Edinburgh Napier University

  This thesis presents methods that can be used to improve the operation of the RSA encryption method. It shows the principles of encryption, and then expands this to give the operation of public-key methods, which includes the number value theorems applied onto RSA system, Modular Multiplication and Modular Exponentiation, and the basic
theory and content of RSA system.
The thesis then presents four methods which can be used to improve the encryption/decryption process. In this, Single Precision Multiplication and Listing Method are used to speed up the modular calculation in the modular multiplication, the
M-ary Sliding window is used to speed up exponentiation multiplication, and Chinese Remainder Theory (CRT) is used to speed up decryption. Single Precision Multiplication is a method of multiplying and modulating to speed up modular multiplication, which after evaluation can increase about operations by four to five times in speed. The Listing Method pre-stores values from earlier calculations which saves in the relocation of figures and calculation time. The M-ary method can be used to complete the exponentiation multiplication. Results show that an exponent of 1024 bits can give the calculation efficiency up to 24%. The Chinese Remainder Theorem is used to give an improvement of the decryption speed up by up to four times.