Hardware Implementation and Study of Inverse Algorithm in Finite Fields

Inverse calculation in finite fields is the base to implement Hyperelliptic Curve Cryptography (HECC) and HECC implementation is the key to fast implement calculating inverse in finite fields. In this paper, fast algorithm of calculating inverse in finite fields and its method to implement with hardware in HECC are discussed, the EEA algorithm and the MIMA algorithm, which are currently in common use, are compared and an improved MIMA algorithm is brought forward. In the algorithm, 2 bits parallel scheme is used and shift register only takes into account of two situations including 2 bits shift and 1 bit shift. The simplest (two situations) barrel shifter can be designed when realizing this algorithm with FPGA and each of shifts is completed in one cycle. Algorithm description carries out function simulation and timing simulation in QuartusII environment, which is improved in both speed and area compared with past algorithms.