Enhancement of encryption techniques using elliptic curve cryptography

Abstract

Encryption and decryption processes consume more time for mathematical calculations. The main goal of this research work is to improve ElGamal, Menezes-Vanstone, and Hill Cipher encryption techniques by using Elliptic Curve Cryptography to speed up the calculations in MEGECC and MMVECC, and increase the security level and key efficiency in ECCHC. In the modified MEGECC, using hexadecimal ASCII code instead of decimal ASCII code reduced the number of doubling and adding operations in the scalar multiplications and sped up the mathematical computations. Only addition and subtraction operations are used in the proposed MMVECC, and no inversion or multiplication operations are used because it consumes a longer time compared to addition and subtraction, besides using hexadecimal ASCII code to speed up calculations. The third modification in this research work is applied on the original Hill Cipher algorithm, it has a simple structure and fast computations, but weak security. A new hybrid encryption approach between Elliptic Curve Cryptosystem and original Hill Cipher has been proposed to convert Hill Cipher from symmetric technique to asymmetric one and increase its security effectiveness. Self-invertible key matrix is used to generate encryption and decryption secret key. The ability to encrypt every character in the 128 ASCII table by using its decimal ASCII value directly without a mapping table is another contribution in ECCHC approach. All the three modifications in this thesis are applied on text messages of different sizes and different grayscale images of size 256256. For text messages, the number of addition and doubling operations and also the encryption/decryption time needed in the proposed techniques are calculated and compared with other techniques.