A fast and secure image encryption algorithm using number theoretic transforms and discrete logarithms

Many of the Internet applications such as video conferencing, military image databases, personal online photograph albums and cable television require a fast and efficient way of encrypting images for storage and transmission. In this paper, discrete logarithms are used for generation of random keys and Number Theoretic Transform (NTT) is used as a transformation technique prior to encryption. The implementation of NTT is simple as it uses arithmetic for real sequences. Encryption and decryption involves the simple and reversible XOR operation of image pixels with the random keys based on discrete logarithms generated independently at the transmitter and receiver. Experimental results with the standard bench mark test images proposed in the USC-SIPI data base confirm the enhanced key sensitivity and strong resistivity of the algorithm against brute force attack and statistical crypt analysis. The computational complexity of the algorithm in terms of number of operations and number of rounds is very small in comparison with the other image encryption algorithms. The randomness of the keys generated has been tested and is found in accordance with the statistical test suite for security requirements of cryptographic modules as recommended by National Institute of Standards and Technology (NIST).