Joseph P. Noonan

Local Shannon entropy measure with statistical tests for image randomness

In this paper we propose a new image randomness measure using Shannon entropy over local image blocks. The proposed local Shannon entropy measure overcomes several weaknesses of the conventional global Shannon entropy measure, including unfair randomness comparisons between images of different sizes, failure to discern image randomness before and after image shuffling, and possible inaccurate scores for synthesized images. Statistical tests pertinent to this new measure are also derived. This new measure is therefore both quantitative and qualitative. The parameters in the local Shannon entropy measure are further optimized for a better capture of local image randomness. The estimated statistics and observed distribution from 50,000 experiments match the theoretical ones. Finally, two examples are given, applying the proposed measure to image randomness among shuffled images and encrypted images. Both examples show that the proposed method is more effective and more accurate than the global Shannon entropy measure.The quality of image encryption is commonly measured by the Shannon entropy over the ciphertext image. However, this measurement does not consider to the randomness of local image blocks and is inappropriate for scrambling based image encryption methods. In this paper, a new information entropy-based randomness measurement for image encryption is introduced which, for the first time, answers the question of whether a given ciphertext image is sufficiently random-like. It measures the randomness over the ciphertext in a fairer way by calculating the averaged entropy of a series of small image blocks within the entire test image. In order to fulfill both quantitative and qualitative measurement, the expectation and the variance of this averaged block entropy for a true-random image are strictly derived and corresponding numerical reference tables are also provided. Moreover, a hypothesis test at significance α-level is given to help accept or reject the hypothesis that the test image is ideally encrypted/random-like. Simulation results show that the proposed test is able to give both effectively quantitative and qualitative results for image encryption. The same idea can also be applied to measure other digital data, like audio and video.

Design of image cipher using latin squares

In this paper, we introduce a symmetric-key Latin square image cipher (LSIC) for grayscale and color image encryption. Our main contributions include (1) we propose new Latin square image encryption primitives including Latin Square Whitening, Latin Square S-box and Latin Square P-box; (2) we develop probabilistic image encryption by embedding random noise into the least significant bit-plane of images; and (3) we design a new loom-like 2D substitution-permutation network maintaining good confusion and diffusion properties with extra error tolerance. Theoretical analysis and simulation results show that the proposed method has many desired properties of a secure cipher, shows robustness against different attack models, and outperforms state of the art suggested by many peer algorithms. Open-source implementation can be found on the webpage https://sites.google.com/site/tuftsyuewu/source-code.In this paper, we introduce a symmetric-key Latin square image cipher (LSIC) for grayscale and color images. Our contributions to the image encryption community include 1) we develop new Latin square image encryption primitives including Latin Square Whitening, Latin Square S-box and Latin Square P-box ; 2) we provide a new way of integrating probabilistic encryption in image encryption by embedding random noise in the least significant image bit-plane; and 3) we construct LSIC with these Latin square image encryption primitives all on one keyed Latin square in a new loom-like substitution-permutation network. Consequently, the proposed LSIC achieve many desired properties of a secure cipher including a large key space, high key sensitivities, uniformly distributed ciphertext, excellent confusion and diffusion properties, semantically secure, and robustness against channel noise. Theoretical analysis show that the LSIC has good resistance to many attack models including brute-force attacks, ciphertext-only attacks, known-plaintext attacks and chosen-plaintext attacks. Experimental analysis under extensive simulation results using the complete USC-SIPI Miscellaneous image dataset demonstrate that LSIC outperforms or reach state of the art suggested by many peer algorithms. All these analysis and results demonstrate that the LSIC is very suitable for digital image encryption. Finally, we open source the LSIC MATLAB code under webpage https://sites.google.com/site/tuftsyuewu/source-code.

Image encryption using the two-dimensional logistic chaotic map

Chaos maps and chaotic systems have been proved to be useful and effective for cryptography. In our study, the two-dimensional logistic map with complicated basin structures and attractors are first used for image encryption. The proposed method adopts the classic framework of the permutation-substitution network in cryptography and thus ensures both confusion and diffusion properties for a secure cipher. The proposed method is able to encrypt an intelligible image into a random-like one from the statistical point of view and the human visual system point of view. Extensive simulation results using test images from the USC-SIPI image database demonstrate the effectiveness and robustness of the proposed method. Security analysis results of using both the conventional and the most recent tests show that the encryption quality of the proposed method reaches or excels the current state-of-the-art methods. Similar encryption ideas can be applied to digital data in other formats (e.g., digital audio and video). We also publish the cipher MATLAB open-source-code under the web page https://sites.google.com/site/tuftsyuewu/source-code.

Probabilistic Non-Local Means

In this letter, we propose a so-called probabilistic non-local means (PNLM) method for image denoising. Our main contributions are: 1) we point out defects of the weight function used in the classic NLM; 2) we successfully derive all theoretical statistics of patch-wise differences for Gaussian noise; and 3) we employ this prior information and formulate the probabilistic weights truly reflecting the similarity between two noisy patches. Our simulation results indicate the PNLM outperforms the classic NLM and many NLM recent variants in terms of the peak signal noise ratio (PSNR) and the structural similarity (SSIM) index. Encouraging improvements are also found when we replace the NLM weights with the PNLM weights in tested NLM variants.

James–Stein Type Center Pixel Weights for Non-Local Means Image Denoising

Non-Local Means (NLM) and its variants have proven to be effective and robust in many image denoising tasks. In this letter, we study approaches to selecting center pixel weights (CPW) in NLM. Our key contributions are 1) we give a novel formulation of the CPW problem from a statistical shrinkage perspective; 2) we construct the James-Stein shrinkage estimator in the CPW context; and 3) we propose a new local James-Stein type CPW (LJSCPW) that is locally tuned for each image pixel. Our experimental results showed that compared to existing CPW solutions, the LJSCPW is more robust and effective under various noise levels. In particular, the NLM with the LJSCPW attains higher means with smaller variances in terms of the peak signal and noise ratio (PSNR) and structural similarity (SSIM), implying it improves the NLM denoising performance and makes the denoising less sensitive to parameter changes.

A wheel-switch chaotic system for image encryption

Because of high sensitivity for initial values and random-like behaviors, chaotic systems are widely used in image encryption. Conventionally, encryption keys for these image encryption methods based chaotic systems are limited to manipulate the initial values or parameters of the chaotic system. However, effective attacks are found to crack encryption systems by using prior information about the system chaotic map. In this paper, we introduce a wheel-switch chaotic system for image encryption. The used chaotic map is not fixed but changeable via the wheel-switch structure according to the controlling sequence. Further, a substitution and permutation network based image encryption algorithm using the wheel-switch chaotic system is also provided. Experimental results showed that the proposed system with the key schedule inherits the random-like property of single chaotic system with additional security level from the wheel-switch structure. The same idea is also applicable to secure communication, and data encryption for other multimedia.

Parametric Slant-Hadamard transforms with applications

In this letter, we propose a new construction method for a class of parametric Slant-Hadamard transforms that includes but is not limited to the commonly used Slant-Hadamard and Hadamard transforms. This parametric class performs better in generalized Wiener filtering than existing Slant-Hadamard transforms for the first-order Markov and the generalized image correlation models. We also show that the new parametric Slant-Hadamard transform outperforms the commonly used discrete cosine transform for the generalized image correlation model.

A symmetric image cipher using wave perturbations

Abstract Inspired by the natural ripple-like phenomenon that distorts a reflection on a water surface, this paper introduces a new symmetric image cipher using wave perturbations to shuffle images in an n dimensional ( n D) space. Its strong diffusion and confusion properties are ensured by pseudo-random wavefronts and additional salts and peppers bits. Extensive simulations and comparisons demonstrate that the proposed image cipher outperforms several existing bit-level scrambling methods with respect to the encryption quality and computation complexity.

Fuzzy Kohonen network for the classification of transients using the wavelet transform for feature extraction

A system for identifying and classifying short duration signals (transients) is proposed. The transients are perturbed by multiplicative noise, and are embedded in various noise backgrounds to simulate an undersea environment. The transients are generated using FM chirp sum and sinusoidal sum models. The system uses wavelets as linear filters for preprocessing, and a fuzzy Kohonen neural network for classification. The design of the classifier system is presented, as well as results from initial experiments. The system is shown to be able to classify signals down to -1 dB.

Parametric Slant-Hadamard transforms

The purpose of this paper is to develop a class of generalized parametric Slant-Hadamard transform of order (formula available in paper)where k is an arbitrary integer and to present its fast algorithm. As special cases of this class are the classical Slant-Hadamard (k=2 and βN=1), the generalized Slant-Hadamard (βN=1), and the parametric Slant-Hadamard (k=2) transforms. We will show that the parametric Slant-Hadamard transform is slightly superior to the DCT for compression of the geometric test images at a particular quantization matrix scaling factors.