True random bit generation from a double-scroll attractor

IEEE Transactions on Circuits and Systems I: Regular Papers

Volumn 51, Issue 7, 2004, Pages 1395-1404

  Yalçin, Muştak E ^a   Suykens, Johan A K ^a   Vandewalle, Joos ^a  

^a Katholieke Universiteit Leuven   (Belgium)

Author keywords

[No Author keywords available]

Indexed keywords

CHAOS THEORY; RANDOM NUMBER GENERATION; RANDOM PROCESSES; SECURITY OF DATA; STATISTICAL TESTS;

CHAOTIC SIGNALS; DOUBLE SCROLL ATTRACTOR; TRUE RANDOM BIT GENERATOR;

CRYPTOGRAPHY;

EID: 3843152778     PISSN: 10577122     EISSN: None     Source Type: Journal    
DOI: 10.1109/TCSI.2004.830683     Document Type: Article

References (45)

1. V. Bagini and M. Bucci, "A design of reliable true random number generator for cryptographic applications," in Proc. 1st Int. Workshop Cryptographic Hardware and Embedded Systems, vol. LCNS 1717, 1999, pp. 204-218.
2. G. Boffetta, M. Cencini, M. Falcioni, and A. Vulpiani, "Predictability: A way to characterize complexity," Phys. Rep., vol. 356, pp. 367-474, 2002.
3. S. Callegari, A. Cesaroni, and G. Setti, "Mixed mode unpredictable binary information source exploiting complex dynamics and adaptive median thresholding," in Proc. 9th Workshop on Nonlinear Dynamics of Electronic Systems (NDES'01), 2001, pp. 65-68.
4. S. Callegari, R. Rovatti, and G. Setti, "Spectral properties of chaos-based FM signals: Theory and simulation results," IEEE Trans. Circuits Syst. I, vol. 50, pp. 3-15, Jan. 2003.
5. M. Casdagli, "Nonlinear prediction of chaotic time series," Phys. D, vol. 35, pp. 335-356, 1989.
6. G. Chen and T. Ueta, Chaos in Circuits and Systems. Singapore: World Scientific, 2002.
7. L. O. Chua, M. Komuro, and T. Matsumoto, "The double-scroll family," IEEE Trans. Circuits Syst. I, vol. CAS-33, pp. 1072-1118, Oct. 1986.
8. L. O. Chua, W. Wu, A. Huang, and G. Zhong, "A universal circuit for studying and genereting chaos-part II: Strange attractors," IEEE Trans. Circuits Syst. I, vol. 40, pp. 745-761, July 1993.
9. (1999) The Intel random number generator. Techn. Rep.. Intel Corporation, Portland, OR. [Online]. Available: http://www.intel.com/design/security/rng/techbrief.htm
10. D. Davis, R. Ihaka, and P. Fenstermacher, "Cryptographic randomness from air turbulence in disk drives," in Proc. Advances in Cryptology (CRYPTO '94), vol. LNCS 0839, 1994, pp. 114-120.
11. J. Doyne and J. J. Sidorowich, "Predicting chaotic time series," Phys. Rev. Lett., vol. 59, no. 8, pp. 845-848, 1987.
12. D. Eastlake, S. Crocker, and J. Schiller, "RFC 1750: Randomness recommendations for security," Network Working Group, Tech. Rep., 1994.
13. A. S. Elwakil and M. P. Kennedy, "High frequency Wien-type chaotic oscillator," Electron. Lett., vol. 34, no. 12, pp. 1161-1162, 1998.
14. A. S. Elwakil and M. P. Kennedy, "Construction of classes of circuit-independent chaotic oscillators using passive-only nonlinear devices," IEEE Trans. Circuits Syst. I, vol. 48, pp. 289-307, Mar. 2001.
15. A. S. Elwakil, K. N. Salama, and M. P. Kennedy, "An equation for generating chaos and its monolithic implementation," Int. J. Bifurcation Chaos, vol. 12, no. 12, pp. 2885-2896, 2002.
16. R. C. Fairfield, R. L. Mortenson, and K. B. Coulthart, "An LSI random number generator (RNG)," in Proc. Advances in Cryptology (CRYPTO '87), vol. LNCS 0196, 1987, pp. 203-230.
17. A. M. Fraser, "Information and entropy in strange attractors," IEEE Trans. Inform. Theory, vol. 35, pp. 245-262, Mar. 1989.
18. J. A. González, L. I. Reyes, J. J. Suarez, L. E. Guerrero, and G. Gutiérrez, "A mechanism for randomness," Phy. Lett. A, vol. 295, no. 1, pp. 25-34, 2002.
19. J. Guckenheimer, "Toolkit for nonlinear dynamics," IEEE Trans. Circuits Syst. I, vol. CAS-30, pp. 586-590, Aug. 1983.
20. M. Guide, "Concept for a high-performance random number generator based on physical random phenomena," Freq., vol. 39, pp. 187-190, 1985.
21. T. S. Han and M. Hoshi, "Interval algorithm for random number generation," IEEE Trans. Inform. Theory, vol. 43, pp. 599-611, Mar. 1997.
22. M. Jakobsson, E. Shriver, B. K. Hillyer, and A. Juels, "A practical secure physical random bit generator," in Proc. 5th ACM Conf. Computer and Communications Security, 1998.
23. A. Juels, M. Jakobsson, E. Shriver, and B. K. Hillyer, "How to turn loaded dice into fair coins," IEEE Trans. Inform. Theory, vol. 46, pp. 911-921, May 2000.
24. B. Jun and P. Kocher. (1999) The Intel random number generator. Tech. Rep., White Paper. Intel Corporation, Cryptography Research Inc., Portland, OR. [Online]. Available: http://www.intel.com/design/security/rng/CRIwp.htm
25. D. E. Knuth, The Art of Computer Programming. Reading, MA: Addison-Wesley, 1969.
26. G. Kolumban, M. P. Kennedy, and L. O. Chua, "The role of synchronization in digital communications using chaos-Part II: Chaotic modulation of digital communications," IEEE Trans. Circuits Syst. I, vol. 45, pp. 1129-1140, Nov. 1998.
27. D. Lind and B. Marcus, An Introduction to Symbolic Dynamics and Coding. Cambridge, U.K.: Cambridge Univ. Press, 1995.
28. R. N. Madan, Chua's Circuit: A Paradigm for Chaos. Singapore: World Scientific, 1993.
29. D. P. Maher and R. J. Rance, "Random number generators founded on signal and information theory," in Proc. 1st Int. Workshop Cryptographic Hardware and Embedded Systems, vol. 1717, 1999, pp. 219-230.
30. G. Marsalgia. Diehard. [Online]. Available: http://stat.fsu.edu/~geo/diehard.html
31. A. J. Menezes, P. C. van Oorschot, and S. A. Vanstone. (1997) Handbook of applied cryptography. [Online]. Available: http://www.cacr.math.uwaterloo.ca/hac/
32. J. Von Neumann, "Various techniques used in connection with random digits," in Applied Math Series, G. E. Forsythe, Ed. Boulder, CO: National Bureau of Standards, 1951, vol. 12, pp. 36-38.
33. S. Özoǧuz and N. S. Şengör, "On the realization of NPN-only log-domain chaotic oscillators," IEEE Trans. Circuits Syst. I. vol. 50, pp. 291-294, Feb. 2003.
34. A. G. Radwan, A. M. Soliman, and A. El-Sedeek, "MOS realization of the double-scroll-like chaotic equation," IEEE Trans. Circuits Syst. I, vol. 50, pp. 285-288, Feb. 2003.
35. (1999) Hardware-based random number generation. Tech. Rep., An RSA Data Security White Paper. RSA Data Security. [Online]. Available: http://www.intel.com/design/security/rng/IntelG.htm
36. (1999) Using RSA BSAFE Crypto-c With Intel Random Number Generator. Tech. Rep., An RSA Data Security White Paper. RSA Data Security. [Online]. Available: http://www.intel.com/design/security/rng/RSAAFE.htm
37. A. Shamir, "On the generation of cryptographically strong pseudorandom sequences," ACM Trans. Comp. Syst., vol. 1, no. 1, pp. 38-44, 1983.
38. M. Small and C. K. Tse, "Detecting determinism in time series: The method of surrogate data," IEEE Trans. Circuits Syst. I, vol. 50, pp. 663-672, May 2001.
39. T. Stojanovski and L. Kocarev, "Chaos-based random number generators-part I: Analysis," IEEE Trans. Circuits Syst. I, vol. 48, pp. 281-288, Mar. 2001.
40. J. A. K. Suykens, A. Huang, and L. O. Chua, "A family of n-scroll attractors from a generalized Chua's circuit," Arch. Elektron. Ubert., vol. 51, no. 3, pp. 131-138, 1997.
41. J. A. K. Suykens and J. Vandewalle, "The K.U.Leuven time series prediction competition," in Nonlinear Modeling: Advanced Black-Box Techniques, J. A. K. Suykens and J. Vandewalle, Eds., 1998, pp. 241-253.
42. J.A.K. Suykens, M. E. Yalçin, and J. Vandewalle, "Chaotic systems synchronization," in Chaos Control: Theory and Applications, G. Chen and X. Yu, Eds. New York: Springer-Verlag, 2003, vol. 292, pp. 117-136.
43. T. Kohda and A. Tsuneda, "Statistics of chaotic binary sequences," IEEE Trans. Inform. Theory, vol. 43, pp. 104-112, Jan. 1997.
44. B. Vizvari and G. Kolumban, "Quality evaluation of random numbers generated by chaotic sampling phase-locked loops," IEEE Trans. Circuits Syst. I, vol. 45, pp. 216-224, Mar. 1998.
45. M. E. Yalçm, J. A. K. Suykens, J. Vandewalle, and S. Özoǧuz, "Families of scroll grid attractors," Int. J. Bifurcation Chaos, vol. 12, no. 1, pp. 23-41, 2001.