A pseudo random bit generator based on chaotic logistic map and its statistical testing

Informatica (Ljubljana)

Volumn 33, Issue 4, 2009, Pages 441-452

  Patidar, Vinod ^a   Sud, K K ^a   Pareek, N K ^b  

^a SIR PADAMPAT SINGHANIA UNIVERSITY   (India)

^b M L SUKHADIA UNIVERSITY   (India)

Author keywords

Cryptography; Logistic map; PRBG; Pseudo random; Random; Random bit generator; Stream cipher

Indexed keywords

LOGISTIC MAPS; PSEUDO RANDOM; RANDOM; RANDOM BIT GENERATORS; STREAM CIPHERS;

COMPUTATIONAL COMPLEXITY; CRYPTOGRAPHY; HYDRAULICS; NUMBER THEORY; PARALLEL PROCESSING SYSTEMS; STATISTICAL TESTS;

CHAOTIC SYSTEMS;

EID: 72149120032     PISSN: 03505596     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Conference Paper

References (59)

1. Schneier B. Applied Cryptography-Protocols, algorithms and source code in C. John Wiley & Sons, New York, USA, 1996.
2. Menezes A.J., Oorschot P.C.V. and Vanstone S.A. Handbook of Applied Cryptography. CRC Press, Boca Raton, 1997.
3. Alvarez G. and Li S. Some basic cryptographic requirements for chaos based cryptosystems. Int. J. of Bifur. and Chaos, vol.16, pp. 2129-2151, 2006.
4. Pareek N. K., Patidar Vinod and Sud K. K. Discrete chaotic cryptography using external secret key. Physics Letters A, vol.309, pp. 75-82, 2003.
5. Boccaletti S., Grebogi C., Lai Y.-C., Mancini H. and Maza D. The control of chaos: theory and applications. Phys. Reports, vol.329, pp. 103-197, 2000.
6. Schuster H. G. (Ed.) Hand book of chaos control. Wiley-VCH Verlag, Weinheim, Germany, 1999.
7. Kocarev, L., Halle, K. S., Eckert, K., Chua, L. O. & Parlitz, U. Experimental demonstration of secure communications via chaotic synchronization. Int. J. Bifurc. Chaos, vol.2, pp. 709-713, 1992.
8. Wu, C. W. & Chua, L. O. A simple way to synchronize chaotic systems with applications to secure communications systems. Int. J. Bifurc. Chaos, vol.3, pp. 1619-1627, 1993.
9. Cuomo, K. M., Openheim, A. V. & Strogatz, S. H. Synchronization of lorenz-based chaotic circuits with applications to communications. IEEE Trans. Circuits Syst. II, vol.40, pp. 626-633, 1993.
10. Morgul, O. & Feki, M. A chaotic masking scheme by using synchronized chaotic systems. Phys. Lett. A, vol.251, pp. 169-176, 1999.
11. Shahruz, S. M., Pradeep, A. K. & Gurumoorthy, R. Design of a novel cryptosystem based on chaotic oscillators and feedback inversion. J. Sound Vibrat., vol.250, pp. 762-771, 2002.
12. Halle, K. S., Wu, C. W., Itoh, M. & Chua, L. O. Spread spectrum communication through modulation of chaos in Chua's circuit. Int. J. Bifurc. Chaos, vol.3, pp. 469-477, 1993.
13. Cuomo, K. M. & Openheim, A. V. Circuit implementation of synchronized chaos with applications to communications. Phys. Rev. Lett., vol.71, pp. 65-68, 1993.
14. Chen, J. Y., Wong, K. W., Cheng, L. M. & Shuai, J. W. A secure communication scheme based on the phase synchronization of chaotic systems. Chaos, vol.13, pp. 508-514, 2003.
15. Yang, T. & Chua, L. O. Secure communication via chaotic parameter modulation. IEEE Trans. Circuits Syst. I , vol.43, pp. 817-819, 1996. (Pubitemid 126777532)
16. Dedieu, H., Kennedy, M. P. & Hasler, M. Chaos shift keying: Modulation and demodulation of a chaotic carrier using self-synchronizing. IEEE Trans. Circuits Syst. II , vol.40, pp. 634-641, 1993.
17. Parlitz, U., Chua, L. O., Kocarev, L., Halle, K. S. & Shang, A. Transmission of digital signals by chaotic synchronization. Int. J. Bifurc. Chaos , vol.2, pp. 973-977, 1992.
18. Feldmann, U., Hasler, M. & Schwarz, W. Communication by chaotic signals: The inverse system approach. Int. J. Circuit Theory Appl. , vol.24, pp. 551-579, 1996.
19. Zhou, H. & Ling, X. Problems with the chaoticinverse system encryption approach. IEEE Trans. Circuits Syst. I, vol.44, pp. 268-271, 1997.
20. Habutsu, T., Nishio, Y., Sasase, I. & Mori, S. A secret key cryptosystem by iterating a chaotic map. in Advances in Cryptology - EUROCRYPT'91, Lecture Notes in Computer Science, vol.547, pp. 127-140, 1991 (Spinger-Verlag).
21. Pareek N. K., Patidar Vinod and Sud K. K. Cryptography using multiple one-dimensional chaotic maps. Communications in Nonlinear Science and Numerical Simulation, vol.10, pp. 715-723, 2005.
22. Pareek N. K., Patidar Vinod and Sud K. K. Image encryption using chaotic logistic map. Image and Vision Computing, vol.24, pp. 926-934, 2006.
23. Fridrich, J. Symmetric ciphers based on twodimensional chaotic maps. Int. J. Bifurc. Chaos, vol.8, pp. 1259-1284, 1998.
24. Tang, G., Liao, X. & Chen, Y. A novel method for designing S-boxes based on chaotic maps. Chaos Solitons Fractals, vol.23, pp. 413-419, 2005.
25. Kocarev, L., Jakimoski, G., Stojanovski, T. & Parlitz, U. From chaotic maps to encryption schemes. in Proc. IEEE Int. Symposium Circuits and Systems (ISCAS'98), vol.4, pp. 514-517,1998.
26. Guo, D., Cheng, L. M. & Cheng, L. L. A new symmetric probabilistic encryption scheme based on chaotic attractors of neural networks. Applied Intelligence, vol.10, pp. 71-84, 1999.
27. Jakimoski, G. & Kocarev, L. Chaos and cryptography: Block encryption ciphers based on chaotic maps. IEEE Trans. Circuits Syst. I, vol.48, pp. 163-169, 2001.
28. Wolfram, S. Cryptography with cellular automata. in Advances in Cryptology - CRYPTO'85, Lecture Notes in Computer Science, vol.218, pp. 429-432, 1985.
29. Matthews, R. A. J. On the derivation of a 'chaotic' encryption algorithm. Cryptologia, vol.XIII, 29-42, 1989.
30. Berstein, G. M. & Lieberman, M. A. Method and apparatus for generating secure random numbers using chaos. US Patent No. 5007087, 1991.
31. Zhou, H. & Ling, X. Generating chaotic secure sequences with desired statistical properties and high security. Int. J. Bifurc. Chaos, vol.7, 205-213, 1997.
32. Li, S., Mou, X. & Cai, Y. Pseudo-random bit generator based on couple chaotic systems and its application in stream-ciphers cryptography. In Progress in Cryptology - INDOCRYPT 2001, Lecture Notes in Computer Science, vol.2247, 316-329, 2001.
33. Lee, P.-H., Pei, S.-C. & Chen, Y.-Y. Generating chaotic stream ciphers using chaotic systems. Chinese J. Phys. , vol.41, 559-581, 2003.
34. Oishi S. and Inoue H. Pseudo-random number generators and chaos. Transactions of the Institute of Electronics and Communication Engineers of Japan E, vol.65, 534-541, 1982.
35. Lin T. and Chua L. O. New class of pseudo-random number generator based on chaos in digital filters. International Journal of Circuit Theory and Applications, vol.21, 473-480, 1993.
36. Andrecut M. [1998] Logistic map as a random number generator, International Journal of Modern Physics B, vol.12, 921-930.
37. Gonzalez J. A..and Pino R. Random number generator based on unpredictable chaotic functions. Computer Physics Communications, vol.120, 109-114, 1999.
38. Kolesov V. V., Belyaev R. V. and Voronov G. M. A Digital random-number generator based on the chaotic signal algorithm. Journal of Communications Technology and Electronics, vol.46, pp. 1258-1263, 2001.
39. Stojanovski T. and Kocarev L. Chaos-based random number generators - Part I: Analysis. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, vol.48, pp. 281-288, 2001.
40. Stojanovski T., Pihl J. and Kocarev L. Chaosbased random number generators - Part II: Practical realization. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, vol.48, pp. 382-385, 2001. (Pubitemid 32394189)
41. Kocarev L. and Jakimoski G. Pseudorandom bits generated by chaotic maps. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, vol.50, pp. 123-126, 2003.
42. Fu S. -M., Chen Z. -Y. and Zhou Y. -A. Chaosbased random number generators. Computer Research and Development, vol.41, pp. 749-754, 2004.
43. Huaping L., Wang S. and Gang H. Pseudo-random number generator based on coupled map lattices. International Journal of Modern Physics B, vol.18, pp. 2409-2414, 2004.
44. Li X. -M., Shen H. -B. and Yan X. -L. Characteristic analysis of a chaotic random number generator using piece-wise-linear map. Journal of Electronics and Information Technology, vol.27, pp. 874-878, 2005.
45. Liu J. Design of a chaotic random sequence and its application, Computer Engineering, vol.31, pp. 150-152, 2005.
46. Wang Y., Shen H. and Yan X. Design of a chaotic random number generator. Chinese Journal of Semiconductors, vol.26, pp. 2433-2439, 2005.
47. Wang L., Wang F. -P. and Wang Z. -J. Novel chaos-based pseudo-random number generator. Acta Physica Sinica, vol.55, pp. 3964-3968, 2006.
48. Ergun S. and Ozoguz S. Truly random number generators based on a non-autonomous chaotic oscillator. AEU-International J. Electronics & Communications, vol.62, pp. 235-242, 2007.
49. Hu Y., Liao X., Wong K.-W. and Zhou Q. A true random number generator based on mouse movement and chaotic cryptography. Chaos Solitons and Fractals, vol.40, pp. 2286-2293, 2009.
50. Patidar Vinod and Sud K. K. Anovel pseudo random bit generator based on chaotic standard map and its testing. Electronic J. of Theoretical Physics, vol.20, pp. 327-344, 2009.
51. May R.M. Simple mathematical models with very complicated dynamics. Nature, vol.261, pp. 459-467, 1976.
52. Feigenbaum M. J. The universal metric properties of nonlinear transformations. J. Stat. Phys., vol.21, pp. 669-706, 1979.
53. Feigenbaum M. J. Universal behaviour in nonlinear systems. Los Alamos Science, vol.1, pp. 4-27, 1980.
54. Litchenberg A. J. and Lieberman M. A. Regular and stochastic motion. Springer Verlag, New York, USA, 1983.
55. Runkin et al. Statistical test suite for random and pseudo random number generators for cryptographic applications. NIST special publication 800-822, 2001.
56. Marsaglia G. DIEHARD statistical tests, http://stst.fsu.edu/pub/diehard, 1995.
57. Gustafson H. et al. A computer package for measuring the strength of encryption algorithms, J. Computer Security, vol.13, pp. 687-697, 1994.
58. Knuth D. The art of computer programming: semiemperical algorithms. Addison Wesley, Reading, USA, 1998
59. nd National Information System Security Conference, http://csrc.ncsl.gov/nissc/1999/proceeding/papers/p24.pdf