Low space-complexity digit-serial dual basis systolic multiplier over Galois field GF(2m) using Hankel matrix and Karatsuba algorithm

Multiplication is one important finite field arithmetic operation in cryptographic computations. Dual basis multipliers over Galois field GF(2^m) have been widely applied in this kind of computations because of its advantage of small chip area. Nevertheless, up to date, there are only few methods that can keep balance of low space complexity and low time complexity at the same time. In order to achieve such an efficient aim, this study presents a novel digit-serial dual basis multiplier that is different from existing ones with a modified cut-set method using Karatsuba algorithm as well as Hankel matrix. As a result, the proposed multiplier can save much space and thus be particularly suitable for some hand held devices equipped with only limited resources. The proposed digit-serial dual basis multiplier saves 55% space complexity as compared with existing similar studies with National Institute of Standards and Technology (NIST) suggested values for elliptic curve cryptosystem.