本篇論文探討如何加速模指數運算之效能。針對行動通訊裝置如智慧型手機、平板電腦與智慧卡連結網際網路、3G/4G行動通訊、車載通訊與無線通訊系統的需求日益增加，安全通訊上的需求益日顯重要。這些行動通訊裝置需要安全的通訊環境以確保互相交換之訊息可維持機密性並只有經認證的相關人等可存取該些裝置。這樣的安全通訊環境可透過現代密碼函數來建立，而這些函數皆植基於所謂模指數運算上。模指數運算是由模乘法所構成，模乘法又是建立於模數運算與大整數乘法上。本篇論文提出一些策略可用來加速模指數運算效能，包含加速蒙哥瑪利模運算(Montgomery Reduction)、決定最佳切割方法與臨界值可用來加速大整數乘法與模運算。同時，本篇論文亦致力於減少記憶體存取次數可讓大整數乘法更有效率。本篇論文所提之策略均旨於加速模指數運算效能，使現代密碼通訊協定可運用於行動通訊裝置上。 This thesis investigates how to accelerate the performance of modular exponen-tiation. As the requirement for secure communication over the Internet, 3G/4G cel-lular systems, vehicular communication networks and wireless sensor networks is growing, connecting small, mobile devices such as smart phones, tablet PCs, and smart cards to these networks is also a growing trend. Many of these devices require secure connections to ensure that the exchanged information remains confidential and that only authorized persons can access the devices. Such secure communication is established on many modern cryptographic functions, based on the framework of modular exponentiation. Modular exponentiation is composed of modular multipli-cation, which is made of modular reduction, large integer multiplication. In order to speed up modular exponentiation, this thesis proposes some strategies, including speeding up Montgomery reduction, determining the optimal split method and the threshold value so as to speed up the large integer multiplication, and modular reduction. Furthermore, this thesis ponders on reducing the times of memory accesses so as to make the large integer multiplication even more efficient. The goal of all strategies proposed is intended to accelerate the performance of modular exponentiation as far as possible, and make it possible to implement modern cryptographic protocols on mobile devices.
