Shifting primes have proved its efficiency in CPUs without hardware multiplier such as the located at the MSP430 from Texas Instruments. This work analyzes and presents the advantages of the shifting primes for CPUs with hardware multiplier such as the JN5139 from NXP/Jennic based on an OpenRISC architecture. This analysis is motivated because Internet of Things is presenting several solutions and use cases where the integrated sensors and actuators are sometimes enabled with higher capabilities. This work has concluded that shifting primes are offering advantages with respect to other kind of primes for both with and without hardware multiplier. Thereby, offering a suitable cryptography primitives based on Elliptic Curve Cryptography (ECC) for the different families of chips used in the Internet of Things solutions. Specifically, this presents the guidelines to optimize the implementation of ECC when it is presented a limited number of registers.