Information security based on temporal order and ergodic matrix

This thesis proposes some information security systems to aid network temporal security applications with multivariate quadratic polynomial equations, image cryptography and image hiding. In the first chapter, some general terms of temporal logic, multivariate quadratic equations (MQ) problems and image cryptography/hiding are introduced. In particular, explanations of the need for them and research motivations are given, i.e., a formal characterization of time-series, an alternative scheme of MQ systems, a hybrid-key based image encryption and authentication system and a DWT-SVD (Discrete Wavelet Transform and Singular Value Decomposition) based image hiding system. This is followed by a literature review of temporal basis, ergodic matrix, cryptography and information hiding. After these tools are introduced, they are used to show how they can be applied in our research. The main part of this thesis is about using ergodic matrix and temporal logic in cryptography and hiding information. Specifically, it can be described as follows: A formal characterization of time-series has been presented for both complete and incomplete situations, where the time-series are formalized as a triple (ts, R, Dur) which denote the temporal order of time-elements, the temporal relationship between time-elements and the temporal duration of each time-element, respectively. A cryptosystem based on MQ is proposed. The security of many recently proposed cryptosystems is mainly based on the difficulty of solving large MQ systems. Apart from UOV schemes with proper parameter values, the basic types of these schemes can be broken down without great difficulty. Moreover, there are some shortages lying in some of these examined schemes. Therefore, a bisectional multivariate quadratic equation (BMQE) system over a finite field of degree q is proposed. The BMQE system is analysed by Kipnis and Shamir’s relinearization and fixing-variables method. It is shown that if the number of the equations is larger or equal to twice the number of the variables, and qn is large enough, the system is complicated enough to prevent attacks from some existing attacking schemes. A hybrid-key and ergodic-matrix based image encryption/authentication scheme has been proposed in this work. Because the existing traditional cryptosystems, such as RSA, DES, IDEA, SAFER and FEAL, are not ideal for image encryption for their slow speed and not removing the correlations of the adjacent pixels effectively. Another reason is that the chaos-based cryptosystems, which have been extensively used since last two decades, almost rely on symmetric cryptography. The experimental results, statistical analysis and sensitivity-based tests confirm that, compared to the existing chaos-based image cryptosystems, the proposed scheme provides more secure way for image encryption and transmission. However, the visible encrypted image will easily arouse suspicion. Therefore, a hybrid digital watermarking scheme based on DWT-SVD and ergodic matrix is introduced. Compared to other watermarking schemes, the proposed scheme has shown both significant improvement in perceptibility and robustness under various types of image processing attacks, such as JPEG compression, median filtering, average filtering, histogram equalization, rotation, cropping, Gaussian noise, speckle noise, salt-pepper noise. In general, the proposed method is a useful tool for ownership identification and copyright protection. Finally, two applications based on temporal issues were studied. This is because in real life, when two or more parties communicate, they probably send a series of messages, or they want to embed multiple watermarks for themselves. Therefore, we apply a formal characterization of time-series to cryptography (esp. encryption) and steganography (esp. watermarking). Consequently, a scheme for temporal ordered image encryption and a temporal ordered dynamic multiple digital watermarking model is introduced.