi-core CPUs and GPUs

Abstract

Post-quantum cryptosystems based on subset sum and lattice problems have gained much attention from researchers due to their simple construction, their resistance to quantum attacks, the new potential applications they provide, and above all, the mathematical security proofs that rigorously relate them to computational hard problems. However, the computational complexity of these cryptosystems is still high compared to classic number-theoretical ones, which may impede their adoption on a large scale. We studied the performance of three public-key cryptosystems based on subset sum, learning with errors and ring learning with errors problems. We provide a systematic study for choosing their parameters to guarantee sufficient security levels and detail an asymptotic comparison between them in terms of storage and running time complexities. We accelerate the running time of these cryptosystems by exploiting the inherent parallelism in computations through a GPGPU-based parallel implementation. The cryptosystems are implemented using C++ on Intel(R) Xeon(R) multi-core 64-bit processors machine with CUDA-enabled Tesla K80 GPUs. The parallel implementation is based on OpenCL framework and can run on arbitrary hardware platform accelerators with minor changes. Several optimizations and efficient algorithms were used to compute the core operations in each cryptosystem to achieve optimum performance. The ring learning with errors based cryptosystem showed the best performance while the Subset Sum cryptosystem showed the highest speedup gain for the encryption primitive.