Design of Variable Arithmetic Operation Systems for Computing Multiplications and Mulitplicative Inverses in $GF(2^m)$)

$GF(2^m)$ 상의 승법과 승법력 계산을 위한 가변형 산술 연산 시스템의 설계

This paper presents a constructing theory of variable arithmetic operation systems for computing multiplications and multiplicative inverse in GF(2**m) based on a modulo operation of degree on elements in Galois fields. The proposed multiplier is composed of a zero element control part, input element conversion part, inversion circuit, and output element conversion part. These systems can reduce reasonable circuit areas due to the common use of input/output element converison parts, and the PLA and module structure provice a variable property capable of convertible uses as arithmetic operation systems over different finite fields. This type of designs gives simple, regular, expandable, and concurrent properties suitable for VLSI implementation. Expecially, the multiplicative inverse circuit proposed here is expected to offer a characteristics of the high operation speed than conventional method.