Programmable cellular automata based Montgomery hardware architecture

This study presents efficient hardware architectures for Montgomery multiplication and squaring based on programmable cellular automata (PCA). Multiplication and squaring are the key operation in implementing circuits for various applications of error control coding such as Reed-Solomon code. Thus we employ Montgomery multiplication and squaring algorithms and construct simple hardware architectures based on PCA in GF(2m). Our architectures are highly optimized and have low-complexity based on irreducible all one polynomial (AOP).