Development of a GF(2) Math Coprocessor

The mathematics of Galois fields GF(2) and the extension fields GF(2^m) underpin applications in error control coding and cryptology yet these binary operations are not directly supported in most digital computer instruction sets. A set of hardware blocks to perform low level GF(2) operations as a math coprocessor is described. The circuits were elaborated in VHDL and integrated into an FPGA-based soft processor (Nios II). Performance tests and detailed timing measurements are reported for typical GF(2) calculations.