A flexible processor for the characteristic 3 η_T pairing

The ητ pairing is an efficient method for the calculation of the Tate pairing. In this paper, we describe the hardware implementation of the η_τ pairing on a supersingular elliptic curve of characteristic 3. All characteristic 3 operations required for the computation of the pairing are outlined in detail. We describe how the required extension field operations can be performed in terms of subfield operations, many of which can be computed in parallel in hardware. The hardware architectures required for pairing computation are also described. An efficient and reconfigurable processor utilising these hardware architectures is presented and discussed. The processor is highly reconfigurable and can easily be tailored for a low area implementation, or for a high throughput implementation or for a desired balance between the two. Results are provided for various configurations of the processor when implemented over the field F₃97 on an FPGA.