Resilient Digital Image Watermarking for Document Authentication

Abstract—We consider the applications of the Discrete Cosine Transform (DCT) and then a Chirp coding method for producing a highly robust system for watermarking images using a block partitioning approach subject to a self-alignment strategy and bit error correction. The applications for the algorithms presented and the system developed include the copyright protection of images and Digital Right Management for image libraries, for example. However, the principal focus of the research reported in this paper is on the use of printscan and e-display-scan image authentication for use in e-tickets where QR code, for example, are embedded in a full colour image of the ticket holder. This requires that an embedding procedure is developed that is highly robust to blur, noise, geometric distortions such as rotation, shift and barrel and the partial removal of image segments, all of which are considered in regard to the resilience of the method proposed and its practical realisation in a real operating environment

On the application of two dimensional chirplets for resilient digital image watermarking

Chirplets (swept-frequency harmonic signals) find applications in several areas, including real and synthetic aperture radar, (Fresnel) optics and image processing. The robustness of chirplets to extreme (additive) noise make them an ideal choice in the role of embedding patterns for resilient digital signal and image watermarking. In this paper we present a new watermarking technique which is based on embedding twodimensional chirplet coded binary sequences in digital images. This approach provides a pattern embedded recovery algorithm which is robust to a variety of distortions. However, chirplets have certain parameters that need to be specified, and, given a set of target characteristics, some particular chirplet parameters can be considered optimal. This paper reports on the optimisation of both the chirplet sets and their associated parameters focusing on a classification of their resilience to image distortion

The Chirp Function Revisited: A Uniqueness Conjecture for Chirplet Modulation

The chirp function (a unit amplitude quadratic phase-only function with linear frequency modulation) is well known and is used in a wide range of applications including radar, digital communications, information coding and hiding and many other forms of signal and image processing. This is because the chirp provides an optimal solution to the problem of retrieving information from low energy signals with a low Signal-to-Noise Ratio (SNR). The chirp function also occurs in the solution to many mathematical models used to describe the propagation and scattering of waves (in the Fresnel zone), in quantum mechanics (the quantum shutter problem) and optical fiber communications to name but a few. In a ‘systems and signals’ context, the chirp function is accepted to be unique in that no other function has properties which yield such an optimal solution to the problem of extracting information from noise. In this context, we revisit the chirp function, consider a theorem and conjecture that attempt to quantify its unique properties through an analysis of its Fourier transform and re-establish the principles associated with the chirplet transform for functions of compact support. We then consider the principles of chirplet modulation for the transmission and reconstruction of bit-streams from signals with a low SNRs and show how this approach can be used to secure chirplet modulated signals using the prime number factorisation of a semi-prime derived from the value of the bandwidth of a communications channel

On the Chirp Function, the Chirplet Transform and the Optimal Communication of Information

—The purpose of this extended paper is to provide a review of the chirp function and the chirplet transform and to investigate the application of chirplet modulation for digital communications, in particular, the transmission of binary strings. The significance of the chirp function in the solution to a range of fundamental problems in physics is revisited to provide a background to the case and to present the context in which the chirp function plays a central role, the material presented being designed to show a variety of problems with solutions and applications that are characterized by a chirp function in a fundamental way. A study is then provided whose aim is to investigate the uniqueness of the chirp function in regard to its use for convolutionalcodinganddecoding,thelattercase(i.e.decoding) being related to the autocorrelation of the chirp function which provides a unique solution to the deconvolution problem. Complementary material in regard to the uniqueness of a chirp is addressed through an investigation into the selfcharacterizationofthechirpfunctionuponFouriertransformation. This includes a short study on the eigenfunctions of the Fourier transform, leading to a uniqueness conjecture which is based on an application of the Bluestein decomposition of a Fourier transform. The conjecture states that the chirp function is the only phase-only function to have a self-characteristic Fourier transform, and, for a specific scaling constant, a conjugate eigenfunction. In the context of this conjecture, we consider the transmission of information through a channel characterized by additive noise and the detection of signals with very low Signal-to-Noise Ratios. It is shown that application of chirplet modulation can provide a simple and optimal solution to the problem of transmitting binary strings through noisy communication channels, a result which suggests that all digital communication systems should ideally by predicated on the application of chirplet modulation. In the latter part of the paper, a method is proposed for securing the communication of information (in the form of a binary string) through chirplet modulation that is based on prime number factorization of the chirplet (angular) bandwidth. Coupled with a quantum computer for factorizing very large prime numbers using Shor’s algorithm, the method has the potential for designing a communications protocol specifically for users with access to quantum computing when the factorization of very large prime numbers is required. In thisrespect,and,inthefinalpartofthepaper,weinvestigatethe application of chirplet modulation for communicating through the ‘Water-Hole’. This includes the introduction of a method for distinguishing between genuine ‘intelligible’ binary strings through the Kullback-Leibler divergence which is shown to be statistically significant for a number of natural languages

Resilient Digital Image Watermarking Using a DCT- Component Perturbation Model

The applications of the Discrete Cosine Transform (DCT) for Computer Generated Imagery, image processingand, in particular, image compression are well known and the DCT also forms the central kernel for a number ofdigital image watermarking methods. In this paper we consider the application of the DCT for producing a highlyrobust method of watermarking images using a block partitioning approach subject to a self-alignment strategyand bit error correction. The applications for the algorithms presented include the copyright protection of imagesand Digital Right Management for image libraries, for example. However, the principal focus of the researchreported in this paper is on the use of print-scan and e-display-scan image authentication for use in e-ticketswhere QR code, for example, are embedded in an full colour image of the ticket holder. This requires that a DCTembedding procedure is developed that is highly robust to blur, noise, geometric distortions such as rotation, shift and barrel and the partial removal of image segments, all of which are consider ed in regard to the resilience of the method proposed and its practical realisation in a real operating environment

The Discrete Linear Chirp Transform and its Applications

In many applications in signal processing, the discrete Fourier transform (DFT) plays a significant role in analyzing characteristics of stationary signals in the frequency domain. The DFT can be implemented in a very efficient way using the fast Fourier transform (FFT) algorithm. However, many actual signals by their nature are non--stationary signals which make the choice of the DFT to deal with such signals not appropriate. Alternative tools for analyzing non--stationary signals come with the development of time--frequency distributions (TFD). The Wigner--Ville distribution is a time--frequency distribution that represents linear chirps in an ideal way, but it has the problem of cross--terms which makes the analysis of such tools unacceptable for multi--component signals. In this dissertation, we develop three definitions of linear chirp transforms which are: the continuous linear chirp transform (CLCT), the discrete linear chirp transform (DLCT), and the discrete cosine chirp transform (DCCT). Most of this work focuses on the discrete linear chirp transform (DLCT) which can be considered a generalization of the DFT to analyze non--stationary signals. The DLCT is a joint frequency chirp--rate transformation, capable of locally representing signals in terms of linear chirps. Important properties of this transform are discussed and explored. The efficient implementation of the DLCT is given by taking advantage of the FFT algorithm. Since this novel transform can be implemented in a fast and efficient way, this would make the proposed transform a candidate to be used for many applications, including chirp rate estimation, signal compression, filtering, signal separation, elimination of the cross--terms in the Wigner--Ville distribution, and in communication systems. In this dissertation, we will explore some of these applications

On Achieving Unconditionally Secure Communications Via the Physical Layer Approaches

Due to the broadcast nature, wireless links are open to malicious intrusions from outsiders, which makes the security issues a critical concern in the wireless communicationsover them. Physical-layer security techniques, which are based on the Shannon’s unconditional secrecy model, are effective in addressing the security issue while meeting the required performance level. According to the Wyner’s wiretap channel model, to achieve unconditionally security communication, the first step is to build up a wiretap channel with better channel quality between the legitimate communication peers than that of the eavesdropper; and the second step is to employ a robust security code to ensure that the legitimate users experience negligible errors while the eavesdropper is subject to 0.5 error probability. Motivated by this idea, in this thesis, we build wiretap channels for the single antenna systems without resorting to the spatial degree in commonly observed the multiple-input multiple-output (MIMO) systems. Firstly, to build effective wiretap channels, we design a novel scheme, called multi-round two-way communications (MRTWC). By taking feedback mechanisms into the design of Low Density Parity Check (LDPC) codes, our scheme adds randomness to the feedback signals from the destination to keep the eavesdropper ignorant while adding redundancy with the LDPC codes so that the legitimate receiver can correctly receive and decode the signals. Then, the channel BERs are specifically quantified according to the crossover probability in the case of Binary Symmetric Channel (BSC), or the Signal to Noise Ratio (SNR) in the case of AWGN and Rayleigh channels. Thus, the novel scheme can be utilized to address the security and reliability. Meanwhile, we develop a cross-layer approach to building the wiretap channel, which is suitable for high dynamic scenarios. By taking advantage of multiple parameters freedom in the discrete fractional Fourier transform (DFRFT) for single antenna systems, the proposed scheme introduces a distortion parameter instead of a general signal parameter for wireless networks based on DFRFT. The transmitter randomly flip-flops the uses of the distortion parameter and the general signal parameter to confuse the eavesdropper. An upper-layer cipher sequence will be employed to control the flip-flops. This cryptographic sequence in the higher layer is combined with the physical layer security scheme with random parameter fipping in DFRFT to guarantee security advantages over the main communication channel. As the efforts on the second step, this thesis introduces a novel approach to generate security codes, which can be used for encoding with low complexity by taking advantage of a matrix general inverse algorithm. The novel constructions of the security codes are based on binary and non-binary resilient functions. With the proposed security codes, we prove that our novel security codes can ensure 0.5 error probability seen by the wiretapper while close to zero by the intended receiver if the error probability of the wiretapper’s channel is over a derived threshold. Therefore, the unconditionally secure communication of legitimate partners can be guaranteed. It has been proved mathematically that the non-binary security codes could achieve closer to the security capacity bound than any other reported short-length security codes under BSC. Finally, we develop the framework of associating the wiretap channel building approach with the security codes. The advantages between legitimate partners are extended via developing the security codes on top of our cross-layer DFRFT and feedback MRTWC security communication model. In this way, the proposed system could ensure almost zero information obtained by the eavesdroppers while still keeping rather lower error transmissions for legitimate users. Extensive experiments are carried out to verify the proposed security schemes and demonstrate the feasibility and implement ability. An USRP testbed is also constructed, under which the physical layer security mechanisms are implemented and tested. Our study shows that our proposed security schemes can be implemented in practical communications settings