Abstract: Polynomial bases and normal bases are both used for
elliptic curve cryptosystems, but field arithmetic operations such as
multiplication, inversion and doubling for each basis are implemented
by different methods. In general, it is said that normal bases, especially
optimal normal bases (ONB) which are special cases on normal bases,
are efficient for the implementation in hardware in comparison with
polynomial bases. However there seems to be more examined by
implementing and analyzing these systems under similar condition. In
this paper, we designed field arithmetic operators for each basis over
GF(2233), which field has a polynomial basis recommended by SEC2
and a type-II ONB both, and analyzed these implementation results.
And, in addition, we predicted the efficiency of two elliptic curve
cryptosystems using these field arithmetic operators.