Hardware Architecture for Exponentiation Based on Square Root Extraction over GF(2m)

Square root extraction over GF(2
^m
) is introduced and a new hardware architecture for exponentiation over GF(2
^m
) based on the square root extraction is proposed. Compared with the classical square-and-multiply architecture, the proposed architecture is shown to calculate exponentiation with fewer cycles over GF(2
^m
) in most cases.