A Plain-Image-Related Chaotic Image Encryption Algorithm Based on DNA Sequence Operation and Discrete Logarithm

According to the research works of the literatures on chaotic cryptanalysis, many recent chaotic image encryption algorithms cannot resist chosen-plaintext attack. Although some chaotic image encryption algorithms introduce plain-image information, they still violate some design requirements of modern cryptosystems. Therefore, after analyzing many literatures related to chaotic image encryption, we propose a plain-image-related chaotic image encryption algorithm based on the deoxyribonucleic acid (DNA) sequence operation and discrete logarithm. As we know, the discrete logarithm calculation is a complex non-linear calculation, introducing it can increase the complexity of the encryption process. More importantly, discrete logarithm values are significantly different under different generators, and the multiplicative group adopted in the proposed algorithm has as many as 128 generators. Therefore, by using two generators determined by the secret key and the hash value of the plain-image respectively, we not only expand the key space, but also greatly improve the plain-image sensitivity and plain-image relevancy of the encryption process. In addition, the proposed algorithm improves the way of using the hash value of the plain-image. In this way, once the secret key is selected, chaotic sequences can be generated in advance and reused to improve the encryption efficiency. Similarly, the proposed algorithm also introduces the DNA sequence operation with high parallelism to further improves the encryption efficiency. Simulation tests and comparative analyses show that the proposed algorithm can not only resist common attacks, but also outperform some recent chaotic image encryption algorithms in many aspects.