I have just finished skimming through “Elliptic Curve Cryptography for Constrained Devices – Algorithms, Architectures and Practical Implementation” by Sandeep S. Kumar.
The guy have done software design of ECDH key exchange on an 8-bit processor, hardware/software co-design on extensions for an 8-bit processor and 32-bit processor, hardware design for optimal digit multipliers for , hardware design for ECC in the frequency domain and hardware design for tiny ECC processor over !!!
He just did everything! The open problems he mentioned at the end of the book was those stuff related to optimizing power to be extremely efficient on constrained devices, thus to make it strong against the side channel attacks.