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In this paper, we propose an enhanced version of modulo-based image encryption suggested by Rozouvan. Rozouvan et al. employed a fractal image to generate strong keys for image pixels encryption. The proposed enhanced version conflates the merits of chaos theory along with the use of fractal keys thereby inherit the features of original algorithm. The security enhancements are proposed to provide better robustness and security to realize trustworthy image encryption. To achieve the purpose, chaotic map is incorporated to create image information dependency so as to thwart the attacks launched by Yoon et al. on Rozouzan algorithm. Arnold cat map is used to perform pixels shuffling before pixels encryption to complicate the attack complexity. The simulation results on standard analyses demonstrate its effectiveness in providing better security and robustness to digital media.

We introduce a novel approach for the characterization of the quality of a laser beam that is not based on particular criteria for beam width definition. The Lorenz curve of a light beam is a sophisticated version of the so-called power-in-the-bucket curve, formed by the partial sums of discretized joint intensity distribution in the near and far fields, sorted in decreasing order. According to majorization theory, a higher Lorenz curve implies that all measures of spreading in phase space, and, in particular, all Rényi (and Shannon) entropy-based measures of the beam width products in near and far fields, are unanimously smaller, providing a strong assessment of a better beam quality. Two beams whose Lorenz curves intersect can be considered of relatively better or lower quality only according to specific criteria, which can be inferred from the plot of the respective Lorenz curves.

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