Studying Software Implementations of Elliptic Curve Cryptography

Elliptic Curve Cryptography (ECC) provides a similar level of security to conventional integer-based public-key algorithms, but with much shorter keys. ECC over binary field is of special interest because the operations in binary field are thought more space and time efficient. However, the software implementations of ECC over binary field are still slow, especially on low-end processors that are used in small computing devices such as sensor nodes. In this paper, we study the software implementations of ECC on processors with different word sizes. With a set of algorithms that we identified, we can perform 163-bit ECC in 13.9 seconds on an 8-bit processor at a clock rate of 8 MHz.