Scalable Gaussian Normal Basis Multipliers over GF(2~m) Using Hankel Matrix-Vector Representation

摘要

This work presents a novel scalable multiplication algorithm for a type-t Gaussian normal basis (GNB) of GF(2~m). Utilizing the basic characteristics of MSD-first and LSD-first schemes with d-bit digit size, the GNB multiplication can be decomposed into n(n+1) Hankel matrix-vector multiplications. where n=[mt+1)/d]. The proposed scalable architectures for computing GNB multiplication comprise of one d×d Hankel multiplier, four registers and one final reduction polynomial circuit. Using the relationship of the basis conversion from the GNB to the normal basis, we also present the modified scalable multiplier which requires only nk Hankel multiplications, where k=[mt/2d] if m is even or k=[(mt-t+2)/2d] if m is odd. The developed scalable multipliers have the feature of scalability. It is shown that, as the selected digit size d≥8, the proposed scalable architectures have significantly lower time-area complexity than existing digit-serial multipliers. Moreover, the proposed architectures have the features of regularity, modularity, and local interconnection ability. Accordingly, they are well suited for VLSI implementation.