Fast random bit generation with bandwidth-enhanced chaos in semiconductor lasers

Hirano, Kunihito; Yamazaki, T.; Morikatsu, Shinichiro; Okumura, Haruka; Aida, Hiroki; Uchida, Atsushi; Yoshimori, Shigeru; Yoshimura, Kazuyuki; Harayama, Takahisa; Davis, Peter

doi:10.1364/oe.18.005512

Cited by 186 publications

(105 citation statements)

References 22 publications

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“…By making the time-delays of both external cavities and the sampling time of the ADC incommensurate, a 1.7 Gb/s sequence of bits that passed randomness statistical tests was achieved. Shortly afterwards, this scheme was simplified using only one chaotic laser diode and comparing its digitized output with a time-shifted version of it 107 (Fig 4b). Again, the time-shift, time-delay of the external-cavity and sampling clock time must be incommensurate to avoid any recurrence in the output.…”

Section: Random Number Generationmentioning

confidence: 99%

Physics and applications of laser diode chaos

Sciamanna¹,

Shore²

2015

Nature Photon

580

327

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-An overview of chaos in laser diodes is provided which surveys experimental achievements in the area and explains the theory behind the phenomenon. The fundamental physics underpinning this behaviour and also the opportunities for harnessing laser diode chaos for potential applications are discussed. The availability and ease of operation of laser diodes, in a wide range of configurations, make them a convenient test-bed for exploring basic aspects of nonlinear and chaotic dynamics. It also makes them attractive for practical tasks, such as chaos-based secure communications and random number generation. Avenues for future research and development of chaotic laser diodes are also identified.The emergence of irregular pulsations and dynamical instabilities from a laser were first noted in the very early stages of the laser development. Pulses whose amplitude "vary in an erratic manner" were reported in the output of the ruby solid-state laser 1 [ Fig. 1 a] and then found in numerical simulations 2 . However the lack of knowledge of what would later be termed "chaos" resulted in these initial observations being either left unexplained or wrongly attributed to noise.The situation changed in the late 1960s with the discovery of sensitivity to initial conditions by Lorenz 3 , later popularized as the "butterfly effect". As illustrated in Fig. 1 (b), numerical simulations of a deterministic model of only three nonlinear equations showed an irregular pulsing with a remarkable feature: the state variables evolve along very different trajectories despite starting from approximately the same initial values [ Fig. 1 b]. The distance δ(t) between nearby trajectories diverges exponentially : δ(t) = δ(0) exp(λt) provided that λ, the effective Lyapunov exponent of the dynamical system, is positive. Consequently such systems are unpredictable in the long term. Plotted in the x-y-z phase space of the state variables, the trajectories converge to an "attractor" which has the geometric property of being bounded in space despite the exponential divergence of nearby trajectories [ Fig. 1 c]. Such attractors are found to have a fractional dimension 4 and are thus termed strange. Aperiodicity, sensitive dependency to initial conditions and strangeness are commonly considered as the main properties for "chaos" The fields of laser physics and chaos theory developed independently until 1975 8 when Haken discovered a striking analogy between the Lorenz equations that model fluid convection and the MaxwellBloch equations modelling light-matter interaction in single-mode lasers. The nonlinear interaction between the wave propagation in the laser cavity (represented by the electric field E) and radiative recombination producing macroscopic polarization (encapsulated in the polarization P and carrier inversion N) yield similar dynamical instabilities to those found in the Lorenz equations. More specifically, in addition to the conventional laser threshold, Haken suggested a second threshold would exist above which "spiking occurs ...

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Section: Random Number Generationmentioning

confidence: 99%

Physics and applications of laser diode chaos

Sciamanna¹,

Shore²

2015

Nature Photon

580

327

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“…As ECLs are recognized as being simple and inexpensive sources of high-dimensional chaos [30], as is of interest for applications such as chaos radar [15] and ultrahigh rate randombit generation [16][17][18], our work demonstrates the ability to generate such microwave signals …”

mentioning

confidence: 92%

“…It is notable that certain applications [14] of chaotic laser dynamics, and in particular chaotic radar [15] and ultrahigh-rate random-bit generation [16][17][18], do not intrinsically make use of the chaotic optical signal, but of an electrical signal detected by one or more PDs. These comments also apply for the work cited above on the generation of periodic microwave signals: a PD separate from the LD is always necessary to create an electrical signal while the optical signal itself is often not used directly [unless low-loss optical transmission of the signal is needed prior to optical-to-electrical (O/E) conversion].…”

mentioning

confidence: 99%

A multi-GHz chaotic optoelectronic oscillator based on laser terminal voltage

Chang

Choi

Locquet

et al. 2016

Applied Physics Letters

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A multi-GHz chaotic optoelectronic oscillator based on an external cavity semiconductor laser (ECL) is demonstrated. Unlike standard optoelectronic oscillators for microwave applications, we do not employ the dynamic light output incident on a photodiode to generate the microwave signal, but instead generate the microwave signal directly by measuring the terminal voltage V (t) of the laser diode of the ECL under constant-current operation, thus obviating the photodiode entirely.

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“…This method is cited in Ref. 10. This operation is an integral part of any evaluation of physical-random-numbers when we use the examination method for pseudo-random number's randomness, such as NIST SP 800-22 tests.…”

Section: Resultsmentioning

confidence: 99%

Frequency noise characteristics of a diode laser and its application to physical random number generation

et al. 2013

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Abstract. We describe a method of generating physical random numbers by means of a diode laser that has an extremely wide-band frequencynoise profile. Fluctuations in the laser frequency affect the intensity of the light transmitted through the optical frequency discriminator, detected thereafter as random fluctuations. This allows us to simultaneously generate 8 random bit streams, due to the parallel processing of 8-digit binary numbers sampled by an 8-bit analog-to-digital converter. Finally, we generated physical random numbers at a rate of 3 Gbit∕s, by combining one data stream with another stream that is delayed by 2 ms, by exclusive-OR.

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Fast random bit generation with bandwidth-enhanced chaos in semiconductor lasers

Cited by 186 publications

References 22 publications

Physics and applications of laser diode chaos

Physics and applications of laser diode chaos

A multi-GHz chaotic optoelectronic oscillator based on laser terminal voltage

Frequency noise characteristics of a diode laser and its application to physical random number generation

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