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Design and test of pseudorandom number generator using a star network of Lorenz oscillators. (English) Zbl 1379.94033
MSC:
94A60 Cryptography
37A45 Relations of ergodic theory with number theory and harmonic analysis (MSC2010)
65C10 Random number generation in numerical analysis
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[1] Federal Information Processing Standard Publication, 197, (2001), NIST
[2] Alvarez, G.; Li, S., Some basic cryptographic requirements for chaos-based cryptosystems, Int. J. Bifurcation and Chaos, 16, 2129-2151, (2006) · Zbl 1192.94088
[3] Barakat, M. L.; Manisingka, A. S.; Radwan, A. G.; Salama, K. N., Hardware stream cipher with controllable chaos generator for colour image encryption, IET Imag. Process., 8, 33-43, (2014)
[4] Bennett, C. H.; Brassard, G., Quantum cryptography: public key distribution and coin tossing, Proc. IEEE Int. Conf. Comput. Syst. Sign. Process., 1, 175-179, (1984)
[5] Camargo, S.; Vianna, R. L.; Anteneodo, C., Intermingled basin in coupled Lorenz systems, Phys. Rev. E, 85, 036207-1-10, (2012)
[6] Cho, K.; Miyano, T.; Toriyama, T., Chaotic gas turbine subject to augmented Lorenz equations, Phys. Rev. E, 86, 036308-1-12, (2012)
[7] Cho, K. & Miyano, T. [2015] “Chaotic cryptography using augmented Lorenz equations aided by quantum key distribution,” IEEE Trans. Circuits Syst.-I — Reg. Papers62, 478-487.
[8] Cho, K.; Miyano, T., Entropy test for complexity in chaotic time series, NOLTA, IEICE, 7, 21-29, (2016)
[9] Cho, K.; Miyano, T., Intermittent and partial synchrony of coupled augmented Rössler oscillators, NOLTA, IEICE., (2018)
[10] Cuomo, K. M.; Oppenheim, A. V., Circuit implementation of synchronized chaos with application to communications, Phys. Rev. Lett., 71, 65-68, (1993)
[11] Cuomo, K. M.; Oppenheim, A. V.; Strogatz, S. H., Synchronization of Lorenz-based chaotic circuits with applications to communications, IEEE Trans. Circuits Syst.-II — Anal. Digit. Sign. Process., 40, 626-633, (1993)
[12] Dedieu, H.; Kennedy, M.; Hasler, M., Chaos shift keying: modulation and demodulation of a chaotic carrier using self-synchronizing chua’s circuits, IEEE Trans. Circuits Syst.-II — Anal. Digit. Sign. Process., 40, 634-642, (1993)
[13] Ekdahl, P.; Johansson, T., Selected Areas in Cryptography 2002, 2595, A new version of the stream cipher SNOW, 47-61, (2003), Springer · Zbl 1027.68596
[14] Ekert, A. K., Quantum cryptography based on bell’s theorem, Phys. Rev. Lett., 67, 661-663, (1991) · Zbl 0990.94509
[15] eSTREAM [2012] The ECRYPT stream cipher project, http://www.ecrypt.eu.org/stream/index.html. Last updated in March 2012.
[16] Gisin, N.; Ribordy, G.; Tittel, W.; Zbinden, H., Quantum cryptography, Rev. Mod. Phys., 74, 145-195, (2002) · Zbl 1371.81006
[17] Hamalainen, P.; Hannikainen, M.; Hamalainen, T.; Saarinen, J., Hardware implementation of the improved WEP and RC4 encryption algorithms for wireless terminals, Proc. Eur. Signal Proc. Conf., 2289-2292, (2000)
[18] Hayes, S.; Grebogi, C.; Ott, E.; Mark, A., Experimental control of chaos for communications, Phys. Rev. Lett., 73, 1781-1784, (1994)
[19] Killmann, W. & Schindler, W. [2011] “A proposal for functionality classes and evaluation methodology for true (physical) random number generators,” version 3.1, 25.09.2001, mathematical-technical reference of [16] (English translation); www.bsi.bund.de/ zertifiz/zert/interpr/trngk31e.pdf.
[20] Lai, Y.; Bolt, E.; Grebogi, C., Communicating with chaos using two-dimensional symbolic dynamics, Phys. Lett. A, 255, 75-81, (1999)
[21] L’Ecuyer, P.; Simard, R., Testu01: A C library for empirical testing of random number generators, ACM Trans. Math. Soft., 33, 1-40, (2007) · Zbl 1365.65008
[22] Li, C.; Zhang, Y.; Ou, R.; Wong, K. W., Breaking a novel colour image encryption algorithm based on chaos, Nonlin. Dyn., 70, 2383-2388, (2012)
[23] Li, J.; Liu, H., Colour image encryption based on advanced encryption standard algorithm with two-dimensional chaotic map, IET Inf. Secur., 7, 265-270, (2013)
[24] Li, C.; Xie, T.; Liu, Q.; Cheng, G., Cryptanalyzing image encryption using chaotic logistic map, Nonlin. Dyn., 78, 1545-1551, (2014)
[25] Masuda, N., Jakimoski, G., Aihara, K. & Kocarev, L. [2006] “Chaotic block ciphers: From theory to practical algorithms,” IEEE Trans. Circuits Syst.-I — Reg. Papers53, 1341-1352. · Zbl 1374.94796
[26] Munir, R., Security analysis of selective image encryption algorithm based on chaos and CBC-like mode, Proc. 7th Int. Conf. Telecommun. Syst. Service. Appl., 142-146, (2012)
[27] Murillo-Escobar, M. A.; Cruz-Hernández, C.; Abundiz-Pérez, F.; López-Guitiérrez, R. M.; Acosta Del Campo, O. R., A RGB image encryption algorithm based on total plain image characteristics and chaos, Sign. Process., 109, 119-131, (2015)
[28] Ott, E.; Sommerer, J. C., Blowout bifurcations: the occurrence of riddled basins and on-off intermittency, Phys. Lett. A, 188, 39-47, (1994)
[29] Rössler, O. E., An equation for continuous chaos, Phys. Lett. A, 57, 397-398, (1976) · Zbl 1371.37062
[30] Rukhin, A., Soto, J., Nechvatal, J., Smid, M., Barker, E., Leigh, S., Levenson, M., Vangel, M., Banks, D., Heckert, A., Dray, J. & Vo, S. [2010] “A statistical test suite for random and pseudorandom number generators for cryptographic applications,” NIST Special Publication 800-22, Revision 1a (Revised April 2010).
[31] Schindler, W. [1999] “Functionality classes and evaluation methodology for deterministic random number generators,” version 2.0, 02.12.1999, mathematical-technical reference of [15] (English translation); www. bsi.bund.de/zertifiz/zert/interpr/ais20e.pdf.
[32] Shannon, C. E., Communication theory of secrecy systems, Bell Syst. Tech. J., 28-4, 656-715, (1949) · Zbl 1200.94005
[33] Tong, X.; Cui, M., Image encryption with compound chaotic sequence cipher shifting dynamically, Imag. Vis. Comput., 26, 843-850, (2008)
[34] Wang, X.; Teng, L.; Qin, X., A novel colour image encryption algorithm based on chaos, Sign. Process., 92, 1101-1108, (2012)
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