FPGA Implementation of Elliptic Curve Point Multiplication for a 256-bit Processor on NIST Prime Field

Elliptic curve cryptography (ECC) has long been a prevailing technique among security researchers for developing security architectures of digital devices to their hardware levels. With the proliferation of advanced technological ecosystems, the necessity for secured information transfer has become even more pronounced. Elliptical Curve Cryptography can substantially outperform other cryptographic schemes in addressing the security concerns of such intricate digital hardware environments. An influential and inalienable part of the ECC architecture is the Group Operation part. In this work, an area & time-efficient Point Doubling and Point Addition architectures have been implemented by combining modular arithmetic units for Elliptic Curve Group Operation. Koblitz curve in Jacobian coordinates have been used to reduce the cost of group operation. Two architectures have also been proposed to compute point doubling & point addition using equations for the Koblitz Curve for 256-bits. For minimizing area and reducing time spent for computing, we have used an interleaved modular multiplier in this work. An area & time-efficient Elliptic Curve Point Multiplication (ECPM) module have been designed. The designed ECPM module for 256 bits has been observed to require 0.53 ms for execution, which is a significant improvement compared to other contemporary studies.