Communication Security: The Degree of Security of a Scrambling Algorithm

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A Communication scheme is said to be secure if it is capable to protect the data from any kind of eavesdropping. Scrambling is a technique which is used to obscure the content of transmission and is mainly employed in data hiding, water marking and encryption applications for providing information security against illegal surveillance and wire tapping. In the time domain scrambling process, a segment of time domain samples are taken and scrambles them into a different segment of samples. This scrambled data is transmitted and at the receiving end it is descrambled into its original form. The scrambling and descrambling operations are based on a scrambling/descrambling matrix. The disadvantage of earlier audio scrambling matrices constructed by pseudorandom sequences cite{lin2007secure}, Hadamard transform cite{senk1997new}, Fibonacci transform cite{nan2004audio} etc., is that, since these matrices are invariable, they could easily be deciphered. Some improved algorithms such as stochastic matrix cite{li2010n} and latin square cite{satti2009multilevel} were developed to overcome this problem, but they result in heavy transmission load. Speech compression methods like G.729 mixed excitation linear prediction (MELP) and adaptive multi-rate (AMR) cite{servetti2002perception} audio codec are then employed along with the process of scrambling to reduce the transmission load, but these methods shows low robustness in the presence of noise.

The degree of security of a scrambling algorithm depends on residual intelligibility and key space. Residual intelligibility is the amount of intelligibility left over in the scrambled signal. The lower the residual intelligibility of a scrambling method, the higher its degree of security. S...

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...number of samples. More specifically, if a signal is composed of a linear combination of $ T $ vectors, we can reconstruct the signal using $ kT $ samples, where $ k $ is a small positive integer formed as random linear combinations of the $ N $ original samples. It is then clear that if $ κT $ is much smaller than $ N $, we have achieved a compression provided the level of sparsity is known a priori. Compressive sensing uses random measurements in a basis that is incoherent with the sparse basis. Incoherence cite{donoho2006compressed} means that no element of one basis has a sparse representation in terms of the other basis. CS has found applications in many areas such as image processing, spatial localization, medical signal processing etc.. In addition, CS is particularly suited to multiple sensor scenarios, making it a good choice for wireless sensor networks.

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