Energy-efficient implementations of GF (p) and GF(2m) elliptic curve cryptography

While public-key cryptography is essential for secure communications, the energy cost of even the most efficient algorithms based on Elliptic Curve Cryptography (ECC) is prohibitive on many ultra-low energy devices such as sensor-network nodes and identification tags. Although an abundance of hardware acceleration techniques for ECC have been proposed in literature, little research has focused on understanding the energy benefits of these techniques. Therefore, we evaluate the energy cost of ECC on several different hardware/software configurations across a range of security levels. Our work comprehensively explores implementations of both GF(p) and GF(2^m) ECC, demonstrating that GF(2^m) provides a 1.31 to 2.11 factor improvement in energy efficiency over GF(p) on an extended RISC processor. We also show that including a 4KB instruction cache in our system can reduce the energy cost of ECC by as much as 30%. Furthermore, our GF(2^m) coprocessor achieves a 2.8 to 3.61 factor improvement in energy efficiency compared to instruction set extensions and significantly outperforms prior work.