Hardware implementation and performance comparison of normal basis multiplication methods over GF (2m)

Abstract

Elliptic curve cryptography (ECC) and error control coding techniques over binary extension fields require efficient computation of finite field multiplication. Polynomial basis and normal basis are widely used in binary fields. Since inversion can be computed by performing repeated multiplication and squaring can be computed by performing only one cyclic shift operation using normal basis, it is considered as more efficient than polynomial basis. This research paper presents hardware implementation and performance comparison of various normal basis multiplication methods in terms of space and time complexities.