Subquadratic space complexity digit-serial multiplier over binary extension fields using Toom-Cook algorithm

In this paper, we present a new (4,2)-way Toom-Cook algorithm using finite field interpolation. The proposed algorithm uses multi-evaluation scheme to construct a digit-serial multiplier over GF(2^m) which involves subquadratic space-complexity. From theoretical analysis, it is found that the proposed architecture has O(m^{log4 5}) space complexity and O(m^{log4 2}) latency, which is significantly less than traditional digit-serial multipliers.