Fast and Generic Inversion Architectures 

Finite field inversion is the most computationally intensive field operation in public-key cryptographic algorithms such as elliptic curve cryptography. In this paper, we propose two inversion acceleration techniques for Itoh-Tsujii algorithm (ITA) over binary extended field. First, we reformulate the ternary ITA algorithm to generalize the primitive one, so that a universal algorithm procedure for all fields is achieved.

Next, we devise a parallel ITA algorithm to advance the parallelism of ITA. These two techniques are implemented on FPGA platform and it is experimentally shown that a fast ternary ITA inverter supporting all NIST fields can be obtained, with 22.9% timing improvement on average compared to ITA inverter. In addition, the parallel- ITA inverter is a more balancing design that achieves averagely 25.7% of timing decrease compared to ITA inverter while maintaining 31.3% reduction of area-time product compared to ternary-ITA inverter.