On the Security of a Class of Diffusion Mechanisms for Image Encryption

• Published in: IEEE transactions on cybernetics Vol. 48; no. 4; pp. 1163 - 1175
• Main Authors: Zhang, Leo Yu, Liu, Yuansheng, Pareschi, Fabio, Zhang, Yushu, Wong, Kwok-Wo, Rovatti, Riccardo, Setti, Gianluca
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.04.2018; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Ciphers; Complexity; Computer systems; Cryptanalysis; Cryptography; diffusion; Diffusion rate; Digital imaging; Encryption; High-speed optical techniques; image encryption; Multimedia communication; plaintext attack; Security; Streaming media
• ISSN: 2168-2267; 2168-2275; 2168-2275
• DOI: 10.1109/TCYB.2017.2682561

The need for fast and strong image cryptosystems motivates researchers to develop new techniques to apply traditional cryptographic primitives in order to exploit the intrinsic features of digital images. One of the most popular and mature technique is the use of complex dynamic phenomena, including chaotic orbits and quantum walks, to generate the required key stream. In this paper, under the assumption of plaintext attacks we investigate the security of a classic diffusion mechanism (and of its variants) used as the core cryptographic primitive in some image cryptosystems based on the aforementioned complex dynamic phenomena. We have theoretically found that regardless of the key schedule process, the data complexity for recovering each element of the equivalent secret key from these diffusion mechanisms is only <inline-formula> <tex-math notation="LaTeX">{O} </tex-math></inline-formula>(1). The proposed analysis is validated by means of numerical examples. Some additional cryptographic applications of this paper are also discussed.