Two hardware implementations of the group operations necessary for implementing an elliptic curve cryptosystem over a characteristic two finite field

Two FPGA (field-programmable gate array) implementations of the elliptic curve scalar multiplication operation are presented. The main design objective influencing all implementation decisions was complete scalability. Scalability refers to being able to change both the field size and the elliptic curve parameters without reprogramming the hardware. Measures were taken during the design process to ensure near-optimal performance for the set of algorithms used despite the scalable nature of the hardware. A new field multiplication algorithm is used in one of the implementations, improving performance by approximately 50%.