#TITLE_ALTERNATIVE# - Sasongko NIM. 23298017, Arif
Abstract: Elliptic Curves Cryptosystem is public key cryptosvstem+ which uses elliptic curve group. The elliptic curve is usually defined over finite field. There are several alternatives of field and their representation that can be used. Between these alternatives, F2n with subfield extension representation could be an interesting alternative. As the subfield and its extension we chose optimal normal basis. To constrict this elliptic curve group we need multiplication, addition and inversion in the field Multiplication is the most expensive operation. There are two alternatives to construct this operation in optimal normal basis. These two are Massey-Omura multiplier and Agnew et a! multiplier. Both alternatives need n clocks, which n is the lenght of Ike key. Inversion need more clock than multiplication since. it construct by performing several multiplication and squaring. So it evil/ be worth if we can perform multiplication faster. In this thesis, I try to implement field operation in F211x14 as extension field of subfield F211. This scheme gives us faster operation for multiplication and inversion. We conclude that subfield extension can become advantageous alternative in the trade of benveen speed and area.