Abstract

The chaotic light signals generated by an external cavity semiconductor laser have been experimentally demonstrated to extract fast random numbers. However, the photon round-trip time in the external cavity can cause the occurrence of the periodicity in random sequences. To overcome it, the exclusive-or operation on corresponding random bits in samples of the chaotic signal and its time-delay signal from a chaotic laser is required. In this scheme, the proper selection of delay length is a key issue. By doing a large number of experiments and theoretically analyzing the interplay between the Runs test and the threshold value of the autocorrelation function, we find when the corresponding delay time of autocorrelation trace with the correlation coefficient of less than 0.007 is considered as the delay time between the chaotic signal and its time-delay signal, streams of random numbers can be generated with verified randomness.

© 2012 Optical Society of America

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References

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2011

J. Z. Zhang, A. B. Wang, M. J. Zhang, X. C. Li, and Y. C. Wang, “Elimination of time-delay signature in an external cavity semiconductor laser by randomly modulating feedback phase,” Acta Phys. Sin. 60, 094207 (2011).

T. Harayama, S. Sunada, K. Yoshimura, P. Davis, K. Tsuzuki, and A. Uchida, “Fast nondeterministic random-bit generation using on-chip chaos lasers,” Phys. Rev. A 83, 031803 (2011).
[CrossRef]

Y. Y. Zhang, J. Z. Zhang, M. J. Zhang, and Y. C. Wang, “2.87  Gb/s random bit generation based on bandwidth-enhanced chaotic laser,” Chin. Opt. Lett. 9, 031404 (2011).
[CrossRef]

2010

2009

2008

A. Argyris, M. Hamacher, K. E. Chlouverakis, A. Bogris, and D. Syvridis, “Photonic integrated device for chaos applications in communications,” Phys. Rev. Lett. 100, 194101 (2008).
[CrossRef]

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photon. 2, 728–732 (2008).
[CrossRef]

A. B. Wang, Y. C. Wang, and H. C. He, “Enhancing the bandwidth of the optical chaotic signal generated by a semiconductor laser with optical feedback,” IEEE Photon. Technol. Lett. 20, 1633–1635 (2008).
[CrossRef]

2005

2003

S. K. Hwang and J. M. Liu, “Dynamical characteristics of an optically injected semiconductor laser,” Opt. Commun. 183, 195–205 (2003).
[CrossRef]

2001

T. Stojanovski and L. Kocarev, “Chaos-based random number generators—part I: analysis,” IEEE Trans. Circuits Syst. I 48, 281–288 (2001).
[CrossRef]

T. Stojanovski, J. Pihl, and L. Kocarev, “Chaos-based random number generators-part II: Practical realization,” IEEE Trans. Circuits Syst. I 48, 382–385 (2001).
[CrossRef]

S. Tang and J. M. Liu, “Chaotic pulsing and quasi-periodic route to chaos in a semiconductor laser with delayed opto-electronic feedback,” IEEE J. Quantum Electron. 37, 329–336(2001).
[CrossRef]

2000

C. S. Petrie and J. A. Connelly, “A noise-based IC random number generator for applications in cryptography,” IEEE Trans. Circuits Syst. I 47, 615–621 (2000).
[CrossRef]

Aida, H.

Amano, K.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photon. 2, 728–732 (2008).
[CrossRef]

Argyris, A.

A. Argyris, S. Deligiannidis, E. Pikasis, A. Bogris, and D. Syvridis, “Implementation of 140 Gb/s true random bit generator based on a chaotic photonic integrated circuit,” Opt. Express 18, 18763–18768 (2010).
[CrossRef]

A. Argyris, M. Hamacher, K. E. Chlouverakis, A. Bogris, and D. Syvridis, “Photonic integrated device for chaos applications in communications,” Phys. Rev. Lett. 100, 194101 (2008).
[CrossRef]

Aviad, Y.

I. Kanter, M. Butkovski, Y. Peteg, M. Zigzag, Y. Aviad, I. Reidler, M. Rosenbluh, and W. Kinzel, “Synchronization of random bit generators based on coupled chaotic lasers and application to cryptography,” Opt. Express 18, 18292–18302 (2010).
[CrossRef]

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photon. 4, 58–61 (2010).
[CrossRef]

I. Reidler, Y. Aviad, M. Rosenbluh, and I. Kanter, “Ultrahigh-speed random number generation based on a chaotic semiconductor laser,” Phys. Rev. Lett. 103, 024102 (2009).
[CrossRef]

Banks, D.

A. Rukhin, J. Soto, J. Nechvatal, M. Smid, E. Barker, S. Leigh, M. Levenson, M. Vangel, D. Banks, A. Heckert, J. Dray, and S. Vo, “A statistical test suite for random and pseudorandom number generators for cryptographic applications,” NIST Spec. Publ. 800–22, rev. 1 (2008).

Barker, E.

A. Rukhin, J. Soto, J. Nechvatal, M. Smid, E. Barker, S. Leigh, M. Levenson, M. Vangel, D. Banks, A. Heckert, J. Dray, and S. Vo, “A statistical test suite for random and pseudorandom number generators for cryptographic applications,” NIST Spec. Publ. 800–22, rev. 1 (2008).

Bogris, A.

A. Argyris, S. Deligiannidis, E. Pikasis, A. Bogris, and D. Syvridis, “Implementation of 140 Gb/s true random bit generator based on a chaotic photonic integrated circuit,” Opt. Express 18, 18763–18768 (2010).
[CrossRef]

A. Argyris, M. Hamacher, K. E. Chlouverakis, A. Bogris, and D. Syvridis, “Photonic integrated device for chaos applications in communications,” Phys. Rev. Lett. 100, 194101 (2008).
[CrossRef]

Butkovski, M.

Chlouverakis, K. E.

A. Argyris, M. Hamacher, K. E. Chlouverakis, A. Bogris, and D. Syvridis, “Photonic integrated device for chaos applications in communications,” Phys. Rev. Lett. 100, 194101 (2008).
[CrossRef]

Cho, Y. W.

Cohen, E.

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photon. 4, 58–61 (2010).
[CrossRef]

Connelly, J. A.

C. S. Petrie and J. A. Connelly, “A noise-based IC random number generator for applications in cryptography,” IEEE Trans. Circuits Syst. I 47, 615–621 (2000).
[CrossRef]

Davis, P.

T. Harayama, S. Sunada, K. Yoshimura, P. Davis, K. Tsuzuki, and A. Uchida, “Fast nondeterministic random-bit generation using on-chip chaos lasers,” Phys. Rev. A 83, 031803 (2011).
[CrossRef]

K. Hirano, T. Yamazaki, S. Morikatsu, H. Okumura, H. Aida, A. Uchida, S. Yoshimori, K. Yoshimura, T. Harayama, and P. Davis, “Fast random bit generation with bandwidth-enhanced chaos in semiconductor lasers,” Opt. Express 18, 5512–5524 (2010).
[CrossRef]

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photon. 2, 728–732 (2008).
[CrossRef]

Deligiannidis, S.

Dray, J.

A. Rukhin, J. Soto, J. Nechvatal, M. Smid, E. Barker, S. Leigh, M. Levenson, M. Vangel, D. Banks, A. Heckert, J. Dray, and S. Vo, “A statistical test suite for random and pseudorandom number generators for cryptographic applications,” NIST Spec. Publ. 800–22, rev. 1 (2008).

Fan, L. L.

Fürst, M.

Hamacher, M.

A. Argyris, M. Hamacher, K. E. Chlouverakis, A. Bogris, and D. Syvridis, “Photonic integrated device for chaos applications in communications,” Phys. Rev. Lett. 100, 194101 (2008).
[CrossRef]

Harayama, T.

T. Harayama, S. Sunada, K. Yoshimura, P. Davis, K. Tsuzuki, and A. Uchida, “Fast nondeterministic random-bit generation using on-chip chaos lasers,” Phys. Rev. A 83, 031803 (2011).
[CrossRef]

K. Hirano, T. Yamazaki, S. Morikatsu, H. Okumura, H. Aida, A. Uchida, S. Yoshimori, K. Yoshimura, T. Harayama, and P. Davis, “Fast random bit generation with bandwidth-enhanced chaos in semiconductor lasers,” Opt. Express 18, 5512–5524 (2010).
[CrossRef]

He, H. C.

A. B. Wang, Y. C. Wang, and H. C. He, “Enhancing the bandwidth of the optical chaotic signal generated by a semiconductor laser with optical feedback,” IEEE Photon. Technol. Lett. 20, 1633–1635 (2008).
[CrossRef]

Heckert, A.

A. Rukhin, J. Soto, J. Nechvatal, M. Smid, E. Barker, S. Leigh, M. Levenson, M. Vangel, D. Banks, A. Heckert, J. Dray, and S. Vo, “A statistical test suite for random and pseudorandom number generators for cryptographic applications,” NIST Spec. Publ. 800–22, rev. 1 (2008).

Hirano, K.

K. Hirano, T. Yamazaki, S. Morikatsu, H. Okumura, H. Aida, A. Uchida, S. Yoshimori, K. Yoshimura, T. Harayama, and P. Davis, “Fast random bit generation with bandwidth-enhanced chaos in semiconductor lasers,” Opt. Express 18, 5512–5524 (2010).
[CrossRef]

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photon. 2, 728–732 (2008).
[CrossRef]

Hwang, S. K.

S. K. Hwang and J. M. Liu, “Dynamical characteristics of an optically injected semiconductor laser,” Opt. Commun. 183, 195–205 (2003).
[CrossRef]

Inoue, M.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photon. 2, 728–732 (2008).
[CrossRef]

Jun, B.

B. Jun and P. Kocher, “The Intel random number generator,” white paper prepared for Intel Corporation (1999).

Kanter, I.

I. Kanter, M. Butkovski, Y. Peteg, M. Zigzag, Y. Aviad, I. Reidler, M. Rosenbluh, and W. Kinzel, “Synchronization of random bit generators based on coupled chaotic lasers and application to cryptography,” Opt. Express 18, 18292–18302 (2010).
[CrossRef]

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photon. 4, 58–61 (2010).
[CrossRef]

I. Reidler, Y. Aviad, M. Rosenbluh, and I. Kanter, “Ultrahigh-speed random number generation based on a chaotic semiconductor laser,” Phys. Rev. Lett. 103, 024102 (2009).
[CrossRef]

Kim, Y. H.

Kinzel, W.

Kocarev, L.

T. Stojanovski, J. Pihl, and L. Kocarev, “Chaos-based random number generators-part II: Practical realization,” IEEE Trans. Circuits Syst. I 48, 382–385 (2001).
[CrossRef]

T. Stojanovski and L. Kocarev, “Chaos-based random number generators—part I: analysis,” IEEE Trans. Circuits Syst. I 48, 281–288 (2001).
[CrossRef]

Kocher, P.

B. Jun and P. Kocher, “The Intel random number generator,” white paper prepared for Intel Corporation (1999).

Kong, L. Q.

Kurashige, T.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photon. 2, 728–732 (2008).
[CrossRef]

Kurtsiefer, C.

Kwon, O.

Leigh, S.

A. Rukhin, J. Soto, J. Nechvatal, M. Smid, E. Barker, S. Leigh, M. Levenson, M. Vangel, D. Banks, A. Heckert, J. Dray, and S. Vo, “A statistical test suite for random and pseudorandom number generators for cryptographic applications,” NIST Spec. Publ. 800–22, rev. 1 (2008).

Levenson, M.

A. Rukhin, J. Soto, J. Nechvatal, M. Smid, E. Barker, S. Leigh, M. Levenson, M. Vangel, D. Banks, A. Heckert, J. Dray, and S. Vo, “A statistical test suite for random and pseudorandom number generators for cryptographic applications,” NIST Spec. Publ. 800–22, rev. 1 (2008).

Li, P.

Li, X. C.

J. Z. Zhang, A. B. Wang, M. J. Zhang, X. C. Li, and Y. C. Wang, “Elimination of time-delay signature in an external cavity semiconductor laser by randomly modulating feedback phase,” Acta Phys. Sin. 60, 094207 (2011).

Liu, J. M.

S. K. Hwang and J. M. Liu, “Dynamical characteristics of an optically injected semiconductor laser,” Opt. Commun. 183, 195–205 (2003).
[CrossRef]

S. Tang and J. M. Liu, “Chaotic pulsing and quasi-periodic route to chaos in a semiconductor laser with delayed opto-electronic feedback,” IEEE J. Quantum Electron. 37, 329–336(2001).
[CrossRef]

Ma, H. Q.

Marangon, D. G.

Morikatsu, S.

Naito, S.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photon. 2, 728–732 (2008).
[CrossRef]

Nauerth, S.

Nechvatal, J.

A. Rukhin, J. Soto, J. Nechvatal, M. Smid, E. Barker, S. Leigh, M. Levenson, M. Vangel, D. Banks, A. Heckert, J. Dray, and S. Vo, “A statistical test suite for random and pseudorandom number generators for cryptographic applications,” NIST Spec. Publ. 800–22, rev. 1 (2008).

Okumura, H.

Oowada, I.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photon. 2, 728–732 (2008).
[CrossRef]

Peteg, Y.

Petrie, C. S.

C. S. Petrie and J. A. Connelly, “A noise-based IC random number generator for applications in cryptography,” IEEE Trans. Circuits Syst. I 47, 615–621 (2000).
[CrossRef]

Pihl, J.

T. Stojanovski, J. Pihl, and L. Kocarev, “Chaos-based random number generators-part II: Practical realization,” IEEE Trans. Circuits Syst. I 48, 382–385 (2001).
[CrossRef]

Pikasis, E.

Reidler, I.

I. Kanter, M. Butkovski, Y. Peteg, M. Zigzag, Y. Aviad, I. Reidler, M. Rosenbluh, and W. Kinzel, “Synchronization of random bit generators based on coupled chaotic lasers and application to cryptography,” Opt. Express 18, 18292–18302 (2010).
[CrossRef]

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photon. 4, 58–61 (2010).
[CrossRef]

I. Reidler, Y. Aviad, M. Rosenbluh, and I. Kanter, “Ultrahigh-speed random number generation based on a chaotic semiconductor laser,” Phys. Rev. Lett. 103, 024102 (2009).
[CrossRef]

Rosenbluh, M.

I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photon. 4, 58–61 (2010).
[CrossRef]

I. Kanter, M. Butkovski, Y. Peteg, M. Zigzag, Y. Aviad, I. Reidler, M. Rosenbluh, and W. Kinzel, “Synchronization of random bit generators based on coupled chaotic lasers and application to cryptography,” Opt. Express 18, 18292–18302 (2010).
[CrossRef]

I. Reidler, Y. Aviad, M. Rosenbluh, and I. Kanter, “Ultrahigh-speed random number generation based on a chaotic semiconductor laser,” Phys. Rev. Lett. 103, 024102 (2009).
[CrossRef]

Rukhin, A.

A. Rukhin, J. Soto, J. Nechvatal, M. Smid, E. Barker, S. Leigh, M. Levenson, M. Vangel, D. Banks, A. Heckert, J. Dray, and S. Vo, “A statistical test suite for random and pseudorandom number generators for cryptographic applications,” NIST Spec. Publ. 800–22, rev. 1 (2008).

Shiki, M.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photon. 2, 728–732 (2008).
[CrossRef]

Smid, M.

A. Rukhin, J. Soto, J. Nechvatal, M. Smid, E. Barker, S. Leigh, M. Levenson, M. Vangel, D. Banks, A. Heckert, J. Dray, and S. Vo, “A statistical test suite for random and pseudorandom number generators for cryptographic applications,” NIST Spec. Publ. 800–22, rev. 1 (2008).

Someya, H.

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photon. 2, 728–732 (2008).
[CrossRef]

Soto, J.

A. Rukhin, J. Soto, J. Nechvatal, M. Smid, E. Barker, S. Leigh, M. Levenson, M. Vangel, D. Banks, A. Heckert, J. Dray, and S. Vo, “A statistical test suite for random and pseudorandom number generators for cryptographic applications,” NIST Spec. Publ. 800–22, rev. 1 (2008).

Stojanovski, T.

T. Stojanovski, J. Pihl, and L. Kocarev, “Chaos-based random number generators-part II: Practical realization,” IEEE Trans. Circuits Syst. I 48, 382–385 (2001).
[CrossRef]

T. Stojanovski and L. Kocarev, “Chaos-based random number generators—part I: analysis,” IEEE Trans. Circuits Syst. I 48, 281–288 (2001).
[CrossRef]

Sunada, S.

T. Harayama, S. Sunada, K. Yoshimura, P. Davis, K. Tsuzuki, and A. Uchida, “Fast nondeterministic random-bit generation using on-chip chaos lasers,” Phys. Rev. A 83, 031803 (2011).
[CrossRef]

Syvridis, D.

A. Argyris, S. Deligiannidis, E. Pikasis, A. Bogris, and D. Syvridis, “Implementation of 140 Gb/s true random bit generator based on a chaotic photonic integrated circuit,” Opt. Express 18, 18763–18768 (2010).
[CrossRef]

A. Argyris, M. Hamacher, K. E. Chlouverakis, A. Bogris, and D. Syvridis, “Photonic integrated device for chaos applications in communications,” Phys. Rev. Lett. 100, 194101 (2008).
[CrossRef]

Tang, S.

S. Tang and J. M. Liu, “Chaotic pulsing and quasi-periodic route to chaos in a semiconductor laser with delayed opto-electronic feedback,” IEEE J. Quantum Electron. 37, 329–336(2001).
[CrossRef]

Tsuzuki, K.

T. Harayama, S. Sunada, K. Yoshimura, P. Davis, K. Tsuzuki, and A. Uchida, “Fast nondeterministic random-bit generation using on-chip chaos lasers,” Phys. Rev. A 83, 031803 (2011).
[CrossRef]

Uchida, A.

T. Harayama, S. Sunada, K. Yoshimura, P. Davis, K. Tsuzuki, and A. Uchida, “Fast nondeterministic random-bit generation using on-chip chaos lasers,” Phys. Rev. A 83, 031803 (2011).
[CrossRef]

K. Hirano, T. Yamazaki, S. Morikatsu, H. Okumura, H. Aida, A. Uchida, S. Yoshimori, K. Yoshimura, T. Harayama, and P. Davis, “Fast random bit generation with bandwidth-enhanced chaos in semiconductor lasers,” Opt. Express 18, 5512–5524 (2010).
[CrossRef]

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photon. 2, 728–732 (2008).
[CrossRef]

Vangel, M.

A. Rukhin, J. Soto, J. Nechvatal, M. Smid, E. Barker, S. Leigh, M. Levenson, M. Vangel, D. Banks, A. Heckert, J. Dray, and S. Vo, “A statistical test suite for random and pseudorandom number generators for cryptographic applications,” NIST Spec. Publ. 800–22, rev. 1 (2008).

Vo, S.

A. Rukhin, J. Soto, J. Nechvatal, M. Smid, E. Barker, S. Leigh, M. Levenson, M. Vangel, D. Banks, A. Heckert, J. Dray, and S. Vo, “A statistical test suite for random and pseudorandom number generators for cryptographic applications,” NIST Spec. Publ. 800–22, rev. 1 (2008).

Wang, A. B.

J. Z. Zhang, A. B. Wang, M. J. Zhang, X. C. Li, and Y. C. Wang, “Elimination of time-delay signature in an external cavity semiconductor laser by randomly modulating feedback phase,” Acta Phys. Sin. 60, 094207 (2011).

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[CrossRef]

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[CrossRef]

Wang, Y. C.

Y. Y. Zhang, J. Z. Zhang, M. J. Zhang, and Y. C. Wang, “2.87  Gb/s random bit generation based on bandwidth-enhanced chaotic laser,” Chin. Opt. Lett. 9, 031404 (2011).
[CrossRef]

J. Z. Zhang, A. B. Wang, M. J. Zhang, X. C. Li, and Y. C. Wang, “Elimination of time-delay signature in an external cavity semiconductor laser by randomly modulating feedback phase,” Acta Phys. Sin. 60, 094207 (2011).

P. Li, Y. C. Wang, and J. Z. Zhang, “All-optical fast random number generator,” Opt. Express 18, 20360–20369 (2010).
[CrossRef]

Y. C. Wang, L. Q. Kong, A. B. Wang, and L. L. Fan, “Coherence length tunable semiconductor laser with optical feedback,” Appl. Opt. 48, 969–973 (2009).
[CrossRef]

A. B. Wang, Y. C. Wang, and H. C. He, “Enhancing the bandwidth of the optical chaotic signal generated by a semiconductor laser with optical feedback,” IEEE Photon. Technol. Lett. 20, 1633–1635 (2008).
[CrossRef]

Weier, H.

Weinfurter, H.

Wu, L. A.

Xie, Y. J.

Yamazaki, T.

Yoshimori, S.

K. Hirano, T. Yamazaki, S. Morikatsu, H. Okumura, H. Aida, A. Uchida, S. Yoshimori, K. Yoshimura, T. Harayama, and P. Davis, “Fast random bit generation with bandwidth-enhanced chaos in semiconductor lasers,” Opt. Express 18, 5512–5524 (2010).
[CrossRef]

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[CrossRef]

Yoshimura, K.

T. Harayama, S. Sunada, K. Yoshimura, P. Davis, K. Tsuzuki, and A. Uchida, “Fast nondeterministic random-bit generation using on-chip chaos lasers,” Phys. Rev. A 83, 031803 (2011).
[CrossRef]

K. Hirano, T. Yamazaki, S. Morikatsu, H. Okumura, H. Aida, A. Uchida, S. Yoshimori, K. Yoshimura, T. Harayama, and P. Davis, “Fast random bit generation with bandwidth-enhanced chaos in semiconductor lasers,” Opt. Express 18, 5512–5524 (2010).
[CrossRef]

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photon. 2, 728–732 (2008).
[CrossRef]

Zhang, J. Z.

Y. Y. Zhang, J. Z. Zhang, M. J. Zhang, and Y. C. Wang, “2.87  Gb/s random bit generation based on bandwidth-enhanced chaotic laser,” Chin. Opt. Lett. 9, 031404 (2011).
[CrossRef]

J. Z. Zhang, A. B. Wang, M. J. Zhang, X. C. Li, and Y. C. Wang, “Elimination of time-delay signature in an external cavity semiconductor laser by randomly modulating feedback phase,” Acta Phys. Sin. 60, 094207 (2011).

P. Li, Y. C. Wang, and J. Z. Zhang, “All-optical fast random number generator,” Opt. Express 18, 20360–20369 (2010).
[CrossRef]

Zhang, M. J.

J. Z. Zhang, A. B. Wang, M. J. Zhang, X. C. Li, and Y. C. Wang, “Elimination of time-delay signature in an external cavity semiconductor laser by randomly modulating feedback phase,” Acta Phys. Sin. 60, 094207 (2011).

Y. Y. Zhang, J. Z. Zhang, M. J. Zhang, and Y. C. Wang, “2.87  Gb/s random bit generation based on bandwidth-enhanced chaotic laser,” Chin. Opt. Lett. 9, 031404 (2011).
[CrossRef]

Zhang, Y. Y.

Zigzag, M.

Acta Phys. Sin.

J. Z. Zhang, A. B. Wang, M. J. Zhang, X. C. Li, and Y. C. Wang, “Elimination of time-delay signature in an external cavity semiconductor laser by randomly modulating feedback phase,” Acta Phys. Sin. 60, 094207 (2011).

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[CrossRef]

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A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photon. 2, 728–732 (2008).
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T. Harayama, S. Sunada, K. Yoshimura, P. Davis, K. Tsuzuki, and A. Uchida, “Fast nondeterministic random-bit generation using on-chip chaos lasers,” Phys. Rev. A 83, 031803 (2011).
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A. Rukhin, J. Soto, J. Nechvatal, M. Smid, E. Barker, S. Leigh, M. Levenson, M. Vangel, D. Banks, A. Heckert, J. Dray, and S. Vo, “A statistical test suite for random and pseudorandom number generators for cryptographic applications,” NIST Spec. Publ. 800–22, rev. 1 (2008).

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Figures (7)

Fig. 1.
Fig. 1.

Experimental setup of random number generation using a chaotic laser. PC, polarization controller; OI, optical isolator; PD, photodetector; TODL, tunable optical delay line; VOA, variable optical attenuator; FM, fiber mirror; 1 bit ADC, 1 bit analog-to-digital converter consisting of a comparator and a D flip-flop; XOR, exclusive-OR.

Fig. 2.
Fig. 2.

RF spectrum of chaotic laser output. The inset shows the enlargement of the small part of the chaotic RF spectrum over 2.52.6GHz.

Fig. 3.
Fig. 3.

Autocorrelation function of the chaotic laser signal. The y-coordinate represents the correlation coefficient. The inset shows the enlargement of the short-time autocorrelation from 0 and 120 ns.

Fig. 4.
Fig. 4.

Summary of the number of passed tests for NIST SP 800–22 at different chaotic autocorrelation coefficients, which corresponds to the delay line length.

Fig. 5.
Fig. 5.

Number of passed tests for NIST SP 800–22 at different chaotic autocorrelation coefficients, which corresponds to the delay line length.

Fig. 6.
Fig. 6.

Extraction of random number sequence from chaotic signals. (a) Time series of the chaotic waveforms; (b) time series of the time-delay signal; (c) and (d) the extracted binary bit signals; (e) output random number sequence after XOR operation.

Fig. 7.
Fig. 7.

Real-time output random bit sequence from RNG experimental system. (a) The temporal waveform of the random sequence at 1.44Gbit/s after the XOR operation. (b) An eye diagram of the random sequence. (c) A random dot diagram of the random sequence. Random bit patterns with 500×500 bits are shown in a two-dimensional plane. Bits “1” and “0” are converted to white and black dots, respectively, and placed from left to right (and from top to bottom).

Tables (1)

Tables Icon

Table 1. Results of NIST SP 800–22 Statistical Tests. For “Success” Using 1000 Samples of 1-Mbit Data and Significance Level α=0.01, the P-value (Uniformity of P-values) Should Be Larger Than 0.0001 and the Proportion Should Be within the Range of 0.99±0.0094392. For the Tests that Produce Multiple P-values and Proportions, the Worst Case Is Shown

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

Vn(obs)=k=1n1r(k)+1,
r(k)={0,εk=εk+10,εkεk+1,
ρ=1nk=1n1ξkξk+1
ξkξk+1=2r(k)+1
ρ=1+1n2nVn(obs),
Pvalue=erfc[|Vn(obs)2nδ(1δ)|22nδ(1δ)],

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