A Super-Serial Galois Fields Multiplier for FPGAs and its Application to Public-Key Algorithms

This contribution introduces a scalable multiplier architecture for Galois field GF(2 k) amenable for field programmable gate arrays (FPGAs) implementations. This architecture is well suited for the implementation of public-key cryptosystems which require pro-grammable multipliers in large Galois fields. The architecture trades a reduction in resources with an increase in the number of clock cycles. This architecture is also fine grain scalable in both the time and the area (or logic) dimensions thus facilitating implementations that maximize their use of finite FPGA resources while achieving fast computational speed. This leads to an architecture that requires less resources than traditional bit serial multipliers, which we demonstrated with implementations of multipliers in the field GF(2 167). Our results demonstrate that for this field one can realize super-serial multipliers that use 2.76 times fewer function generators and 6.84 times fewer flip-flops than their serial multiplier counterparts. We also extrapolated the performance of these multipliers in an elliptic curve cryptosystem.