Chaos-based joint image compression and encryption

Abstract

In recent years, the size of multimedia files as well as the need for the secure transmission of confidential data over public networks keeps rising. This leads to a growing interest in the investigation of joint operation of compression and encryption on the same set of data, i.e. perform these two operations simultaneously, instead of separately. The objectives are to reduce the computation time without sacrificing the image quality, and to maintain or even enhance the protection on the multimedia content. In general, there are two different research directions in this area: embed encryption into compression algorithms or incorporate compression in cryptographic schemes. In this work, we will propose different schemes along both directions, depending on the intrinsic properties of the compression or encryption method. Among the proposed schemes, chaos is utilized for encryption due to the following favorable properties. Firstly, chaotic systems are highly sensitive to the initial condition and the control parameters, i.e. any tiny changes in the initial condition or the control parameters lead to a totally different iterated sequence. This property makes them a favorable candidate for symmetric key encryption that requires high key sensitivity. Secondly, the sequences generated by chaotic systems possess good randomness. In the proposed schemes, they pass the statistical test suite recommended by the U.S. National Institute of Standards and Technology (NIST). Thus, chaotic systems are suitable to be employed in pseudo-random sequence generators for cryptographic purpose. In the first part of this work, we incorporate compression into Baptista's cryptosystem, which divides the phase space of a chaotic map into many equal-width partitions. Each partition represents a possible plaintext symbol. The plaintext is encrypted as the number of iterations required to make the chaotic trajectory land on the partition corresponding to the symbol being coded. The ciphertext produced by the cryptosystem may be longer than the plaintext as the number of iterations can be very large. In our scheme, only the most frequent plaintext symbols are associated to the phase space. The number of iterations is limited, and the unreached plaintext symbols will be masked by the chaotic sequence directly. The proposed scheme is able to compress the standard files in the Calgary Corpus. It is then extended to compress and encrypt digital images by interpolation and relaxing the matching criteria of the search trajectory. In the second part of this thesis, encryption is embedded into different image compression algorithms. In general, image compression schemes can be classified into two types: operate in the frequency domain or otherwise. For the former type, the Discrete Cosine Transform (DCT) and Huffman coding are studied. They form the basis of the popular JPEG standard. In our scheme, the DCT coefficients are arranged into two separate sequences according to the associated frequency value. The energy of an image usually concentrates at low-frequency DCT coefficients. Therefore, these coefficients are encrypted using both permutation and diffusion as required in strong cryptosystems. Besides, they also act as a partial key of the Secure Hash Algorithm 1 (SHA-1) to encrypt the sequence composing of the remaining DCT coefficients. As an image compression method not operating in the frequency domain, fractal image coding is studied. Here, the security of an existing selective encryption algorithm for fractal image coding is analyzed. Some weaknesses of this scheme will be discussed. It is found that selective encryption is not able to provide sufficient protection for images. Therefore, a full encryption scheme based on chaos is proposed for fractal image coding. In this scheme, the fractal parameters are packed according to their characteristics and the packed pairs are encrypted in different ways.

Date of Award	2 Oct 2013
Original language	English
Awarding Institution	City University of Hong Kong
Supervisor	Kwok Wo WONG (Supervisor)