The Unified Image Encryption Algorithm based on Discrete Logarithm and Chaos

Image cryptography is an indispensable component of symmetric cryptography, aiming to provide high-strength information security for images and big data. This research proposes a unified image cryptography algorithm based on discrete logarithm, which is typical private-key cryptography with identical encryption and decryption processes. The proposed cryptographic algorithm mainly consists of two diffusion modules based on additive modulo operations and two diffusion modules based on discrete logarithm, and the latter are integer exponential and logarithmic operations on the Galois field GF(257) conducted by the lookup-table method. The image cryptosystem has a secret key of length 300 bits. For the cipher images, the values of the histogram are less than 293.15, the <i>t-</i>values of correlation are less than 2.1315, and the values of information entropy are greater than 7.9920, which confirms that the cipher images hold good pseudo-randomness. The system sensitivity analysis results show the image cryptosystem possesses excellent key, plain-image and cipher-image sensitivities with the relative errors of each test index less than 0.1%. The proposed image encryption system can be applied to the internet and cloud end to protect images and big data with sensitive information.