Families of binary sequences with low correlation are required in applications such as wireless communications, ranging and time delay measurement and digital watermarking, among others. Many constructions have been proposed that employ m-sequences as basic building blocks, such as the Gordon-Mills-Welch (GMW) sequences. In this work we present a unified construction of GMW sequences derived from suitable m-sequences by using the method of composition, producing sequences of length$2^{n}-1$with$n$being an integer composite number. A given m-sequence is folded using the Chinese remainder theorem (CRT) into a two dimensional array, whose columns are either constant or cyclic shifts of a short$m$-sequence. Then, the array can be summarized by a short$m$-sequence and the sequence of shifts (shift sequence). By looking at array interpretation, we avoid using Trace representation of intermediate fields, which makes its implementation more straightforward and secure. Pseudonoise arrays can be produced by constructing all the valid columns and shift sequences, the latter obtained by proper decimations and proper multiplication. Equivalences are removed by selecting a cyclotomic set leader from the degenerate conjugacy class. The window properties of these sequences can be exploited to construct generalized GMW sequence generators for lengths as large as the long codes in GPS i.e.$2^{42}-1$. A similar generalisation of the small Kasami sets can be constructed using this algorithm. The complexity of the algorithms is$\sqrt{L}$where$L$is the length of the sequence, improving known algorithms. Finally, the shift sequences constructed in this work are good candidates to frequency hopping and time hopping sequences in UWB wireless communications and localisation systems.

In this paper, we present two generators for the group of symmetries of the generic (m+1) -dimensional periodic Costas arrays over elementary abelian (\BBZp)mgroups: one that is defined by multiplication onmdimensions and the other by shear (addition) onmdimensions. Through exhaustive search, we observe that these two generators characterize the group of symmetries for the examples we were able to compute. Following the results, we conjecture that these generators characterize the group of symmetries of the generic (m+1) -dimensional periodic Costas arrays over elementary abelian (\BBZp)mgroups.

This paper presents two new classes of families of multi-periodic arrays suitable for digital watermarking. These families are large and all arrays have good auto and cross-correlation, and are available in many sizes. The construction is based on log quadratic and exponential quadratic maps. The maps applied to elements in an extension field on a natural multi-dimensional grid. The grid also leads to a generalized multi-dimensional Legendre array, which can be used in the family constructions.

New families of three-dimensional (3-D) optical orthogonal codes for applications to optical code-division multiple access (OCDMA) networks are proposed. The families are based in the three dimensional periodic Welch Costas array over elementary Abelian groups. These new families are shown to be asymptotically optimal through the Johnson bound.

Digital fingerprinting is a technique for tracing the distribution of multimedia content, and protecting it from unauthorized manipulation. Unique identification information is embedded into each distributed copy of the signal. In a collusion attack, fingerprints are combined to remove or distort the fingerprints. Audio signals are good candidates for fingerprinting, because of the forgiving nature of the human auditory system to cross-talk between channels. We use principal components of the audio signal to construct an abstract vector space. The fingerprints are ordered rotations in that space. The rotations are determined by arrays with good correlation properties. These arrays are embedded in real audio, and are imperceptible, according to a panel of experts. These fingerprints are resistant to an averaging collusion attack by hundreds or thousands of colluders, and can withstand a worst case RandNeg attack by up to 30 colluders.

This paper presents new families of two and three-dimensional arrays designed for watermarking. The array construction is algebraic, based on finite fields. The arrays have good auto and cross-correlation with other family members. The family size is large enough to be used in watermarking at the point of origin, providing a unique watermark for every video and image. Such watermarks have applications in surveillance, sub-image object tracking and as fingerprints for proof of tampering, audit trail monitoring and traitor tracing.

This paper describes the synthesis of matrices with good correlation, from cyclic shifts of pseudonoise columns. Optimum matrices result whenever the shift sequence satisfies the constant difference property. Known shift sequences with the constant (or almost constant) difference property are: quadratic (polynomial) and reciprocal shift modulo prime, exponential shift, Legendre shift, Zech logarithm shift, and the shift sequences of some m-arrays. We use these shift sequences to produce arrays for watermarking of digital images. Matrices can also be unfolded into long sequences by diagonal unfolding (with no deterioration in correlation) or row-by-row unfolding, with some degradation in correlation

Angles derived from sets of image pixel values present an effective medium for embedding "invisible" watermarks. The derived angles can be dithered by the addition of small offset angles. The watermark is a pseudo-noise sequence of dither angles. The watermark embedding is followed by re-quantisation for image storage or transmission. Watermark recovery is achieved by performing a complex correlation between the watermarked image and the reference pseudo-noise sequence. This occurs without recourse to the original image. The paper analyses the form of the observed decorrelation as the watermark to image ratio is decreased. The dependence of sequence recovery on: (1) the magnitude of the added dithered angle; (2) the angle derivation scheme used; and (3) on the level of quantisation in the original data is discussed. The spatially distributed embedding method used also offers potential robust data encryption advantages.

This paper introduces two-dimensional arrays for watermarking images. Binary, greyscale and colour (3D) arrays are examined. New constructions known as the "distinct sums" arrays are presented.

The paper discusses the feasibility of coding an "undetectable" digital water mark on a standard 512/spl times/512 intensity image with an 8 bit gray scale. The watermark is capable of carrying such information as authentication or authorisation codes, or a legend essential for image interpretation. This capability is envisaged to find application in image tagging, copyright enforcement, counterfeit protection, and controlled access. Two methods of implementation are discussed. The first is based on bit plane manipulation of the LSB, which offers easy and rapid decoding. The second method utilises linear addition of the water mark to the image data, and is more difficult to decode, offering inherent security. This linearity property also allows some image processing, such as averaging, to take place on the image, without corrupting the water mark beyond recovery. Either method is potentially compatible with JPEG and MPEG processing.>