Cryptographic algorithms are computationally costly and the challenge is more if we need to execute them in resource constrained embedded systems. Field Programmable Gate Arrays (FPGAs) having programmable logic de- vices and processing cores, have proven to be highly feasible implementation platforms for embedded systems providing lesser design time and reconfig- urability. Design parameters like throughput, resource utilization and power requirements are the key issues. The popular Elliptic Curve Cryptography (ECC), which is superior over other public-key crypto-systems like RSA in many ways, such as providing greater security for a smaller key size, is cho- sen in this work and the possibilities of its implementation in FPGA based embedded systems for both single and dual processor core architectures in- volving task parallelization have been explored. This exploration, which is first of its kind considering the other existing works, is a needed activity for evaluating the best possible architectural environment for ECC implementa- tion on FPGA (Virtex4 XC4VFX12, FF668, -10) based embedded platform.