Efficient Subquadratic Space Complexity Digit-Serial Multipliers over GF(2m) based on Bivariate Polynomial Basis Representation

Digit-serial finite field multipliers over GF($2^{m}$) with subquadratic space complexity are critical components to many applications such as elliptic curve cryptography. In this paper, we propose a pair of novel digit-serial multipliers based on bivariate polynomial basis (BPB). Firstly, we have proposed a novel digit-serial BPB multiplication algorithm based on a new decomposition strategy. Secondly, the proposed algorithm is properly mapped into a pair of pipelined and non-pipelined digit-serial multipliers. Lastly, through the detailed complexity analysis and comparison, the proposed designs are found to have less area-time complexities than the competing ones.