Security support for small and smart devices is one of the most important issues in the Future Internet of things, since technologies such as 6LoWPAN are opening the access to the real world through Internet. 6LoWPAN devices are highly constrained in terms of computational capabilities, memory, communication bandwidth, and battery power. Therefore, in order to support security, it is necessary to implement new optimized and scalable cryptographic mechanisms, which provide security, authentication, privacy and integrity to the communications. Our research is focused on the mathematical optimization of cryptographic primitives for Public Key Cryptography (PKC) based on Elliptic Curve Cryptography (ECC) for 6LoWPAN. Specifically, the contribution presented is a set of mathematical optimizations and its implementation for ECC in the 6LoWPAN devices based on the microprocessor Texas Instrument MSP430. The optimizations presented are focused on Montgomery multiplication operation, which has been implemented with bit shifting, and the definition of special pseudo-Mersenne primes, which we have denominated ”shifting primes”. These optimizations allow to implement the scalar multiplication (operation used for ECC operations) reaching a time of 1,2665 seconds, which is 42,8% lower of the reached by the state of the art solution TinyECC (2,217 seconds).