Subquadratic space complexity Gaussian normal basis multipliers over GF(2m) based on Dickson–Karatsuba decomposition

Gaussian normal basis (GNB) of the even-type is popularly used in elliptic curve cryptosystems. Efficient GNB multipliers could be realised by Toeplitz matrix-vector decomposition to realise subquadratic space complexity architectures. In this study, Dickson polynomial representation is proposed as an alternative way to represent an GNB of characteristic two. The authors have derived a novel recursive Dickson-Karatsuba decomposition to achieve a subquadratic space-complexity parallel GNB multiplier. By theoretical analysis, it is shown that the proposed subquadratic multiplier saves about 50% bit-multiplications compared with the corresponding subquadratic GNB multiplication using Toeplitz matrix-vector product approach.