### Abstract

We analyze the time for growth of bit entropy when generating nondeterministic bits using a chaotic semiconductor laser model. The mechanism for generating nondeterministic bits is modeled as a 1-bit sampling of the intensity of light output. Microscopic noise results in an ensemble of trajectories whose bit entropy increases with time. The time for the growth of bit entropy, called the memory time, depends on both noise strength and laser dynamics. It is shown that the average memory time decreases logarithmically with increase in noise strength. It is argued that the ratio of change in average memory time with change in logarithm of noise strength can be used to estimate the intrinsic dynamical entropy rate for this method of random bit generation. It is also shown that in this model the entropy rate corresponds to the maximum Lyapunov exponent.

Original language | English |
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Article number | 016211 |

Journal | Physical Review E - Statistical, Nonlinear, and Soft Matter Physics |

Volume | 85 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2012 Jan 23 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Condensed Matter Physics
- Statistical and Nonlinear Physics
- Statistics and Probability

### Cite this

*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*,

*85*(1), [016211]. https://doi.org/10.1103/PhysRevE.85.016211

**Estimation of entropy rate in a fast physical random-bit generator using a chaotic semiconductor laser with intrinsic noise.** / Mikami, Takuya; Kanno, Kazutaka; Aoyama, Kota; Uchida, Atsushi; Ikeguchi, Tohru; Harayama, Takahisa; Sunada, Satoshi; Arai, Ken Ichi; Yoshimura, Kazuyuki; Davis, Peter.

Research output: Contribution to journal › Article

*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, vol. 85, no. 1, 016211. https://doi.org/10.1103/PhysRevE.85.016211

}

TY - JOUR

T1 - Estimation of entropy rate in a fast physical random-bit generator using a chaotic semiconductor laser with intrinsic noise

AU - Mikami, Takuya

AU - Kanno, Kazutaka

AU - Aoyama, Kota

AU - Uchida, Atsushi

AU - Ikeguchi, Tohru

AU - Harayama, Takahisa

AU - Sunada, Satoshi

AU - Arai, Ken Ichi

AU - Yoshimura, Kazuyuki

AU - Davis, Peter

PY - 2012/1/23

Y1 - 2012/1/23

N2 - We analyze the time for growth of bit entropy when generating nondeterministic bits using a chaotic semiconductor laser model. The mechanism for generating nondeterministic bits is modeled as a 1-bit sampling of the intensity of light output. Microscopic noise results in an ensemble of trajectories whose bit entropy increases with time. The time for the growth of bit entropy, called the memory time, depends on both noise strength and laser dynamics. It is shown that the average memory time decreases logarithmically with increase in noise strength. It is argued that the ratio of change in average memory time with change in logarithm of noise strength can be used to estimate the intrinsic dynamical entropy rate for this method of random bit generation. It is also shown that in this model the entropy rate corresponds to the maximum Lyapunov exponent.

AB - We analyze the time for growth of bit entropy when generating nondeterministic bits using a chaotic semiconductor laser model. The mechanism for generating nondeterministic bits is modeled as a 1-bit sampling of the intensity of light output. Microscopic noise results in an ensemble of trajectories whose bit entropy increases with time. The time for the growth of bit entropy, called the memory time, depends on both noise strength and laser dynamics. It is shown that the average memory time decreases logarithmically with increase in noise strength. It is argued that the ratio of change in average memory time with change in logarithm of noise strength can be used to estimate the intrinsic dynamical entropy rate for this method of random bit generation. It is also shown that in this model the entropy rate corresponds to the maximum Lyapunov exponent.

UR - http://www.scopus.com/inward/record.url?scp=84856686385&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84856686385&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.85.016211

DO - 10.1103/PhysRevE.85.016211

M3 - Article

C2 - 22400647

AN - SCOPUS:84856686385

VL - 85

JO - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

JF - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

SN - 1063-651X

IS - 1

M1 - 016211

ER -