Large Field-Size Throughput/Area Accelerator for Elliptic-Curve Point Multiplication on FPGA

Abstract

This article presents a throughput/area accelerator for elliptic-curve point multiplication over GF(2571). To optimize the throughput, we proposed an efficient hardware accelerator architecture for a fully recursive Karatsuba multiplier to perform polynomial multiplications in one clock cycle. To minimize the hardware resources, we have utilized the proposed Karatsuba multiplier for modular square implementations. Moreover, the Itoh-Tsujii algorithm for modular inverse computation is operated using multiplier resources. These strategies permit us to reduce the hardware resources of our implemented accelerator over a large field size of 571 bits. A controller is implemented to provide control functionalities. Our throughput/area accelerator is implemented in Verilog HDL using the Vivado IDE tool. The results after the place-and-route are given on Xilinx Virtex-6 and Virtex-7 devices. The utilized slices on Virtex-6 and Virtex-7 devices are 6107 and 5683, respectively. For the same FPGA devices, our accelerator can operate at a maximum of 319 MHz and 361 MHz. The latency values for Virtex-6 and Virtex-7 devices are 28.73 μs and 25.38 μs. The comparison to the state-of-the-art shows that the proposed architecture outperforms in throughput/area values. Thus, our accelerator architecture is suitable for cryptographic applications that demand a throughput and area simultaneously.