Chaos in cryptography: the escape from the strange attractor

Cryptologia

Volumn 16, Issue 1, 1992, Pages 52-72

  Carroll, John M ^a   Verhagen, Jeff ^a   Wong, Perry T ^a  

^a UNIVERSITY OF WESTERN ONTARIO   (Canada)

Author keywords

Chaos theory; Lorenz equations; Random number generators (RNG); Statistical testing

Indexed keywords

EID: 0007829130     PISSN: 01611194     EISSN: 15581586     Source Type: Journal    
DOI: 10.1080/0161-119291866766     Document Type: Article

References (26)

1. Barnsley, M. 1988. Fractals Everywhere. Toronto: Academic Press.
2. Bernstein, G. M. and M. A. Lieberman. 1990. Secure Random Number Generation Using Chaotic Circuits. IEEE Transactions on Circuits and Systems. 37(9): 1157-1164.
3. Bratley, P., B. L. Fox and L. E. Schräge. 1987. A Guide to Simulation, '2nd ed. New York: Springer-Verlag.
4. Carroll, J. M., J. Verhagen, and P. Wong. 1991. Chaotic Cryptography, TR #284, London CANADA: Dept, of Computer Science, University of Western Ontario, London. March.
5. Char, B. W., K. O. Geddes, G. H. Gonnet et al. 1988. MAPLE Reference Manual, 5th ed. Waterloo CANADA: Dept, of Computer Science, University of Waterloo. March.
6. Dagpunar, J. 1988. Principles of Random Variate Generation. New York: Oxford University Press.
7. Dewdney, A. K. 1987. Probing the strange attractions of chaos. Scientific American. (July). 257(1): 108-111.
8. Dudewicz, E. J. 1976. Speed and Quality of Random Numbers for Simulation. Journal of Quality Technology 8(3): 171-178.
9. Gleick, J. 1988. Chaos. New York: Penguin Books.
10. Gorenstein, S. 1967. Testing a Random Number Generator. Communications of the ACM. 10(2): 111-118.
11. Kendall, M. G., and B. Babington-Smith. 1938. Randomness and Random Sampling Numbers. Journal of the Royal Statistical Society. 101: 147-166.
12. Kendall, M. G., and B. Babington-Smith. 1939. Second Paper on Random Sampling Numbers. Supplement to the Jour. Royal Statistical Society. 6(1): 51- 61.
13. Knuth, D. E. 1981. The Art of Computer Programming, Vol. 2, 2nd ed. Don Mills CANADA: Addison-Wesley.
14. Lorenz, E. N. 1963. Deterministic Nonperiodic Flow. Journal of the Atmospheric Sciences. 20(2): 130-141.
15. Matthews, R. 1989. On the derivation of a “chaotic” encryption algorithm. Cryptologia. 13(1): 29-42.
16. Mitchell, D. W. 1990. Nonlinear key generators. Cryptologia. 14(4): 350-354.
17. Mitrani, I. 1982. Simulation Techniques for Discrete Event Systems. New York: Cambridge University Press.
18. Rayleigh, Lord. 1916. On Convection Currents in a Horizontal Layer of Fluid, When the Higher Temperature is on the Under Side. Philosophical Magazine and Journal of Science. 32(192): 529-546.
19. Rietman, E. 1989. Exploring the Geometry of Nature. PA: Windcrest Books.
20. Salzman, B. 1962. Finite Amplitude Free Convection as an Initial Value Problem - 1. Journal of the Atmospheric Sciences. 19(4): 329-341.
21. Sparrow, C. 1982. The Lorenz Equations: Bifurcations, Chaos, and Strange Attractors. Vol. 41 in series, Applied Mathematical Sciences. New York: Springer-Verlag.
22. Sedgewick, R. and T. G. Szymanski. 1979. The Complexity of Finding Periods. In Proc. ACM Symposium on Theory of Computing. 11: 74-80.
23. Ulam, S. M. and J. von Neumann. 1947. On combination of stochastic and deterministic processes. Bulletin of the American Mathematical Society. 53: 1120.
24. Vanstone, S. 1991. Elliptic Curve Ciphers. Proc. AUSCRYPT’91, University of New South Wales, Sydney, Australia. January.
25. Wheeler, D. D. 1989. Problems with chaotic cryptosystems. Cryptologia. 13(3): 243-250.
26. Wheeler, D. D. and R. A. J. Matthews. 1991. Supercomputer investigations of a chaotic encryption algorithm. Cryptologia 15(2): 140-152.