Fully paramaterisable Galois Field arithmetic processor over GF(3m) suitable for elliptic curve cryptography

In this paper we present an architecture for a flexible GF(3^m) multiplicative arithmetic processor. The ABC processor performs computations of the form R = (AB/C) mod F in 27n clock cycles, where A,B,C and F are polynomials over GF(3). The same hardware can be used for different field sizes offering full paramaterisability up to a maximum field size. We present prototype implementation results on FPGA for a field size of GF(3²⁵⁵). The processor is suitable for cryptographic applications where variable levels of security are required.