Abstract

A high speed physical random bit generator is applied for the first time to a gigahertz clocked quantum key distribution system. Random phase-modulation in a differential-phase-shift quantum key distribution (DPS-QKD) system is performed using a 1-Gbps random bit signal which is generated by a physical random bit generator with chaotic semiconductor lasers. Stable operation is demonstrated for over one hour, and sifted keys are successfully generated at a rate of 9.0 kbps with a quantum bit error rate of 3.2% after 25-km fiber transmission.

©2009 Optical Society of America

1. Introduction

Quantum key distribution (QKD) has been widely investigated to realize unconditional secure communication [1]. Up to now, many QKD experiments have been successfully demonstrated, and the performance of the QKD system has been improved year after year. In particular, several high speed QKD experiments have been performed [4–8]. 1–10 GHz clock differential-phase-shift QKD (DPS-QKD) experiments were done by our group [2–5]. Gigahertz clock BB84 QKD was demonstrated by a Toshiba group [6]. In order to properly implement such a high speed QKD system, a high speed physical random bit generator is indispensible. However, random bit generators using physically random processes have been too slow to satisfy this requirement. Recently, a high speed random bit generator operating at a rate of more than one gigabit per second using high-bandwidth chaotic semiconductor lasers has been demonstrated experimentally [9]. Chaotic states of semiconductor lasers were used to achieve efficient and stable generation of random bit signal at high frequency. In this paper, we report the first gigahertz clocked DPS-QKD experiment that employs a fast physical random bit generator. 1-Gbps (Gigabits per second) random bit signal which was generated by physical random bit generator with chaotic semiconductor lasers was used to perform random phase-modulation in DPS-QKD system. We successfully demonstrated a stable operation for over one hour, and achieved a sifted key generation rate of 9.0 kbps with a quantum bit error rate (QBER) of 3.2% after 25-km fiber transmission.

2. Differential-phase-shift QKD (DPS-QKD)

First of all, we briefly explain our QKD scheme. Differential-phase-shift QKD (DPS-QKD) is a new quantum key distribution scheme that was proposed by K. Inoue et al. [10]. Figure 1 shows the setup of the DPS-QKD scheme. Alice randomly phase-modulates a pulse train of weak coherent states by {0, π} for each pulse and sends it to Bob with an average photon number of less than one per pulse. Bob measures the phase difference between two sequential pulses using a 1-bit delay Mach-Zehnder interferometer and photon detectors, and records the photon arrival time and which detector clicked. After transmission of the optical pulse train, Bob tells Alice the time instances at which a photon was counted. From this time information and her modulation data, Alice knows which detector clicked at Bob’s site. Under an agreement that a click by detector 1 denotes “0” and a click by detector 2 denotes “1”, for example, Alice and Bob obtain an identical bit string.

The DPS-QKD scheme has certain advantageous features including a simple configuration, efficient time domain use, and robustness against photon number splitting attack [10,11]. In particular, a high repetition frequency is possible through the use of oneway transmission and a pulse train. The longest transmission distance and the highest key generation rate in QKD systems were demonstrated experimentally with this scheme [4].

 

Fig. 1. Schematic diagram of differential-phase-shift QKD. LD, laser diode; IM, intensity modulator; PM, phase modulator; ATT, attenuator; MZI, Mach-Zehnder interferometer.

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3. Fast physical random bit generator with chaotic semiconductor lasers

Next we describe the fast physical random bit generator. Random physical phenomena are used to realize physical random bit generators. However, so far it has not been possible to achieve gigahertz speed random bit generation using random phenomena such as photon noise, thermal noise in resistors or frequency jitter of oscillators [12–17]. Recently, a fast physical random bit generator using physical chaos in semiconductor lasers has been demonstrated experimentally [9]. By directly sampling the output of two chaotic semiconductor lasers, fast physical random bit generation at rate of up to 1.7 Gbps was realized. The amplification of intrinsic laser noise by unstable chaotic dynamics means the generated bits cannot be predicted from the previously generated bits. The random bit sequences passed all of the statistical tests of randomness in the National Institute of Standard Technology (NIST) and Diehard test suites [18–19].

Figure 2 shows a schematic diagram of the random bit generator using two chaotic lasers. Semiconductor lasers with external optical feedback are used to generate optical chaos with high-bandwidth in the gigahertz regime. Single-mode distributed-feedback lasers are modified to allow optical feedback from an external fiber reflector which reflects a fraction of the light back into the laser, which induces high-frequency chaotic oscillations. High-bandwidth chaotic intensity oscillations with different average frequency and autocorrelation characteristics are generated in two separate semiconductor lasers. In order to satisfy the condition where their largest oscillation components and the clock frequency are incommensurate, the parameters of the two lasers are adjusted to detune their chaotic oscillation, using the procedure described in [9]. The output light of each laser is converted to an electrical signal by photo-detector, amplified and converted to a binary signal using a 1-bit analog-digital converter (ADC) driven by a fast clock. The binary signals obtained from the two lasers are combined by a logical Exclusive-OR (XOR) operation to generate a single random bit signal.

 

Fig. 2. Schematic diagram of physical random bit generator with two chaotic lasers: LD, laser diode; FC, fiber coupler; VR, variable reflector; VA, variable attenuator; PD, photo diode; Amp, Amplifier; Synth, Synthesizer; ADC, analog-digital converter.

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4. Experimental setup

We implemented a 1-GHz clocked DPS-QKD system using the physical random bit generator with chaotic semiconductor lasers. Figure 3 shows the experimental setup.

For the random bit generator (RBG) we used the same experimental system as used in [9] with the clock rate reduced to generate a random bit stream at a repetition rate of 1 Gbps with the Non-Return-to-Zero (NRZ) format. The laser parameters were adjusted to achieve randomness of bit sequences at the required clock rate, following the procedure described in [9]. Specifically, we set the injection currents of 16.05 and 15.20 mA for Laser 1 and 2, respectively. The dominant frequencies of chaotic waveforms are 3.00 and 2.56 GHz. We set the external-cavity fiber lengths of 5.63 and 4.46 m for Laser 1 and 2, corresponding to the external-cavity delay times of 54.2 and 42.9 ns, respectively. It was confirmed that bit sequences generated at 1 Gbps could pass all of the 15 statistical tests of randomness in the NIST test suite [18]. Typical results of the NIST tests are shown in Table 1 for 1000 samples of 1 Mbit sequences.

Tables Icon

Table 1. Results of NIST Special Publication 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 in the range of 0.99 ± 0.0094392. For the tests which produce multiple P-values and proportions, the worst case is shown.

At Alice’s site the DPS-QKD system and the physical random bit generator were synchronized with a 1GHz clocked synthesizer. The random bit signal from the random bit generator was captured by the FPGA (Field Programmable Gate Array, XILINX Virtex-5) board. The FPGA board saved the random bit signal to the 512 MB DRAM (Dynamic Random Access Memory) in a FIFO (First In First Out) manner, and simultaneously generated a 1-GHz NRZ random signal to drive the phase modulator as described below. In the DPS-QKD system, 1-GHz master clock signal from the synthesizer was converted into 3 different synchronized clocks (1GHz, 100MHz, 10MHz) by a clock divider (National Semiconductor LMK01000). The 1-GHz clock was for a pulse generator, the 100-MHz clock was for the FPGA board and the 10-MHz clock was for the receiver’s site. A quantum channel was organized as follows. A 1551-nm continuous light from an external cavity semiconductor laser was modulated into a pulse stream with a 1-GHz clock frequency using a LiNbO3 intensity modulator. The intensity modulator was driven by the pulse generator (Picosecond Pulse Labs 3600) synchronized with the 1-GHz clock. The pulse width was 70 ps. Each pulse was randomly phase-modulated by {0, π} with a LiNbO3 phase modulator which was driven by the random bit signal from the FPGA board. The optical pulse was attenuated to 0.2 photons per pulse and then transmitted to Bob’s site over 25-km dispersion shifted fiber (DSF). The excess loss of the DSF was 5.7 dB.

The 100-kHz start signal, which indicated the head of a 10-kbit block of random bits in the sequence, was also generated by the FPGA board, and converted into an optical start pulse by a distributed feedback laser with an electro-absorption modulator (EA-DFB). The wavelength of the start pulse was 1547 nm. The 10-MHz clock signal from the clock divider was also converted into an optical clock pulse by a distributed feedback laser with an EA-DFB. The wavelength of the 10-MHz clock pulse was 1555 nm. These signals were combined with a WDM (Wavelength Division Multiplexing) coupler, and transmitted over the other 25-km DSF.

 

Fig. 3. Experimental setup: LD, laser diode; IM, intensity modulator; PG, pulse generator; PM, phase modulator; ATT, attenuator; PLC-MZI, planar lightwave circuit Mach-Zehnder interferometer; Synth, synthesizer; CD, clock divider; RBG, random bit generator; PD, photo diode; TIA, time interval analyzer; PC, personal computer.

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After the transmission, the 1-GHz pulse stream was input into a Mach-Zehnder interferometer based on planar lightwave circuit technology. The path length difference and the excess loss were 20 cm and 2.0 dB, respectively. The extinction ratio was greater than 20 dB and the polarization dependence was negligible. The phase difference between the two paths in the Mach-Zehnder interferometer could be stably adjusted by controlling the temperature of the waveguide chip. In this experiment, no feed-back mechanism that adjusted the temperature of the Mach-Zehnder interferometer depending on the fluctuation of the center frequency of the laser source was implemented. The output ports of the Mach-Zehnder interferometer were connected to single photon detectors based on InGaAs APDs (Id-quantique id200). The detectors were operated in a gate mode, and the gate frequency was 4 MHz. The 4-MHz trigger signal for the detectors was generated from the 10-MHz optical clock pulses received by a photo diode (PD). The quantum efficiency and dark count rate were 7.5% and 189 cps, respectively. The detected signals were input into a time interval analyzer (TIA) (Fastcomtec P7889) by way of a logic gate to record the photon detection events. The start pulses were received by a PD and converted into an electrical signal, which was used as a reference time in the TIA. The TIA device was installed in a personal computer (PC2). The TIA server, Bob’s server and monitor server were installed on PC2. The TIA server continuously retrieved the detection events from the TIA device, and sent them to Bob’s server. Bob’s server was driven by a detection event packet sent from the TIA server. From these packets, Bob’s server generated his sifted key and sent the time information to Alice’s server, installed on PC1, through the Ethernet. Bob’s server also sent his key to the monitor server. On the other hand, Alice’s server generated her key from the phase modulation information and the time information received from Bob’s server. Alice’s server could access to the DRAM on the FPGA board through the Ethernet interface to retrieve the phase modulation information. Her key was sent to the monitor server. The monitor server received the keys from Alice’s and Bob’s servers, and estimated the key generation and quantum bit error rates.

5. Experimental results

Using the setup described above, we performed DPS-QKD experiment. Figure 4 and 5 show the experimental results. Figure 4 shows the sifted key generation rate and quantum bit error rate as a function of time. We successfully demonstrated the continuous operation over an hour and generated sifted keys at a rate of 9.0 kbps with an average QBER of 3.2%. Note that the sifted key generation rate is not an estimated value but an actually obtained value including data processing described in Section 4, which means the sifted key was continuously generated at a rate of 9.0 kbps at Alice’s and Bob’s servers. Error correction and privacy amplification were not performed in this experiment.

Figure 5 shows the 1/0 ratio of the physical random bit generator as a function of time. We measured the 0/1 ratio of 1-Mbit samples to monitor the quality of the random bit signal. 97% of the samples were within the range 50.00 ± 0.13%, corresponding to a p-value greater than 0.01 for the statistical significance level of α = 0.01 [18]. This confirmed the stability of the operation of the physical random bit generator throughput the QKD experiment.

In the following, we describe the experimental conditions of the key generation in more detail. First, we discuss the key generation rate. Throughout the experiment, the total detector count rate was 10.2 kcps. When Bob’s server generated a sifted key, a 500-ps time window was employed to reduce errors caused by the timing jitter and dark counts, through which some of the detection events were discarded. In addition, the time interval analyzer had a dead time of 1 μsec per start pulse. As a result of the effect of the time window and the dead time of the TIA, the sifted key generation rate was 10 % lower than the count rate. Next, we discuss the origin of the quantum bit error rate (QBER). The dark count rate was 189 bps. The QBER due to the dark count was estimated to be 1.85 %. The QBER as a result of the imperfection of the Mach-Zehnder interferometer was estimated to be 1 % because the extinction ratio was 20 dB. The remaining QBER must be due to system operation errors including the timing jitter of the detectors. The QBER resulting from system error was estimated to be 0.3 %. Finally, we discuss the secure key generation rate. Although only sifted keys were generated in this experiment, the observed error rate was good enough to distill a secure key using error correction and privacy amplification. Based on an analysis of the security against a general individual attack [9], the secure key generation rate was estimated to be 0.98 kbps. Note that the unconditional security of DPS-QKD has not been proved yet [20]. Several attacks which are not included in a general individual attack model have been proposed [21,22]. However, these attacks are effective for long distance transmission systems. For the short distance transmission system described in this paper, the general individual attack is currently the strictest security model.

 

Fig. 4. Experimental results of quantum bit error rate (QBER) and sifted key generation rate.

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Fig. 5. Experimental result of occurrences of “1” bits for the fast physical random bit generator used in the QKD experiment.

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6. Summary

We report the first gigahertz clocked DPS-QKD experiment using a fast physical random bit generator. We employed a physical random bit generator with chaotic semiconductor lasers in a DPS-QKD system. We successfully demonstrated stable operation for over one hour, and achieved a sifted key generation rate of 9.0 kbps with a quantum bit error rate of 3.2% after 25-km fiber transmission. The physical random bit generator with chaotic semiconductor lasers provided stable random bit signal continuously throughput the 1-hour duration of the experiment. Thus we showed the possibility of realizing high speed QKD system with a fast physical random bit generator. In particular, we showed that a physical random bit generator with chaotic semiconductor lasers is a promising candidate for the true random bit generator in a high speed QKD system.

Acknowledgments

This work was supported in part by the National Institute of Information and Communications Technology (NICT) of Japan. We thank Yoshinobu Tonomura, Naonori Ueda, Kenji Nakazawa, and Masato Miyoshi for their support and encouragement. A. U. acknowledges support from NTT Corporation, JGC-S Scholarship Foundation, The Mazda Foundation, CASIO Science Promotion Foundation, TEPCO Research Foundation, and Grants-in-Aid for Young Scientists from the Japan Society for the Promotion of Science.

References and links

1. N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74,145–195 (2002). [CrossRef]  

2. T. Honjo, K. Inoue, and H. Takahashi, “Differential-phase-shift quantum key distribution experiment with a planar light-wave circuit Mach-Zehnder interferometer,” Opt. Lett. 29, 2797 (2004). [CrossRef]   [PubMed]  

3. E. Diamanti, H. Takesue, C. Langrock, M. M. Fejer, and Y. Yamamoto, “100 km differential phase shift quantum key distribution experiment with low jitter up-conversion detectors,” Opt. Express 14, 13073–13082 (2006). [CrossRef]   [PubMed]  

4. H. Takesue, S. W. Nam, Q. Zhang, R. H. Hadfield, T. Honjo, K. Tamaki, and Y. Yamamoto, “Quantum key distribution over 40 dB channel loss using superconducting single-photon detectors,” Nature Photonics 1, 343 (2007). [CrossRef]  

5. T. Honjo, S. Yamamoto, T. Yamamoto, H. Kamada, Y. Nishida, O. Tadanaga, M. Asobe, and K. Inoue, “Field trial of differential-phase-shift quantum key distribution using polarization independent frequency up-conversion detectors,” Opt. Express 15, 15920–15927 (2007). [CrossRef]   [PubMed]  

6. Z. L. Yuan, A. R. Dixon, J. F. Dynes, A. W. Sharpe, and A. J. Shields, “Gigahertz quantum key distribution with InGaAs avalanche photodiodes,” Appl. Phys. Lett. 92, 201104 (2008). [CrossRef]  

7. R. T. Thew, S. Tanzilli, L. Krainer, S. C Zeller, A. Rochas, I. Rech, S. Cova, H. Zbinden, and N Gisin, ”Low jitter up-conversion detectors for telecom wavelength GHz QKD,” New J. Phys. 8, 32 (2006). [CrossRef]  

8. A. Tanaka, M. Fujiwara, S. W. Nam, Y. Nambu, S. Takahashi, W. Maeda, K. Yoshino, S. Miki, B. Baek, Z. Wang, A. Tajima, M. Sasaki, and A. Tomita, “Ultra fast quantum key distribution over a 97 km installed telecom fiber with wavelength division multiplexing clock synchronization,” Opt. Express 16, 11354–11360 (2008). [CrossRef]   [PubMed]  

9. 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,” Nature Photonics 2, 728 (2008). [CrossRef]  

10. K. Inoue, E. Waks, and Y. Yamamoto, “Differential-phase-shift quantum key distribution using coherent light,” Phys. Rev. A 68,022317 (2003). [CrossRef]  

11. E. Waks, H. Takesue, and Y. Yamamoto, “Security of differential-phase-shift quantum key distribution against individual attacks,” Phys. Rev. A 73,012344 (2006). [CrossRef]  

12. B. Jun and P. Kocher, “The Intel random number generator,”, White paper prepared for Intel Corporation, Cryptography Research Inc. Available at http://www.cryptography.com/resources/whitepapers/IntelRNG.pdf. (1999).

13. W. T. Holman, J. A. Connelly, and A. B. Dowlatabadi, “An integrated analog/digital random noise source,” IEEE Trans. Circuits Syst. I44, 521–528 (1997). [CrossRef]  

14. J. F. Dynes, Z. L. Yuan, A. W. Sharpe, and A. J. Shields, “A high speed, post-processing free, quantum random number generator,” Appl. Phys. Letts. 93, 031109 (2008). [CrossRef]  

15. F. Cortigiani, C. Petri, S. Rocchi, and V. Vignoli, “Very high-speed true random noise generator,” The 7th IEEE International Conference on Electronics, Circuits and Systems, 2000 (ICECS 2000) 1, 120–123 (2000).

16. M. Bucci, L. Germani, R. Luzzi, A. Trifiletti, and M. Varanouvo, “A high-speed oscillator-based truly random number source for cryptographic applications on a Smart Card IC,” IEEE Trans. Comput. 52, 403–409 (2003). [CrossRef]  

17. C. Tokunaga, D. Blaauw, and T. Mudge, “True random number generator with a metastability-based quality control,” IEEE J. Solid-State Circuits 43, 78–85 (2008). [CrossRef]  

18. 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,” National Institute of Standards and Technology, Special Publication 800-22 Revision 1 (2008).

19. G. Marsaglia, “DIEHARD: A battery of tests of randomness,” Available at http://stat.fsu.edu/~geo (1996).

20. K. Wen, K. Tamaki, and Y. Yamamoto, “Unconditional security of single photon differential phase shift quantum key distribution,” arXiv:0806.2684v2 (2008).

21. M. Curty, L. L. X. Zhang, H. K. Lo, and N. Lutkenhaus, “Sequential attacks against differential-phase-shift quantum key distribution with weak coherent states,” Quantum Information & Computation , 7 (7), 665–688 (2007).

22. T. Tsurumaru, “Sequential attack with intensity modulation on the differential-phase-shift quantum key distribution protocol,” Phys. Rev. A 75, 062319 (2007). [CrossRef]  

References

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  1. N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74,145–195 (2002).
    [Crossref]
  2. T. Honjo, K. Inoue, and H. Takahashi, “Differential-phase-shift quantum key distribution experiment with a planar light-wave circuit Mach-Zehnder interferometer,” Opt. Lett. 29, 2797 (2004).
    [Crossref] [PubMed]
  3. E. Diamanti, H. Takesue, C. Langrock, M. M. Fejer, and Y. Yamamoto, “100 km differential phase shift quantum key distribution experiment with low jitter up-conversion detectors,” Opt. Express 14, 13073–13082 (2006).
    [Crossref] [PubMed]
  4. H. Takesue, S. W. Nam, Q. Zhang, R. H. Hadfield, T. Honjo, K. Tamaki, and Y. Yamamoto, “Quantum key distribution over 40 dB channel loss using superconducting single-photon detectors,” Nature Photonics 1, 343 (2007).
    [Crossref]
  5. T. Honjo, S. Yamamoto, T. Yamamoto, H. Kamada, Y. Nishida, O. Tadanaga, M. Asobe, and K. Inoue, “Field trial of differential-phase-shift quantum key distribution using polarization independent frequency up-conversion detectors,” Opt. Express 15, 15920–15927 (2007).
    [Crossref] [PubMed]
  6. Z. L. Yuan, A. R. Dixon, J. F. Dynes, A. W. Sharpe, and A. J. Shields, “Gigahertz quantum key distribution with InGaAs avalanche photodiodes,” Appl. Phys. Lett. 92, 201104 (2008).
    [Crossref]
  7. R. T. Thew, S. Tanzilli, L. Krainer, S. C Zeller, A. Rochas, I. Rech, S. Cova, H. Zbinden, and N Gisin, ”Low jitter up-conversion detectors for telecom wavelength GHz QKD,” New J. Phys. 8, 32 (2006).
    [Crossref]
  8. A. Tanaka, M. Fujiwara, S. W. Nam, Y. Nambu, S. Takahashi, W. Maeda, K. Yoshino, S. Miki, B. Baek, Z. Wang, A. Tajima, M. Sasaki, and A. Tomita, “Ultra fast quantum key distribution over a 97 km installed telecom fiber with wavelength division multiplexing clock synchronization,” Opt. Express 16, 11354–11360 (2008).
    [Crossref] [PubMed]
  9. 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,” Nature Photonics 2, 728 (2008).
    [Crossref]
  10. K. Inoue, E. Waks, and Y. Yamamoto, “Differential-phase-shift quantum key distribution using coherent light,” Phys. Rev. A 68,022317 (2003).
    [Crossref]
  11. E. Waks, H. Takesue, and Y. Yamamoto, “Security of differential-phase-shift quantum key distribution against individual attacks,” Phys. Rev. A 73,012344 (2006).
    [Crossref]
  12. B. Jun and P. Kocher, “The Intel random number generator,”, White paper prepared for Intel Corporation, Cryptography Research Inc. Available at http://www.cryptography.com/resources/whitepapers/IntelRNG.pdf. (1999).
  13. W. T. Holman, J. A. Connelly, and A. B. Dowlatabadi, “An integrated analog/digital random noise source,” IEEE Trans. Circuits Syst. I 44, 521–528 (1997).
    [Crossref]
  14. J. F. Dynes, Z. L. Yuan, A. W. Sharpe, and A. J. Shields, “A high speed, post-processing free, quantum random number generator,” Appl. Phys. Letts. 93, 031109 (2008).
    [Crossref]
  15. F. Cortigiani, C. Petri, S. Rocchi, and V. Vignoli, “Very high-speed true random noise generator,” The 7th IEEE International Conference on Electronics, Circuits and Systems, 2000 (ICECS 2000) 1, 120–123 (2000).
  16. M. Bucci, L. Germani, R. Luzzi, A. Trifiletti, and M. Varanouvo, “A high-speed oscillator-based truly random number source for cryptographic applications on a Smart Card IC,” IEEE Trans. Comput. 52, 403–409 (2003).
    [Crossref]
  17. C. Tokunaga, D. Blaauw, and T. Mudge, “True random number generator with a metastability-based quality control,” IEEE J. Solid-State Circuits 43, 78–85 (2008).
    [Crossref]
  18. 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,” National Institute of Standards and Technology, Special Publication 800-22 Revision 1 (2008).
  19. G. Marsaglia, “DIEHARD: A battery of tests of randomness,” Available at http://stat.fsu.edu/~geo (1996).
  20. K. Wen, K. Tamaki, and Y. Yamamoto, “Unconditional security of single photon differential phase shift quantum key distribution,” arXiv:0806.2684v2 (2008).
  21. M. Curty, L. L. X. Zhang, H. K. Lo, and N. Lutkenhaus, “Sequential attacks against differential-phase-shift quantum key distribution with weak coherent states,” Quantum Information & Computation,  7 (7), 665–688 (2007).
  22. T. Tsurumaru, “Sequential attack with intensity modulation on the differential-phase-shift quantum key distribution protocol,” Phys. Rev. A 75, 062319 (2007).
    [Crossref]

2008 (5)

Z. L. Yuan, A. R. Dixon, J. F. Dynes, A. W. Sharpe, and A. J. Shields, “Gigahertz quantum key distribution with InGaAs avalanche photodiodes,” Appl. Phys. Lett. 92, 201104 (2008).
[Crossref]

A. Tanaka, M. Fujiwara, S. W. Nam, Y. Nambu, S. Takahashi, W. Maeda, K. Yoshino, S. Miki, B. Baek, Z. Wang, A. Tajima, M. Sasaki, and A. Tomita, “Ultra fast quantum key distribution over a 97 km installed telecom fiber with wavelength division multiplexing clock synchronization,” Opt. Express 16, 11354–11360 (2008).
[Crossref] [PubMed]

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,” Nature Photonics 2, 728 (2008).
[Crossref]

J. F. Dynes, Z. L. Yuan, A. W. Sharpe, and A. J. Shields, “A high speed, post-processing free, quantum random number generator,” Appl. Phys. Letts. 93, 031109 (2008).
[Crossref]

C. Tokunaga, D. Blaauw, and T. Mudge, “True random number generator with a metastability-based quality control,” IEEE J. Solid-State Circuits 43, 78–85 (2008).
[Crossref]

2007 (4)

M. Curty, L. L. X. Zhang, H. K. Lo, and N. Lutkenhaus, “Sequential attacks against differential-phase-shift quantum key distribution with weak coherent states,” Quantum Information & Computation,  7 (7), 665–688 (2007).

T. Tsurumaru, “Sequential attack with intensity modulation on the differential-phase-shift quantum key distribution protocol,” Phys. Rev. A 75, 062319 (2007).
[Crossref]

H. Takesue, S. W. Nam, Q. Zhang, R. H. Hadfield, T. Honjo, K. Tamaki, and Y. Yamamoto, “Quantum key distribution over 40 dB channel loss using superconducting single-photon detectors,” Nature Photonics 1, 343 (2007).
[Crossref]

T. Honjo, S. Yamamoto, T. Yamamoto, H. Kamada, Y. Nishida, O. Tadanaga, M. Asobe, and K. Inoue, “Field trial of differential-phase-shift quantum key distribution using polarization independent frequency up-conversion detectors,” Opt. Express 15, 15920–15927 (2007).
[Crossref] [PubMed]

2006 (3)

R. T. Thew, S. Tanzilli, L. Krainer, S. C Zeller, A. Rochas, I. Rech, S. Cova, H. Zbinden, and N Gisin, ”Low jitter up-conversion detectors for telecom wavelength GHz QKD,” New J. Phys. 8, 32 (2006).
[Crossref]

E. Diamanti, H. Takesue, C. Langrock, M. M. Fejer, and Y. Yamamoto, “100 km differential phase shift quantum key distribution experiment with low jitter up-conversion detectors,” Opt. Express 14, 13073–13082 (2006).
[Crossref] [PubMed]

E. Waks, H. Takesue, and Y. Yamamoto, “Security of differential-phase-shift quantum key distribution against individual attacks,” Phys. Rev. A 73,012344 (2006).
[Crossref]

2004 (1)

2003 (2)

K. Inoue, E. Waks, and Y. Yamamoto, “Differential-phase-shift quantum key distribution using coherent light,” Phys. Rev. A 68,022317 (2003).
[Crossref]

M. Bucci, L. Germani, R. Luzzi, A. Trifiletti, and M. Varanouvo, “A high-speed oscillator-based truly random number source for cryptographic applications on a Smart Card IC,” IEEE Trans. Comput. 52, 403–409 (2003).
[Crossref]

2002 (1)

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74,145–195 (2002).
[Crossref]

2000 (1)

F. Cortigiani, C. Petri, S. Rocchi, and V. Vignoli, “Very high-speed true random noise generator,” The 7th IEEE International Conference on Electronics, Circuits and Systems, 2000 (ICECS 2000) 1, 120–123 (2000).

1997 (1)

W. T. Holman, J. A. Connelly, and A. B. Dowlatabadi, “An integrated analog/digital random noise source,” IEEE Trans. Circuits Syst. I 44, 521–528 (1997).
[Crossref]

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,” Nature Photonics 2, 728 (2008).
[Crossref]

Asobe, M.

Baek, B.

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,” National Institute of Standards and Technology, Special Publication 800-22 Revision 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,” National Institute of Standards and Technology, Special Publication 800-22 Revision 1 (2008).

Blaauw, D.

C. Tokunaga, D. Blaauw, and T. Mudge, “True random number generator with a metastability-based quality control,” IEEE J. Solid-State Circuits 43, 78–85 (2008).
[Crossref]

Bucci, M.

M. Bucci, L. Germani, R. Luzzi, A. Trifiletti, and M. Varanouvo, “A high-speed oscillator-based truly random number source for cryptographic applications on a Smart Card IC,” IEEE Trans. Comput. 52, 403–409 (2003).
[Crossref]

Connelly, J. A.

W. T. Holman, J. A. Connelly, and A. B. Dowlatabadi, “An integrated analog/digital random noise source,” IEEE Trans. Circuits Syst. I 44, 521–528 (1997).
[Crossref]

Cortigiani, F.

F. Cortigiani, C. Petri, S. Rocchi, and V. Vignoli, “Very high-speed true random noise generator,” The 7th IEEE International Conference on Electronics, Circuits and Systems, 2000 (ICECS 2000) 1, 120–123 (2000).

Cova, S.

R. T. Thew, S. Tanzilli, L. Krainer, S. C Zeller, A. Rochas, I. Rech, S. Cova, H. Zbinden, and N Gisin, ”Low jitter up-conversion detectors for telecom wavelength GHz QKD,” New J. Phys. 8, 32 (2006).
[Crossref]

Curty, M.

M. Curty, L. L. X. Zhang, H. K. Lo, and N. Lutkenhaus, “Sequential attacks against differential-phase-shift quantum key distribution with weak coherent states,” Quantum Information & Computation,  7 (7), 665–688 (2007).

Davis, P.

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,” Nature Photonics 2, 728 (2008).
[Crossref]

Diamanti, E.

Dixon, A. R.

Z. L. Yuan, A. R. Dixon, J. F. Dynes, A. W. Sharpe, and A. J. Shields, “Gigahertz quantum key distribution with InGaAs avalanche photodiodes,” Appl. Phys. Lett. 92, 201104 (2008).
[Crossref]

Dowlatabadi, A. B.

W. T. Holman, J. A. Connelly, and A. B. Dowlatabadi, “An integrated analog/digital random noise source,” IEEE Trans. Circuits Syst. I 44, 521–528 (1997).
[Crossref]

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,” National Institute of Standards and Technology, Special Publication 800-22 Revision 1 (2008).

Dynes, J. F.

J. F. Dynes, Z. L. Yuan, A. W. Sharpe, and A. J. Shields, “A high speed, post-processing free, quantum random number generator,” Appl. Phys. Letts. 93, 031109 (2008).
[Crossref]

Z. L. Yuan, A. R. Dixon, J. F. Dynes, A. W. Sharpe, and A. J. Shields, “Gigahertz quantum key distribution with InGaAs avalanche photodiodes,” Appl. Phys. Lett. 92, 201104 (2008).
[Crossref]

Fejer, M. M.

Fujiwara, M.

Germani, L.

M. Bucci, L. Germani, R. Luzzi, A. Trifiletti, and M. Varanouvo, “A high-speed oscillator-based truly random number source for cryptographic applications on a Smart Card IC,” IEEE Trans. Comput. 52, 403–409 (2003).
[Crossref]

Gisin, N

R. T. Thew, S. Tanzilli, L. Krainer, S. C Zeller, A. Rochas, I. Rech, S. Cova, H. Zbinden, and N Gisin, ”Low jitter up-conversion detectors for telecom wavelength GHz QKD,” New J. Phys. 8, 32 (2006).
[Crossref]

Gisin, N.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74,145–195 (2002).
[Crossref]

Hadfield, R. H.

H. Takesue, S. W. Nam, Q. Zhang, R. H. Hadfield, T. Honjo, K. Tamaki, and Y. Yamamoto, “Quantum key distribution over 40 dB channel loss using superconducting single-photon detectors,” Nature Photonics 1, 343 (2007).
[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,” National Institute of Standards and Technology, Special Publication 800-22 Revision 1 (2008).

Hirano, 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,” Nature Photonics 2, 728 (2008).
[Crossref]

Holman, W. T.

W. T. Holman, J. A. Connelly, and A. B. Dowlatabadi, “An integrated analog/digital random noise source,” IEEE Trans. Circuits Syst. I 44, 521–528 (1997).
[Crossref]

Honjo, T.

Inoue, K.

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,” Nature Photonics 2, 728 (2008).
[Crossref]

Jun, B.

B. Jun and P. Kocher, “The Intel random number generator,”, White paper prepared for Intel Corporation, Cryptography Research Inc. Available at http://www.cryptography.com/resources/whitepapers/IntelRNG.pdf. (1999).

Kamada, H.

Kocher, P.

B. Jun and P. Kocher, “The Intel random number generator,”, White paper prepared for Intel Corporation, Cryptography Research Inc. Available at http://www.cryptography.com/resources/whitepapers/IntelRNG.pdf. (1999).

Krainer, L.

R. T. Thew, S. Tanzilli, L. Krainer, S. C Zeller, A. Rochas, I. Rech, S. Cova, H. Zbinden, and N Gisin, ”Low jitter up-conversion detectors for telecom wavelength GHz QKD,” New J. Phys. 8, 32 (2006).
[Crossref]

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,” Nature Photonics 2, 728 (2008).
[Crossref]

Langrock, C.

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,” National Institute of Standards and Technology, Special Publication 800-22 Revision 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,” National Institute of Standards and Technology, Special Publication 800-22 Revision 1 (2008).

Lo, H. K.

M. Curty, L. L. X. Zhang, H. K. Lo, and N. Lutkenhaus, “Sequential attacks against differential-phase-shift quantum key distribution with weak coherent states,” Quantum Information & Computation,  7 (7), 665–688 (2007).

Lutkenhaus, N.

M. Curty, L. L. X. Zhang, H. K. Lo, and N. Lutkenhaus, “Sequential attacks against differential-phase-shift quantum key distribution with weak coherent states,” Quantum Information & Computation,  7 (7), 665–688 (2007).

Luzzi, R.

M. Bucci, L. Germani, R. Luzzi, A. Trifiletti, and M. Varanouvo, “A high-speed oscillator-based truly random number source for cryptographic applications on a Smart Card IC,” IEEE Trans. Comput. 52, 403–409 (2003).
[Crossref]

Maeda, W.

Marsaglia, G.

G. Marsaglia, “DIEHARD: A battery of tests of randomness,” Available at http://stat.fsu.edu/~geo (1996).

Miki, S.

Mudge, T.

C. Tokunaga, D. Blaauw, and T. Mudge, “True random number generator with a metastability-based quality control,” IEEE J. Solid-State Circuits 43, 78–85 (2008).
[Crossref]

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,” Nature Photonics 2, 728 (2008).
[Crossref]

Nam, S. W.

Nambu, Y.

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,” National Institute of Standards and Technology, Special Publication 800-22 Revision 1 (2008).

Nishida, Y.

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,” Nature Photonics 2, 728 (2008).
[Crossref]

Petri, C.

F. Cortigiani, C. Petri, S. Rocchi, and V. Vignoli, “Very high-speed true random noise generator,” The 7th IEEE International Conference on Electronics, Circuits and Systems, 2000 (ICECS 2000) 1, 120–123 (2000).

Rech, I.

R. T. Thew, S. Tanzilli, L. Krainer, S. C Zeller, A. Rochas, I. Rech, S. Cova, H. Zbinden, and N Gisin, ”Low jitter up-conversion detectors for telecom wavelength GHz QKD,” New J. Phys. 8, 32 (2006).
[Crossref]

Ribordy, G.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74,145–195 (2002).
[Crossref]

Rocchi, S.

F. Cortigiani, C. Petri, S. Rocchi, and V. Vignoli, “Very high-speed true random noise generator,” The 7th IEEE International Conference on Electronics, Circuits and Systems, 2000 (ICECS 2000) 1, 120–123 (2000).

Rochas, A.

R. T. Thew, S. Tanzilli, L. Krainer, S. C Zeller, A. Rochas, I. Rech, S. Cova, H. Zbinden, and N Gisin, ”Low jitter up-conversion detectors for telecom wavelength GHz QKD,” New J. Phys. 8, 32 (2006).
[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,” National Institute of Standards and Technology, Special Publication 800-22 Revision 1 (2008).

Sasaki, M.

Sharpe, A. W.

Z. L. Yuan, A. R. Dixon, J. F. Dynes, A. W. Sharpe, and A. J. Shields, “Gigahertz quantum key distribution with InGaAs avalanche photodiodes,” Appl. Phys. Lett. 92, 201104 (2008).
[Crossref]

J. F. Dynes, Z. L. Yuan, A. W. Sharpe, and A. J. Shields, “A high speed, post-processing free, quantum random number generator,” Appl. Phys. Letts. 93, 031109 (2008).
[Crossref]

Shields, A. J.

J. F. Dynes, Z. L. Yuan, A. W. Sharpe, and A. J. Shields, “A high speed, post-processing free, quantum random number generator,” Appl. Phys. Letts. 93, 031109 (2008).
[Crossref]

Z. L. Yuan, A. R. Dixon, J. F. Dynes, A. W. Sharpe, and A. J. Shields, “Gigahertz quantum key distribution with InGaAs avalanche photodiodes,” Appl. Phys. Lett. 92, 201104 (2008).
[Crossref]

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,” Nature Photonics 2, 728 (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,” National Institute of Standards and Technology, Special Publication 800-22 Revision 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,” Nature Photonics 2, 728 (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,” National Institute of Standards and Technology, Special Publication 800-22 Revision 1 (2008).

Tadanaga, O.

Tajima, A.

Takahashi, H.

Takahashi, S.

Takesue, H.

H. Takesue, S. W. Nam, Q. Zhang, R. H. Hadfield, T. Honjo, K. Tamaki, and Y. Yamamoto, “Quantum key distribution over 40 dB channel loss using superconducting single-photon detectors,” Nature Photonics 1, 343 (2007).
[Crossref]

E. Diamanti, H. Takesue, C. Langrock, M. M. Fejer, and Y. Yamamoto, “100 km differential phase shift quantum key distribution experiment with low jitter up-conversion detectors,” Opt. Express 14, 13073–13082 (2006).
[Crossref] [PubMed]

E. Waks, H. Takesue, and Y. Yamamoto, “Security of differential-phase-shift quantum key distribution against individual attacks,” Phys. Rev. A 73,012344 (2006).
[Crossref]

Tamaki, K.

H. Takesue, S. W. Nam, Q. Zhang, R. H. Hadfield, T. Honjo, K. Tamaki, and Y. Yamamoto, “Quantum key distribution over 40 dB channel loss using superconducting single-photon detectors,” Nature Photonics 1, 343 (2007).
[Crossref]

K. Wen, K. Tamaki, and Y. Yamamoto, “Unconditional security of single photon differential phase shift quantum key distribution,” arXiv:0806.2684v2 (2008).

Tanaka, A.

Tanzilli, S.

R. T. Thew, S. Tanzilli, L. Krainer, S. C Zeller, A. Rochas, I. Rech, S. Cova, H. Zbinden, and N Gisin, ”Low jitter up-conversion detectors for telecom wavelength GHz QKD,” New J. Phys. 8, 32 (2006).
[Crossref]

Thew, R. T.

R. T. Thew, S. Tanzilli, L. Krainer, S. C Zeller, A. Rochas, I. Rech, S. Cova, H. Zbinden, and N Gisin, ”Low jitter up-conversion detectors for telecom wavelength GHz QKD,” New J. Phys. 8, 32 (2006).
[Crossref]

Tittel, W.

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74,145–195 (2002).
[Crossref]

Tokunaga, C.

C. Tokunaga, D. Blaauw, and T. Mudge, “True random number generator with a metastability-based quality control,” IEEE J. Solid-State Circuits 43, 78–85 (2008).
[Crossref]

Tomita, A.

Trifiletti, A.

M. Bucci, L. Germani, R. Luzzi, A. Trifiletti, and M. Varanouvo, “A high-speed oscillator-based truly random number source for cryptographic applications on a Smart Card IC,” IEEE Trans. Comput. 52, 403–409 (2003).
[Crossref]

Tsurumaru, T.

T. Tsurumaru, “Sequential attack with intensity modulation on the differential-phase-shift quantum key distribution protocol,” Phys. Rev. A 75, 062319 (2007).
[Crossref]

Uchida, A.

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,” Nature Photonics 2, 728 (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,” National Institute of Standards and Technology, Special Publication 800-22 Revision 1 (2008).

Varanouvo, M.

M. Bucci, L. Germani, R. Luzzi, A. Trifiletti, and M. Varanouvo, “A high-speed oscillator-based truly random number source for cryptographic applications on a Smart Card IC,” IEEE Trans. Comput. 52, 403–409 (2003).
[Crossref]

Vignoli, V.

F. Cortigiani, C. Petri, S. Rocchi, and V. Vignoli, “Very high-speed true random noise generator,” The 7th IEEE International Conference on Electronics, Circuits and Systems, 2000 (ICECS 2000) 1, 120–123 (2000).

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,” National Institute of Standards and Technology, Special Publication 800-22 Revision 1 (2008).

Waks, E.

E. Waks, H. Takesue, and Y. Yamamoto, “Security of differential-phase-shift quantum key distribution against individual attacks,” Phys. Rev. A 73,012344 (2006).
[Crossref]

K. Inoue, E. Waks, and Y. Yamamoto, “Differential-phase-shift quantum key distribution using coherent light,” Phys. Rev. A 68,022317 (2003).
[Crossref]

Wang, Z.

Wen, K.

K. Wen, K. Tamaki, and Y. Yamamoto, “Unconditional security of single photon differential phase shift quantum key distribution,” arXiv:0806.2684v2 (2008).

Yamamoto, S.

Yamamoto, T.

Yamamoto, Y.

H. Takesue, S. W. Nam, Q. Zhang, R. H. Hadfield, T. Honjo, K. Tamaki, and Y. Yamamoto, “Quantum key distribution over 40 dB channel loss using superconducting single-photon detectors,” Nature Photonics 1, 343 (2007).
[Crossref]

E. Diamanti, H. Takesue, C. Langrock, M. M. Fejer, and Y. Yamamoto, “100 km differential phase shift quantum key distribution experiment with low jitter up-conversion detectors,” Opt. Express 14, 13073–13082 (2006).
[Crossref] [PubMed]

E. Waks, H. Takesue, and Y. Yamamoto, “Security of differential-phase-shift quantum key distribution against individual attacks,” Phys. Rev. A 73,012344 (2006).
[Crossref]

K. Inoue, E. Waks, and Y. Yamamoto, “Differential-phase-shift quantum key distribution using coherent light,” Phys. Rev. A 68,022317 (2003).
[Crossref]

K. Wen, K. Tamaki, and Y. Yamamoto, “Unconditional security of single photon differential phase shift quantum key distribution,” arXiv:0806.2684v2 (2008).

Yoshimori, 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,” Nature Photonics 2, 728 (2008).
[Crossref]

Yoshimura, 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,” Nature Photonics 2, 728 (2008).
[Crossref]

Yoshino, K.

Yuan, Z. L.

Z. L. Yuan, A. R. Dixon, J. F. Dynes, A. W. Sharpe, and A. J. Shields, “Gigahertz quantum key distribution with InGaAs avalanche photodiodes,” Appl. Phys. Lett. 92, 201104 (2008).
[Crossref]

J. F. Dynes, Z. L. Yuan, A. W. Sharpe, and A. J. Shields, “A high speed, post-processing free, quantum random number generator,” Appl. Phys. Letts. 93, 031109 (2008).
[Crossref]

Zbinden, H.

R. T. Thew, S. Tanzilli, L. Krainer, S. C Zeller, A. Rochas, I. Rech, S. Cova, H. Zbinden, and N Gisin, ”Low jitter up-conversion detectors for telecom wavelength GHz QKD,” New J. Phys. 8, 32 (2006).
[Crossref]

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74,145–195 (2002).
[Crossref]

Zeller, S. C

R. T. Thew, S. Tanzilli, L. Krainer, S. C Zeller, A. Rochas, I. Rech, S. Cova, H. Zbinden, and N Gisin, ”Low jitter up-conversion detectors for telecom wavelength GHz QKD,” New J. Phys. 8, 32 (2006).
[Crossref]

Zhang, L. L. X.

M. Curty, L. L. X. Zhang, H. K. Lo, and N. Lutkenhaus, “Sequential attacks against differential-phase-shift quantum key distribution with weak coherent states,” Quantum Information & Computation,  7 (7), 665–688 (2007).

Zhang, Q.

H. Takesue, S. W. Nam, Q. Zhang, R. H. Hadfield, T. Honjo, K. Tamaki, and Y. Yamamoto, “Quantum key distribution over 40 dB channel loss using superconducting single-photon detectors,” Nature Photonics 1, 343 (2007).
[Crossref]

Appl. Phys. Lett. (1)

Z. L. Yuan, A. R. Dixon, J. F. Dynes, A. W. Sharpe, and A. J. Shields, “Gigahertz quantum key distribution with InGaAs avalanche photodiodes,” Appl. Phys. Lett. 92, 201104 (2008).
[Crossref]

Appl. Phys. Letts. (1)

J. F. Dynes, Z. L. Yuan, A. W. Sharpe, and A. J. Shields, “A high speed, post-processing free, quantum random number generator,” Appl. Phys. Letts. 93, 031109 (2008).
[Crossref]

IEEE J. Solid-State Circuits (1)

C. Tokunaga, D. Blaauw, and T. Mudge, “True random number generator with a metastability-based quality control,” IEEE J. Solid-State Circuits 43, 78–85 (2008).
[Crossref]

IEEE Trans. Circuits Syst. (1)

W. T. Holman, J. A. Connelly, and A. B. Dowlatabadi, “An integrated analog/digital random noise source,” IEEE Trans. Circuits Syst. I 44, 521–528 (1997).
[Crossref]

IEEE Trans. Comput. (1)

M. Bucci, L. Germani, R. Luzzi, A. Trifiletti, and M. Varanouvo, “A high-speed oscillator-based truly random number source for cryptographic applications on a Smart Card IC,” IEEE Trans. Comput. 52, 403–409 (2003).
[Crossref]

Nature Photonics (2)

H. Takesue, S. W. Nam, Q. Zhang, R. H. Hadfield, T. Honjo, K. Tamaki, and Y. Yamamoto, “Quantum key distribution over 40 dB channel loss using superconducting single-photon detectors,” Nature Photonics 1, 343 (2007).
[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,” Nature Photonics 2, 728 (2008).
[Crossref]

New J. Phys. (1)

R. T. Thew, S. Tanzilli, L. Krainer, S. C Zeller, A. Rochas, I. Rech, S. Cova, H. Zbinden, and N Gisin, ”Low jitter up-conversion detectors for telecom wavelength GHz QKD,” New J. Phys. 8, 32 (2006).
[Crossref]

Opt. Express (3)

Opt. Lett. (1)

Phys. Rev. A (3)

K. Inoue, E. Waks, and Y. Yamamoto, “Differential-phase-shift quantum key distribution using coherent light,” Phys. Rev. A 68,022317 (2003).
[Crossref]

E. Waks, H. Takesue, and Y. Yamamoto, “Security of differential-phase-shift quantum key distribution against individual attacks,” Phys. Rev. A 73,012344 (2006).
[Crossref]

T. Tsurumaru, “Sequential attack with intensity modulation on the differential-phase-shift quantum key distribution protocol,” Phys. Rev. A 75, 062319 (2007).
[Crossref]

Quantum Information & Computation (1)

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Figures (5)

Fig. 1.
Fig. 1. Schematic diagram of differential-phase-shift QKD. LD, laser diode; IM, intensity modulator; PM, phase modulator; ATT, attenuator; MZI, Mach-Zehnder interferometer.
Fig. 2.
Fig. 2. Schematic diagram of physical random bit generator with two chaotic lasers: LD, laser diode; FC, fiber coupler; VR, variable reflector; VA, variable attenuator; PD, photo diode; Amp, Amplifier; Synth, Synthesizer; ADC, analog-digital converter.
Fig. 3.
Fig. 3. Experimental setup: LD, laser diode; IM, intensity modulator; PG, pulse generator; PM, phase modulator; ATT, attenuator; PLC-MZI, planar lightwave circuit Mach-Zehnder interferometer; Synth, synthesizer; CD, clock divider; RBG, random bit generator; PD, photo diode; TIA, time interval analyzer; PC, personal computer.
Fig. 4.
Fig. 4. Experimental results of quantum bit error rate (QBER) and sifted key generation rate.
Fig. 5.
Fig. 5. Experimental result of occurrences of “1” bits for the fast physical random bit generator used in the QKD experiment.

Tables (1)

Tables Icon

Table 1. Results of NIST Special Publication 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 in the range of 0.99 ± 0.0094392. For the tests which produce multiple P-values and proportions, the worst case is shown.

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