Novel Area-Efficient and Flexible Architectures for Optimal Ate Pairing on FPGA

TL;DR

This paper presents three innovative FPGA-based architectures for optimal Ate pairing on Barreto-Naehrig curves, focusing on security, resource efficiency, and speed, suitable for constrained environments like the Genesys board.

Contribution

It introduces three novel FPGA implementations combining software, hardware, and parallelism to optimize optimal Ate pairing computations on Barreto-Naehrig curves.

Findings

Achieved 128-bit security on Genesys FPGA board.

Enhanced pairing computation speed through parallel processing.

Optimized resource utilization with advanced mathematical methods.

Abstract

While FPGA is a suitable platform for implementing cryptographic algorithms, there are several challenges associated with implementing Optimal Ate pairing on FPGA, such as security, limited computing resources, and high power consumption. To overcome these issues, this study introduces three approaches that can execute the optimal Ate pairing on Barreto-Naehrig curves using Jacobean coordinates with the goal of reaching 128-bit security on the Genesys board. The first approach is a pure software implementation utilizing the MicroBlaze processor. The second involves a combination of software and hardware, with key operations in $F_{p}$ and $F_{p^{2}}$ being transformed into IP cores for the MicroBlaze. The third approach builds on the second by incorporating parallelism to improve the pairing process. The utilization of multiple MicroBlaze processors within a single system offers both versatility and parallelism to speed up pairing calculations. A variety of methods and parameters are used to optimize the pairing computation, including Montgomery modular multiplication, the Karatsuba method, Jacobean coordinates, the Complex squaring method, sparse multiplication, squaring in $G_{\phi 6}F_{p^{12}}$, and the addition chain method. The proposed systems are designed to efficiently utilize limited resources in restricted environments, while still completing tasks in a timely manner.