Public key cryptography (PKC) is the basic building block for the cryptography applications such as encryption, key distribution, and digital signature scheme. Among many PKC, elliptic curve cryptography (ECC) is the most widely used in IT systems. Recently, very efficient Montgomery-Twisted-Edward (MoTE)-ECC was suggested, which supports low complexity for the finite field arithmetic, group operation, and scalar multiplication. However, we cannot directly adopt the MoTE-ECC to new PKC systems since the cryptography is not fully evaluated in terms of performance on the Internet of Things (IoT) platforms, which only supports very limited computation power, energy, and storage. In this paper, we fully evaluate the MoTE-ECC implementations on the representative IoT devices (16-bit MSP processors). The implementation is highly optimized for the target platform and compared in three different factors (ROM, RAM, and execution time). The work provides good reference results for a gradual transition from legacy ECC to MoTE-ECC on emerging IoT platforms.