Gaussian normal basis multiplier over GF(2 m ) using hybrid subquadratic-and-quadratic TMVP approach for elliptic curve cryptography

In recent years, subquadratric-and-quadratric Toeplitz matrix–vector product (TMVP) computations are widely used for the implementation of binary field multiplication in elliptic curve cryptography. Pure subquadratric TMVP structure involves significantly less space complexity and long computational delay, while quadratric TMVP structure involves larger space complexity and less computation delay. To optimise the tradeoff between time and space complexities, this study presents a novel hybrid multiplier for Gaussian normal basis (GNB) in GF(2 m ) which combines subquadratic and quadratic structures. From the theoretical analysis, it is shown that the proposed hybrid multiplier can save ∼18% space complexity and 12% time complexity than the existing GNB multiplier with pure TMVP decomposition.