Article

Statistical distribution, host for encrypted information

Aston University, Wheaton Aston, England, United Kingdom
Physica A: Statistical Mechanics and its Applications (Impact Factor: 1.73). 05/2005; 359(1). DOI: 10.1016/j.physa.2005.04.044
Source: arXiv

ABSTRACT

The statistical distribution, when determined from an incomplete set of
constraints, is shown to be suitable as host for encrypted information. We
design an encoding/decoding scheme to embed such a distribution with hidden
information. The encryption security is based on the extreme instability of the
encoding procedure. The essential feature of the proposed system lies in the
fact that the key for retrieving the code is generated by random perturbations
of {\em {very small value}}. The security of the proposed encryption relies on
the security to interchange the secret key. Hence, it appears as a good
complement to the quantum key distribution protocol.

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    • "The success of employing multiple pdf 's to enhance the security of the covert information, is critically contingent upon the encryption/decryption strategy being dependent upon the pdf 's of the statistical hosts. This feature permits the pdf dependent statistical encryption/decryption strategy to possess immense qualitative flexibility, as compared with pdf independent models [7] [8]. Numerical simulations demonstrate impressive quantitative performance in securing covert information. "
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    ABSTRACT: A novel strategy to encrypt covert information (code) via unitary projections into the null spaces of ill-conditioned eigenstructures of multiple host statistical distributions, inferred from incomplete constraints, is presented. The host pdf's are inferred using the maximum entropy principle. The projection of the covert information is dependent upon the pdf's of the host statistical distributions. The security of the encryption/decryption strategy is based on the extreme instability of the encoding process. A self-consistent procedure to derive keys for both symmetric and asymmetric cryptography is presented. The advantages of using a multiple pdf model to achieve encryption of covert information are briefly highlighted. Numerical simulations exemplify the efficacy of the model. Comment: 18 pages, 4 figures. Three sentences expanded to emphasize detail. Typos corrected
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    ABSTRACT: The basic goal of a research scientist is to understand a given, unknown system. This innovative book develops a systematic approach for achieving this goal. All science is ultimately dependent upon observation which, in turn, requires a flow of information. Fisher information, in particular, is found to provide the key to understanding the system. It is developed as a new tool of exploratory data analysis, and is applied to a wide scope of systems problems. These range from molecules in a gas to biological organisms in their ecologies, to the socio-economic organization of people in their societies, to the physical constants in the universe and, ultimately, to proto-universes in the multiverse. Examples of system input-output laws discovered by the approach include the famous quarter-power laws of biology and the Tobin q-theory of optimized economic investment. System likelihood laws that can be determined include the probability density functions defining in situ cancer growth and a wide class of systems (thermodynamic, economic, cryptographic) obeying Schrodinger-like equations. Novel uncertainty principles in the fields of biology and economics are also found to hold.B. Roy Frieden and Robert A. Gatenby are professors at the University of Arizona. Frieden is in the College of Optics, and Gatenby is Chairman of the Radiology Dept. at the Arizona Health Sciences Center. Frieden has pioneered the use of information for developing image restoration approaches, and for understanding the physics of unknown systems, both nonliving and living. Gatenby has actively promoted the study of information as a determinant of healthy and malignant growth processes, and has developed integrated mathematical models and empirical techniques for this purpose.
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    ABSTRACT: The theoretical framework for a principled procedure to encrypt/decrypt covert information (code)into/from the null spaces of a hierarchy of statistical distributions possessing ill-conditioned eigenstructures, is suggested. The statistical distributions are inferred using incomplete constraints, employing the generalized nonextensive thermostatistics (NET) Fisher information as the measure of uncertainty. The hierarchy of inferred statistical distributions possess a quantum mechanical connotation for unit values of the nonextensivity parameter. A systematic strategy to encrypt/decrypt code via unitary projections into the null spaces of the ill-conditioned eigenstructures, is presented.
    No preview · Article · Jan 2007 · Proceedings of SPIE - The International Society for Optical Engineering
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