A Improved Logistic Chaotic Map and Its Application to Image Encryption and Hiding

In view of the limited mapping range of the original Logistic map, the small range of chaotic parameters, and the uneven distribution, a new improved Logistic chaotic map is proposed. The mapping has two parameters mu and, alpha, and two initial values of x(n-1)and x(n). The parameter and initial value selection range can be extended to any real number. The chaotic mapping is full mapping, and the mapping range can be adjusted arbitrarily. This mapping is applied to image encryption, and the algorithm uses pixel value Exclusive OR(XOR) encryption and pixel position is scrambled. Afterwards, the ciphertext data is hidden in the image that has nothing to do with the ciphertext. A series of analysis is done on the ciphertext image, including the correlation between adjacent pixels of the image, histogram analysis and key sensitivity test. The analysis result shows that the proposed encryption algorithm has good security and encryption effect.