Analyzing logistic map pseudorandom number generators for periodicity induced by finite precision floating-point representation

Chaos, Solitons and Fractals

Volumn 45, Issue 3, 2012, Pages 238-245

  Persohn, K J ^a   Povinelli, R J ^a  

^a Marquette University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CHAOTIC SYSTEMS; DIGITAL ARITHMETIC; LYAPUNOV METHODS; NUMBER THEORY;

CONVENTIONAL METHODS; FINITE PRECISION; HIGH-THROUGHPUT COMPUTING; INDEPENDENT TASKS; LOGISTIC MAPS; PERIODIC ORBITS; PSEUDO RANDOM NUMBER GENERATORS; PSEUDO-RANDOM NUMBERS;

RANDOM NUMBER GENERATION;

EID: 84855865205     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.chaos.2011.12.006     Document Type: Article

References (21)

1. G. Alvarez, S. Li, F. Montoya, G. Pastor, and M. Romera Breaking projective chaos synchronization secure communication using filtering and generalized synchronization Chaos Solitons Fract 24 3 2005 775 783 (Pubitemid 40114334)
2. M.S. Baptista Cryptography with chaos Phys Lett A 240 1-2 1998 50 54 (Pubitemid 128390514)
3. M. Andrecut Logistic map as a random number generator Int J Modern Phys B 12 9 1998 921 930 (Pubitemid 128527573)
4. F. Dachselt, and W. Schwarz Chaos and cryptography IEEE Trans Circ Syst I: Fundam Theory Appl 48 12 2001 1498 1509 (Pubitemid 34055371)
5. Wang F, Zhang Y, Cao T. Research of chaotic block cipher algorithm based on logistic map. In: Second international conference on intelligent computation technology and automation, 2009, ICICTA'09; 2009. p. 678 -81.
6. G. Jakimoski, and L. Kocarev Chaos and cryptography: block encryption ciphers based on chaotic maps IEEE Trans Circ Syst I: Fundam Theory Appl 48 2 2001 163 169 (Pubitemid 32254607)
7. D. Xiao, X. Liao, and S. Deng One-way hash function construction based on the chaotic map with changeable-parameter Chaos Solitons Fract 24 1 2005 65 71
8. S.K. Park, and K.W. Miller Random number generators: good ones are hard to find Commun ACM 31 10 1988 1192 1201
9. D.E. Knuth 2nd ed. The Art of Computer Programming vol. 2 1981 Addison Wesley
10. S.C. Phatak, and S.S. Rao Logistic map: a possible random-number generator Phys Rev E 51 4 1995 3670 3678
11. Jiang C, Wu S. A valid algorithm of converting chaos sequences to uniformity pseudo-random ones. In: International symposium on information engineering and electronic commerce, 2009, IEEC'09; 2009. p. 295-8.
12. A.M. Ferrenberg, D.P. Landau, and Y.J. Wong Monte Carlo simulations: hidden errors from "good" random number generators Phys Rev Lett 69 23 1992 3382 3384
13. D.H. Lehmer Mathematical methods in large-scale computing units Ann Comput Lab Harvard Univ 26 1951 141 146
14. Oracle. Java 2 platform se random class. ; 2010.
15. M. Matsumoto, and T. Nishimura Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator Trans Model Comput Simul 8 1 1998 3 30
16. Matsumoto M, Nishimura T, Hagita M, Saito M. Cryptographic Mersenne twister and Fubaki stream/block cipher, cryptology ePrint archive, Report 2005/165; 2005.
17. L. Kocarev Chaos-based cryptography: a brief overview IEEE Circ Syst Mag 1 3 2001 6 21 (Pubitemid 33778221)
18. G. Alvarez, and S. Li Some basic cryptographic requirements for chaos-based cryptosystems Int J Bifurcat Chaos 16 2006 2129 2151 (Pubitemid 44671739)
19. M.J. Feigenbaum Quantitative universality for a class of nonlinear transformations J Stat Phys 19 1 1978 25 52
20. Condor high throughput computing. .
21. Standard for floating-point arithmetic, Tech. Rep. 754-2008, IEEE; 2008.