High-Performance FPGA Implementation of Modular Inversion over F_256 for Elliptic Curve Cryptography

Modular Inversion over a prime field is an important operation for public-key cryptographic applications. It is the most crucial operation to speed up the calculation of an elliptic curve crypto-processor (ECC) when affine coordinates are used. In this work, the main goal is to implement a fast, high-performance modular inversion for ECC using field-programmable gate-array (FPGA) technology. A binary inversion algorithm in VHDL has been used for this efficient implementation. Timing simulation shows that the delay for one modular inversion operation in a modern Xilinx Virtex-7 FPGA is only 2.329 us at the maximum frequency of 146.389 MHz. We have implemented an area-efficient design which takes a small amount of resources on the FPGA and needs only 1480 slices. To the best of the authors' knowledge, the proposed modular inversion over F_256 provides a better performance than the available hardware implementations in terms of the area and the timing.