Development of a GF(2)Math Coprocessor

Abstract

The mathematics of Galois fields GF(2) and the extension fields GF(2m) 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.