Double-feedback image encryption based on chaotic dynamic grouping of FRFT

In fractional Fourier transform (FRFT) image encryption algorithm, according to the problem that one plain-text is correlated with one cipher-text encrypted, which can not resist chosen plaintext and chosen cipher-text attack, double-feedback image encryption method based on chaotic dynamic grouping oriented FRFT was proposed. Two chaotic systems were adopted in this method. Firstly, cipher-text feedback was introduced to drive the two systems. And the systems driven by feedback were utilized to encrypt: the keys of system 1 were utilized to realize the dynamic grouping on plain which was later utilized to realize the FRFT, and the first cipher-text was obtained. Then the keys of system 2 were utilized to realize the chaotic encryption on first cipher-text and obtain the second cipher-text. Analysis on Lyapunov index indicated that when feedback coefficient was less than 0.4, the Lyapunov index was more than zero, in which case the system was in chaotic state so that it could resist chosen plaintext attack and chosen cipher-text attack. Compared with the encryption method without feedback, the number of pixels change rate (NPCR) and unified average changing intensity (UACI) of encryption with feedback was improved by 0.5% and 1.49%, respectively. The results prove that the encryption with feedback can better resist differential attack, chosen plaintext attack and chosen cipher-text attack. Finally, the safety condition of system is pointed out that the feedback coefficient is less than 0.4, which provides a new method for evaluating the safety of the feedback system.