A High-Performance Reconfigurable Elliptic Curve Processor for GF (2)

This work proposes a processor architecture for elliptic curves cryptosystems over fields GF (2). This is a scalable architecture in terms of area and speed that exploits the abilities of reconfigurable hardware to deliver optimized circuitry for different elliptic curves and finite fields. The main features of this architecture are the use of an optimized bitparallel squarer, a digit-serial multiplier, and two programmable processors. Through reconfiguration, the squarer and the multiplier architectures can be optimized for any field order or field polynomial. The multiplier performance can also be scaled according to system’s needs. Our results show that implementations of this architecture executing the projective coordinates version of the Montgomery scalar multiplication algorithm can compute elliptic curve scalar multiplications with arbitrary points in 0.21 msec in the field GF (2). A result that is at least 19 times faster than documented hardware implementations and at least 37 times faster than documented software implementations.