Feedback image encryption algorithm with compound chaotic stream cipher based on perturbation

In this paper, two new one-dimensional chaotic functions are designed using Devaney chaotic definition. And a dynamically shifting compound chaotic function is constructed based on the two new one-dimensional chaotic functions. The properties of compound chaotic functions are also proved. A new feedback image encryption algorithm is designed using the new compound chaos and an image pixel permutation, 3D baker scheme is described in detail. In the scheme, a new dynamic block dividing the 3D baker is put forward using the compound chaotic map, and the key space expands. In order to produce avalanche effect and sensitivity of cipher to plaintext, the round times are designed to control the cycle. The entropy analysis, difference analysis, weak-key analysis, statistical analysis, cipher random analysis, and cipher sensibility analysis depending on key and plaintext are introduced to test the security of the new scheme of image encryption. The tests show that the image encryption method passes the random tests of NIST FIPS 140-2(2001) and SP 800-22 standards. This paper also solves the problem of short periods and low precision of one-dimensional chaotic function by perturbation.