Optimised Montgomery domain inversion on FPGA

Modular inversion is a critical operation in elliptic curve cryptosystems (ECC). This paper presents a hardware optimised modular inversion algorithm targeted towards an FPGA implementation. It exploits the underlying structure of the device, leading to a fast and efficient design. Arithmetic is performed in the Montgomery domain, which allows an inversion result to be an input to further operations without the need for domain conversion. Results presented show an increase in throughput over existing inverter designs on reconfigurable logic.