$GF(2^m)$ 상의 산술연산기시스템 구성 이론

A Construction Theory of Arithmetic Operation Unit Systems over $GF(2^m)$

This paper presents a method of constructing an Arithmetic Operation Unit Systems (A.O.U.S.) over Galois Field GF(2**m) for the purpose of the four arithmetical operation(addition, subtraction, multiplication and division between two elements in GF(2**mm). The proposed A.O.U.S. is constructed by following procedure. First of all, we obtained each four arithmetical operation algorithms for performing the four arithmetical operations using by mathematical properties over GF(2**m). Next, for the purpose of realizing the four arithmetical unit module (adder module, subtracter module, multiplier module and divider module), we constructed basic cells using the four arithmetical operation algorithms. Then, we realized the four Arithmetical Operation Unit Modules(A.O.U.M.) using basic cells and we constructd distributor modules for the purpose of merging A.O.U.M. with distributor modules. Finally, we constructed the A.O.U.S. over GF(2**m) by synthesizing A.O.U.M. with distributor modules. We prospect that we are able to construct an Arithmetic & Logical Operation Unit Systems (A.L.O.U.S.) if we will merge the proposed A.O.U.S. in this paper with Logical Operation Unit Systems (L.O.U.S.).