On the efficient implementation of RSA

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Tezin Türü: Yüksek Lisans

Tezin Yürütüldüğü Kurum: Orta Doğu Teknik Üniversitesi, Uygulamalı Matematik Enstitüsü, Kriptografi Anabilim Dalı, Türkiye

Tezin Onay Tarihi: 2015

Öğrenci: HATİCE KÜBRA GÜNER

Danışman: MURAT CENK

Özet:

Modular exponentiation is an essential operation for many asymmetric key cryptosystems such as RSA in which encryption and decryption are based on modular exponentiation. Therefore, efficiency of the system is effected with running time of the modular exponentiation algorithm. At the same time, key sizes also influence the efficiency of the algorithm. Over the years key sizes had to be increased to provide security. To make RSA practical, one of usable choices is acceleration of the modular exponentiation algorithm. There are many methods for fast modular exponentiation, but all of them are not suitable for RSA. To find the most suitable one, we need to examine running time of the algorithms. In this thesis, we have studied some of the proposed fast modular exponentiation methods. They were implemented with using MPIR library and their running time results were compared with the repeated squaring and multiplication algorithm. Moreover, some efficient methods were recommended for RSA. In these methods, at least 23% improvement was obtained for each key sizes on decryption.