An Elliptic Curve Crypto-Processor (ECCP) is a favorite public-key cryptosystem due to its small key size and its high security arithmetic unit. It is applied in constrained devices which often run on batteries and have limited processing, storage capabilities and low power. This research work presents an effective ECCP architecture for security in IoT and embedded devices. A finite field polynomial multiplier takes the most implementation effort of an ECCP because it is the most consuming operation for time and area. So, the objective is to implement the main operation of Point Multiplication (PM) 𝑄=𝑘𝑃 using FPGA. The aim is to obtain the optimal registers number for an area optimization of ECCP architecture. Moreover, it proposes a time optimization of ECCP based on the liveness analysis and exploiting forward paths. Also, a comparison between sequential and parallel hardware design of PM based on Montgomery ladder algorithm is provided.
The developed ECCP design is implemented over Galois Fields GF (2163) and GF (2409) on Xilinx Integrated Synthesizes Environment (ISE) Virtex 6 FPGA. In case of GF (2163), this work achieved an area saving that uses 2083 Flip Flops (FFs), 40876 Lookup Tables (LUTs) and 19824 occupied slices. The execution time is 1.963 s runs at a frequency of 369.529 MHz and consumes 5237.00 mW. In case of GF (2409), this work achieved an area saving that uses 8129 Flip Flops (FFs), 42300 Lookup Tables (LUTs) and 18807 occupied slices. The execution time is 29 s runs at a frequency of 253.770 MHz and consumes 2 W. The obtained results are highly comparable with other state-of-the-art crypto-processor designs. The developed ECCP is applied as a case study of a cryptography protocol in ATMs.