FPGA implementation of extended reconfigurable Binary Edwards Curve based processor

Elliptic Curve Cryptosystem (ECC) is the next generation public key ciphers for securing communications. However, due to its inherent complex mathematical nature, it poses challenges to designers. In this paper, we present a Field Programmable Gate Array (FPGA) design of scalar multiplication on Binary Edwards Curve (BEC) for state of the art field of GF(2²³³). The work contributes to develop shared data and control paths for the processor, to support two important curve operations, namely point halving and doubling based scalar multiplication. Such a unified design has the advantage of reduction in hardware and yet supporting both these important operations. To the best of our knowledge, this is the first reported design of a BEC based processor which supports both point halving and doubling. Detailed experimental results are provided to show that with minimal overhead the design can perform both point doubling and halving based scalar multiplications.