Robust encryption of data by using nonlinear systems

        A new method is proposed for data encryption by using various nonlinear systems (Robot equation, Duffing oscillator, etc.) which provides an effective protection of data from unauthorized modification and use during its storage and transmission.

       In order to generate chaotic sequence, a simple nonlinear one-dimensional robot model has been used. The system is described with the nonlinear differential equation of the second order in time,

which corresponds to the hard spring with coefficients and , with two types of friction. On the right side of equation, we have the periodic time-dependent force with amplitude , and feedback force with the corresponding parameters,

,

,

,

,

, .

PATENTS APPROVED BY THE STATE INTELLECTUAL PROPERTY OFFICE IN CROATIA:

  1. "Cryptographic method of nonrepeated selective assignment of signs using chaotic solutions of robotic differential equation ", in Croatian, State intellectual property office, Croatia, Patent Nr. P980607 (2003).

  2. "Cryptographic method by repeated application of binary ASCII code depending on parity of digits in chaotic solutions of nonlinear robotic equation", in Croatian, State intellectual property office, Croatia,  Patent Nr. P990240A2 (2006).

  3. "Cryptographic protection of series of signs using selective transformation of binary ASCII code using chaotic solutions of nonlinear Duffing equation", in Croatian , State intellectual property office, Croatia, Patent Nr. P990248A2 (2006).

Literature:

  1. R. Matthews, On the derivation of a chaotic encryption algorithm, Cryptologia 12, 29-42 (1989).
  2. W.H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes, Chapter 7.5 Data Encryption Standards, Cambridge University Press, Cambridge (1988).
  3. Data Encryption Standard, Federal Information Processing Standards Publication, No. 46 (U.S. Department of Commerce, National Bureau of Standards, Washington, D.C., 1977).
  4. M. Bianco, An encryption system based on chaos theory, European Patent Office, Publication No. 0 467 239 A2 (1991).
  5. T.L. Carroll, Synchronizing chaotic systems using filtered sygnals, Physical review E50, 2580-2587 (1994).
  6. U. Parlitz, S. Ergezinger, Robust communication based on chaotic spreading sequences, Physics Letters A188, 146-150 (1994).
  7. S.Hayes, C. Grebogi, E. Ott, Communicating with Chaos, Physical review Letters 70, 3031-3034).
  8. A. Oksasoglu, T. Akgul, Chaoting masking scheme with linear inverse system, Physical Review Letters 75, 4595-4597 (1995).

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