Low-complexity design of bit-parallel dual-basis multiplier over GF(2m)

Recently, information security is heavily dependent on cryptosystems such as Rivest-Shamir-Adleman algorithm (RSA algorithm) and elliptic curve cryptosystem (ECC). RSA can provide higher security level than ECC, but it is not suitable for the resource-constrained devices such as smart phones or embedded system. Thus, ECC is attracted on application in resource-constrained devices because it can achieve the same security level, but uses less key length than RSA. Galois or finite field multiplication is the core arithmetic operation of ECC. There are three popular bases in the finite field over GF(2m), polynomial basis, normal basis and dual basis (DB). Each basis representation has its own advantages. In this study, the authors will introduce a low-complexity bit-parallel DB multiplier using the multiplexer approach. Compared with the related work, our design saves up to 60% of space complexity.