Fast asymmetric encryption and decryption of SimpleMatrix scheme for Internet of Things

Asymmetric cryptography plays an essential role in many areas, including cloud computing, big data, blockchain, and the Internet of Things (IoT). However, most of them are based on the difficulty of factorizing large numbers or discrete logarithm problems, which are not secure to quantum computer attacks. SimpleMatrix is a new multivariate encryption scheme based on simple matrix multiplications, which can resist quantum computer attacks. Because of the low speed and demands of large finite fields, SimpleMatrix is limited in applications that use small finite fields. As a result, it is critical to improve the efficiency of SimpleMatrix to make its applications broader. In this paper, we speed up the encryption and decryption of SimpleMatrix by building efficient small finite field arithmetics based on Field-Programmable Gate Arrays (FPGAs) technology. We propose a fast architecture for encryption and decryption of SimpleMatrix based on table look-up based composite field multiplications and inversions and fast Gauss-Jordan elimination for solving systems of linear equations in a composite field. We test and verify the hardware architecture of SimpleMatrix on an FPGA, and the experimental results confirm our estimates and comparisons show that our design is much faster than other implementations. Thus, the hardware architecture can be used in FPGA-based systems of cloud computing, IoT, etc., for accelerating encryption and decryption.