Noise and Chaos Contributions in Fast Random Bit Sequence Generated From Broadband Optoelectronic Entropy Sources

During the last 4 years, chaotic waveforms for random number generation found a deep interest within the community of analogue broadband chaotic optical systems. Earlier investigations on chaos-based RNG were proposed in the 90s and early 2000, however mainly based on piecewise linear (PL) 1D map, with bit rate determined by analog electronic processing capabilities to provide the PL nonlinear function of concern. Optical chaos came with promises for much higher bit rate, and entropy sources based on high complexity (high dimensional) continuous time (differential) dynamics. More specifically in 2009, Reidler published a paper entitled “An optical ultrafast random bit generator”, in which they presented a physical system for a random number generator based on a chaotic semiconductor laser. This generator is claimed to reach potentially the extremely high rate of 300 Gb/s. We report on analysis and experiments of their method, which leads to the discussion about the actual origin of the obtained randomness. Through standard signal theory arguments, we show that the actual binary randomness quality obtained from this method, can be interpreted as a complex mixing operated on the initial analogue entropy source. Our analysis suggests an explanation about the already reported issue that this method does not necessarily require any specific deterministic property (i.e., chaos) from the physical signal used as the source of entropy. The bit stream randomness quality is found to result from “aliasing” phenomena performed by the post-processing method, both for the sampling and the quantization operations. As an illustration, such random bit sequences extracted from different entropy sources are investigated. Optoelectronic noise is used as a non deterministic entropy source. Electro-optic phase chaotic signal, as well as simulations of its deterministic model, are used as deterministic entropy sources. In all cases, the extracted bit sequence reveals excellent randomness.

[1]  Romain Modeste Nguimdo,et al.  Electro-optic phase chaos systems with an internal variable and a digital key. , 2012, Optics express.

[2]  Jacques M. Bahi,et al.  Randomness Quality of CI Chaotic Generators: Applications to Internet Security , 2010, 2010 2nd International Conference on Evolving Internet.

[3]  Laurent Larger,et al.  Crenelated fast oscillatory outputs of a two-delay electro-optic oscillator. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  G. Taylor,et al.  Digital randomness , 2011, IEEE Spectrum.

[6]  S. Deligiannidis,et al.  Implementation of 140 Gb/s true random bit generator based on a chaotic photonic integrated circuit. , 2010, Optics express.

[7]  P ? ? ? ? ? ? ? % ? ? ? ? , 1991 .

[8]  Christoph Meinel,et al.  Digital Communication , 2014, X.media.publishing.

[9]  Rajarshi Roy,et al.  Chaotic lasers: The world's fastest dice , 2008 .

[10]  Rajarshi Roy,et al.  Scalable parallel physical random number generator based on a superluminescent LED. , 2011, Optics letters.

[11]  Adonis Bogris,et al.  Chaos-based communications at high bit rates using commercial fibre-optic links , 2006, SPIE/OSA/IEEE Asia Communications and Photonics.

[12]  T. Yamazaki,et al.  Performance of Random Number Generators Using Noise-Based Superluminescent Diode and Chaos-Based Semiconductor Lasers , 2013, IEEE Journal of Selected Topics in Quantum Electronics.

[13]  Alessandro Trifiletti,et al.  A High-Speed Oscillator-Based Truly Random Number Source for Cryptographic Applications on a Smart Card IC , 2003, IEEE Trans. Computers.

[14]  Atsushi Uchida,et al.  Fast random bit generation with bandwidth-enhanced chaos in semiconductor lasers. , 2010, Optics express.

[15]  Greg M. Bernstein,et al.  Secure random number generation using chaotic circuits , 1990 .

[16]  Thierry Paul,et al.  Quantum computation and quantum information , 2007, Mathematical Structures in Computer Science.

[17]  Donald E. Eastlake,et al.  Randomness Requirements for Security , 2005, RFC.

[18]  R. Gallager.  Principles of Digital Communication , 2008 .

[19]  Alfred Menezes,et al.  Handbook of Applied Cryptography , 2018 .

[20]  I. Kanter,et al.  An optical ultrafast random bit generator , 2010 .

[21]  Mukai,et al.  New route to optical chaos: Successive-subharmonic-oscil- lation cascade in a semiconductor laser coupled to an external cavity. , 1985, Physical review letters.

[22]  Laurent Larger,et al.  Random walks and random numbers from supercontinuum generation. , 2012, Optics express.

[23]  J. F. Dynes,et al.  A high speed , postprocessing free , quantum random number generator , 2008 .

[24]  Caitlin R. S. Williams,et al.  Fast physical random number generator using amplified spontaneous emission. , 2010, Optics express.

[25]  S. Yoshimori,et al.  Characteristics of Fast Physical Random Bit Generation Using Chaotic Semiconductor Lasers , 2009, IEEE Journal of Quantum Electronics.

[26]  I Kanter,et al.  Ultrahigh-speed random number generation based on a chaotic semiconductor laser. , 2009, Physical review letters.

[27]  Sze-Chun Chan,et al.  Random bit generation using an optically injected semiconductor laser in chaos with oversampling. , 2012, Optics letters.

[28]  Douglas R. Stinson,et al.  Cryptography: Theory and Practice , 1995 .

[29]  A. Uchida,et al.  Fast physical random bit generation with chaotic semiconductor lasers , 2008 .

[30]  Carroll,et al.  Synchronization in chaotic systems. , 1990, Physical review letters.

[31]  Pu Li,et al.  Direct generation of all-optical random numbers from optical pulse amplitude chaos. , 2012, Optics express.

[32]  M. Peil,et al.  Electro-optic delay oscillator with nonlocal nonlinearity: Optical phase dynamics, chaos, and synchronization. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[33]  Elaine B. Barker,et al.  A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications , 2000 .

[34]  Romain Modeste Nguimdo,et al.  Fast random bit generation based on a single chaotic semiconductor ring laser , 2013 .

[35]  Ingo Fischer,et al.  Dynamics of a semiconductor laser with polarization-rotated feedback and its utilization for random bit generation. , 2011, Optics letters.

[36]  D. Syvridis,et al.  Sub-Tb/s Physical Random Bit Generators Based on Direct Detection of Amplified Spontaneous Emission Signals , 2012, Journal of Lightwave Technology.

[37]  L. Larger,et al.  Nonlocal Nonlinear Electro-Optic Phase Dynamics Demonstrating 10 Gb/s Chaos Communications , 2010, IEEE Journal of Quantum Electronics.

[38]  Tohru Ikeguchi,et al.  Estimation of entropy rate in a fast physical random-bit generator using a chaotic semiconductor laser with intrinsic noise. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[39]  C. Luchini,et al.  [High speed]. , 1969, Revista De La Escuela De Odontologia, Universidad Nacional De Tucuman, Facultad De Medicina.

[40]  L. Kocarev,et al.  Chaos-based random number generators-part I: analysis [cryptography] , 2001 .

[41]  B. Widrow,et al.  Statistical theory of quantization , 1996 .