RISC-V Galois Field ISA Extension for Non-Binary Error-Correction Codes and Classical and Post-Quantum Cryptography

Due to the recent advances in new communication standards, such as 5G New Radio and beyond 5G, and in quantum computing and communications, new requirements for integrating processors into nodes have appeared. These requirements are meant to provide flexibility in the network to reduce operational costs and support diversity in services and load balancing. They are also designed to integrate both new and classical algorithms into efficient and universal platforms, execute specific operations, and attend to tasks with lower latency. Furthermore, some cryptographic algorithms (classical and post-quantum), which are essential to portable devices, share the same arithmetic with error-correction codes. For example, Advanced Encryption Standard (AES), elliptic curve cryptography, Classic McEliece, Hamming Quasi-Cyclic, and Reed-Solomon codes use <inline-formula><tex-math notation="LaTeX">$GF(2^{m})$</tex-math><alternatives><mml:math><mml:mrow><mml:mi>G</mml:mi><mml:mi>F</mml:mi><mml:mo>(</mml:mo><mml:msup><mml:mn>2</mml:mn><mml:mi>m</mml:mi></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math><inline-graphic xlink:href="kuo-ieq1-3174587.gif"/></alternatives></inline-formula> arithmetic. As this arithmetic is the basis of many algorithms, a versatile RISC-V Galois field ISA extension is proposed in this work. The RISC-V instruction set extension is implemented and validated using SweRV-EL2 1.3 on a Nexys A7 FPGA. In addition, a five-times acceleration is achieved for AES, Reed-Solomon codes, and Classic McEliece (post-quantum cryptography) at the expense of increasing the logic utilization by 1.27%.