Fast Optimal Normal Basis Multiplier with Type-2kw Over GF (2m)

Finite field multiplication over GF (2^m) is an very important arithmetic operation in elliptic curve cryptosystem (ECC). ECC is an attractive cryptosystem for portable devices such as smart phones. Thus, designs of finite field multiplication with low time complexity or low hardware cost become important research issues in recent years. This study will present a fast optimal normal basis multiplier with Type-2^kw over GF (2^m). As compared to other existing similar multipliers, our proposed multiplier will save about 18.6% time complexity on average for NIST suggested m values.