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Abstract
We propose and experimentally demonstrate a physical-layer key distribution scheme using commonly-driven laser synchronization with random modulation of drive light. Two parameter-matched semiconductor lasers injected by a common complex drive light are used as entropy sources for legitimate users. Legitimate users generate their own random signal by randomly time-division multiplexing of two random sequences with a certain duration according to individual control codes, and then independently modulate the drive light. Laser synchronization is achieved during time slots when the modulation sequences of two users are identical, and thus provide highly correlated randomness for extracting random numbers as shared keys. Experimental results show that the random modulation of the drive light reduces the correlation between the drive light and laser outputs. In addition, laser synchronization is sensitive to the modulation delay and then the latter can be used as an additional hardware parameter. These mean that security is enhanced. In addition, the proposed method has a short laser synchronization recovery time of lower than 1.1 ns, meaning a high rate of key distribution. The upper limit of final key rate of 2.55 Gb/s with a criterion of bit error rate of 1.68 × 10−3 is achieved in experiments. Our results provide a promising candidate for protecting the security of optical fiber communication.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Key distribution plays a crucial role in secure communications by generating shared secret keys for legitimate users [1]. From a fundamental perspective, the security of algorithm-based key distribution is compromised when attacked by high-performance computers [2,3]. A recent work shows a quantum computer can cryptanalyze a 2048-bit Rivest-Shamir-Adleman (RSA) key within hours [4]. Quantum key distribution (QKD) provides unconditional information security, but is accompanied by challenges such as susceptibility to noise and slow key rate [5,6].
Maurer et al. proved that two users can exchange partial information on a public channel to generate an information-theoretic key from a correlated random source [7]. In this process, even if an eavesdropper obtains all the information that is revealed in the public channel, the key can still be created from the secure information. Based on this theory, complex physical dynamics has been proposed as a physical entropy source for key distribution [8,9]. The difficulty in fully reconstructing complex dynamics restricts eavesdroppers from accessing the key. Channel reciprocal noise has been proposed for key distribution, while noise bandwidth limits key rate and requirement of reciprocity limits transmission distance [10,11]. Laser dynamic synchronization provides another scheme of physical-layer key distribution. Two matched semiconductor lasers injected by a common complex drive light can generate synchronized outputs with highly correlated randomness [12–16]. Broadband laser dynamic has been experimentally proven to generate random bits in the order of Gb/s [17]. Furthermore, it can be compatible with classical fiber channel and has advantages in long-distance gigabit transmission [18,19]. For example, successful chaos synchronization has been reported with a transmission of 1040 km [20], as well as a demonstration on 120-km commercial fiber optic link in metropolitan area networks of Athens [21].
In the scheme of laser-synchronization key distribution, random and independent parameter-shift keying modulation for the laser systems is generally introduced to enhance security [22–28]. Random synchronization on-off is achieved. Synchronization occurs during the slots when the control parameter values of the users are identical, and the legitimate users can extract shared keys from the corresponding waveforms. The dynamic switching of laser synchronization enhances the security of the entropy source, because it is hard for an eavesdropper to record all the laser dynamics associated with possible modulation codes. Yoshimura et al. proposed phase-shift keying of feedback light in a closed-loop laser configuration, and experimentally achieved a key distribution rate of 182 kb/s [22]. Cascaded lasers [23] and photonic integrated optical-feedback lasers [24] had also been experimentally demonstrated. However, the key generation rate in these schemes is restricted by a synchronization recover time in the order of tens of nanoseconds.
Subsequently, some key distribution methods using open-loop laser synchronization with different synchronization on-off modulation ways, such as dispersion-shift keying [25] and polarization-state-shift keying [26,27] have been numerically studied, in support of Gb/s key distribution rate. In addition, a proof of concept of chaotic optoelectronic oscillator without parameter shift shows a stable key generation using optoelectronic dynamics [29]. More recently, Gao et al. experimentally demonstrated a 0.75 Gb/s key distribution scheme on two Fabry-Perot (FP) lasers with random mode selection [28].
Here, we propose a novel laser-synchronization key distribution approach with random modulation of drive light. We generate the modulation signal by time-division multiplexing of two random sequences according to control codes, and then independently modulate the drive light after achieving laser synchronization between two distributed-feedback lasers. Compared to other open-loop schemes, our random modulation offers two advantages. One is the high speed and stable modulation is more practical by usual modulators; another advantage is that the shift keying is carried out by random sequences rather than by two fixed levels of NRZ. Thus, this provides additional-layer security by reducing the correlation between the drive light and the laser outputs, and introducing sensitive parameters such as modulation delay. Experiments obtained shift keying laser synchronization with a short laser synchronization recovery time lower than 1.1 ns, which increases the key generation rate. Moreover, random modulation introduces synchronization parameter such as modulation delay to enhance the security. A key generation rate of 2.55 Gb/s is successfully achieved with a bit error rate of 1.68 × 10−3 in the experiment.
2. Principle and experimental setup
The schematic diagram and experimental setup of our proposed scheme are depicted in Fig. 1. Legitimate users (Alice and Bob) are equipped with parameter-matched chaotic systems, mainly comprising a distributed-feedback laser diode (LD) and an intensity modulator (IM) based random intensity modulation of the drive light structure (RIMD). A complex light, e.g., noise light from super luminescent diode (SLD), is split by a 3-dB coupler and transmitted to Alice and Bob as a public drive light, whose linewidth and power is controlled by an optical filter (OF) and an erbium-doped-fiber-amplifier (EDFA), respectively. Although filtered SLD light is used in our experiment, other optical complex signals such as optical chaos, constant-amplitude-random-phase light as well as noise light can drive two lasers synchronized [13,15]. Once the injection strength is strong enough, the drive light can induce synchronization between two parameter-matched lasers, for example, their response waveforms are almost identical.
Fig. 1. (a) Schematic diagram of key distribution scheme based on commonly-driven laser synchronization with random modulation of the drive light, (b) a generation example of signal MA according to control codes CA in MUX module and (c) the photograph of experiment systems. SLD, super-luminescent diode; OF, optical filter; EDFA, erbium-doped-fiber-amplifier; OC, optical coupler; PC, polarization controller; IM, intensity modulator; ATT, optical attenuator; OI, optical isolator; LD, distributed-feedback laser diode; PD, photo-detector; MUX, time-division multiplexing module; RF, radio-frequency amplifier.
On each user side, the drive light is first modulated by a private random signal MA, B and then is injected into the laser. Note subscript “A” denotes Alice and “B” denotes Bob. Polarization controllers are used to adjust the polarization state of injected light in IMs and LDs. Once the injection strength is strong enough and using modulation signal MA = MB, two laser response outputs are synchronized and used as physical entropy source for random number generation.
Figure 1(b) shows the generation principle of modulation signals MA and MB. Two different random sequences S0 and S1 with a duration time T are allocated to legitimate users. Alice utilizes his own random binary control codes CA to select the random sequences according to mapping 0→S0 and 1→S1, and thus form the modulation signal MA by time division multiplexing. Similarly, Bob independently generates MB. After intensity modulation, the drive light power is changed as:
It is worth noting that the keying parameter of S0 and S1 in our scheme is algorithmic parameter that can be dynamically modified. Let’s consider two scenarios. First, if using fixed modulation signals, it is the same as other shift keying schemes that using physical parameters [22–28]. However, since the modulation signals generated in the electrical domain, it becomes possible to dynamically change the keying parameters. This represents the second scenario, for example, users can determine the next parameters after each successful key distribution. Here, the pre-shared random sequences S0 and S1 can be generated by either algorithms or integrated chaotic circuits [30] with different seeds. If algorithmic generation is employed, the algorithm can be disclosed while maintaining secrecy over the negotiation of the random number seed.
Users individually record their control codes CA and CB along with corresponding laser outputs waveforms PA and PB, and subsequently sample raw random numbers from their own waveforms. After that, users exchange CA and CB to extract shared keys KA and KB from their own raw random numbers locally according to CA = CB. The exchange of CA and CB in the public does not provide any information about the key, as the information of CA and CB is the order of laser states instead of the extracted numbers. The security of the shared key is ensured by real-time drive light, the complex dynamics of laser response and random modulation, and the randomness of shift keying. It is assumed that a potential eavesdropper (Eve) has access to public information including the drive light and control codes. Compared to legitimate users, Eve would need to perfectly counterfeited two precise hardware systems running in parallel to access the shift-keying laser entropy source, which poses a formidable technical challenge and much higher costs.
Figure 1(c) is the photograph of our experimental setup. In our experiment, IMA and IMB (IXblue, MXAN-LN-40) both operate at the same bias point, corresponding to voltages of 1.05 V and 4.51 V, respectively. The electro-optical bandwidth of IMA and IMB is about 30 GHz, which can realize fast modulation of the drive light. Relaxation-oscillation-frequency enhanced lasers are used as response lasers here [31]. The injection strength for LDA and LDB are both controlled at 0.18 by optical attenuators (ATT). LDA and LDB operate in a central wavelength of 1547.640 nm and a relaxation oscillation frequency of 6.25 GHz. After injecting the drive light into the laser, precise parameter adjustments, such as polarization, are imperative to achieve laser synchronization.
We generate the random signal MA and MB by an arbitrary waveform generator (AWG, Keysight, M8196A). A pseudo-random sequence S1 uniformly distributed between −1 and 1 is generated by a computer, and we generate S0 = –S1. According to private binary codes, we generate MA and MB by time-division multiplexing of S0 and S1, which are then converted into an electrical signal at a sampling rate of 92 GSa/s by the AWG (see Fig. 1(b)), followed by a radio-frequency amplifier (RF, IXblue, DR-AN-40-MO) that amplifies the signal power. A keying code duration T = 11.1 ns (2^10 sampling points in AWG) is applied, corresponding to shift-keying rate = 90 Mb/s. A low-pass filter in AWG with a cutoff frequency of 5 GHz is applied to smooth the electrical signal MA and MB. The modulation depth here is estimated by mp = $\mathrm{Vpp\;\ /\;\ V\pi }$, where Vpp is considered as a peak-to-peak voltage of MA, MB and Vπ = 5 V. The voltage on the RF is 1 V, approximately corresponding to mp = 1.7.
The laser outputs are detected by photodetectors (PD, CONQUER, KG-PD-20G-A-SM-FA-DC) and measured by a 16-GHz real-time oscilloscope (Keysight, DSAV164A). An RF spectrum analyzer (Rohde &Schwarz, FSW50) is used in conjunction with a 50-GHz PD (FINISAR, XPDV2150R).
3. Experimental results
3.1 Laser synchronization and shift-keying modulation
Experimental results of laser synchronization of two lasers are plotted in Figs. 2(a)–2(d). As shown in Fig. 2(a), the optical spectrum in black with a 3-dB bandwidth of 6 GHz is the drive light and its central wavelength is close to that of lasers. Narrow linewidth drive light is beneficial for long-distance transmission [20]. After the injection, the optical spectra of the two LDs show significant broadening and a high level of similarity. The RF spectrum of LDA in Fig. 2(b) is flat with an effective bandwidth (contains 80% of the total energy [32]) of 18.21 GHz. Furthermore, Figs. 2(c) and 2(d) show an example of the temporal waveforms PA and PB, and their correlation plots. It is qualitatively seen that the outputs of both lasers exhibit complex dynamics with a strong waveform similarity. The scatter plot in Fig. 2(d) exhibits a concentrated linear trend. The cross-correlation (CC) value is used to evaluate the synchronization of waveforms, which is defined as:
Fig. 2. Laser synchronization in experiment. (a) Optical spectra of the drive light and two lasers, and (b) RF spectrum of LDA with noise floor. (c) Temporal waveforms and (d) correlation plots of LDA and LDB.
Moreover, we investigated the effects of intensity modulation of the drive light on the correlation of two lasers. A 2-ns slice of modulation signal MA and the corresponding laser temporal waveforms PA are plotted for easy comparison, as illustrated in Figs. 3(a)–3(b). The temporal waveforms between MA and PA are significant different, due to the modulation in Eq. (1) accomplished by two random signals. A high CC value of lasers outputs is 0.93 (see Fig. 3(c)) when modulation signal MA = MB = S1, while a low CC value of 0.22 (see Fig. 3(d)) is obtained when modulation signal MA = −MB = −S1. Therefore, algorithm parameters can be used as shift parameter to control laser synchronization. Compared to schemes that require a difference of dispersion greater than 1000 ps/nm [25], a low residual correlation between the laser output of two lasers can be also achieved with random modulation of the drive light. If the signal MA, B bandwidth is too wide, it can lead to modulation distortion caused by limitation in the response time of IMs. Conversely, if the bandwidth is too narrow, modulation has minimal impact on the driving light. In the aforementioned experimental settings, it is recommended to maintain a modulation signal bandwidth within the range of 1-15 GHz. The experimental RF gain is limited at 26 dB, but a higher gain can further reduce the correlation in Fig. 3(d) by scrambling the drive light. Other S1s, generated with different random number seeds or from Gaussian distributions, have also completed the random modulation.
Fig. 3. Effects on laser synchronization with random intensity modulation of drive light. Examples of 2-ns temporal waveforms and correlation plots when (a), (c) using modulation signals MA = MB, and (b), (d) using modulation signals MA = −MB.
We also investigated the correlation between the drive light and the laser outputs, as well as between the modulation signal and the laser outputs, as plotted at Fig. 4. The correlation between the drive light and the laser outputs is as high as CC = 0.47, and it decreases to CC = 0.27 upon modulation with MA = S1, as shown as Figs. 4(a)–4(b). Random modulation here reduces the risk of Eve who will attempt to obtain the information of laser entropy by intercepting the drive light. In addition, the residual correlation between the modulation signal MA and corresponding laser outputs PA is also as low as CC = 0.28 (see Fig. 4(c)). Assuming that S1 is decrypted, Eve can only get very little information about the entropy source. If Eve successfully intercepts both the drive light and the modulating signal, similar to that in Fig. 4(a), the nonlinearity of response laser combined with random modulation can still provide a certain level of security for the laser entropy source. Despite using an open-loop scheme, our random modulation affects the laser state. As a result, Eve must prepare more matched lasers, which is similar as the requirements of a closed-loop scheme.
Fig. 4. Cross correlation of drive light PD and the laser output PA when (a) modulation signal MA = 0 and (b) MA = S1. (c) Cross correlation of MA and PD when modulation signal MA = S1. The sequence S1 is the same as that in Fig. 3.
The mismatch of laser parameter has been studied a lot [25,28], so we focus on the mismatch of random modulation, as depicted in Fig. 5. We fix the modulation delay and modulation depth of Bob and then change time delay of MA and the voltage of the RF in Alice. Figure 5(a) shows a synchronization degradation as increasing the mismatch of modulation delay, and the CC value is larger than 0.9 upon a mismatch from −34 to 48 ps. The sensitivity of modulation delay mainly depends on the response time of modulator. For a high-performance modulator, the sensitivity of parameter mismatch may be higher, which can further enhance the security of the scheme. Due to the saturation effect of the RF, the right half of the curve in Fig. 5(b) is absent in the experiment and the CC value exceeds 0.9 when the mismatch of modulation depth is lower than 0.2. It is clear that a mismatch in either modulation time delay or modulation depth will reduce the correlation of two laser outputs. The high sensitivity of parameter mismatch is a necessary condition to ensure the security of key distribution at the physical layer. In our proposed scheme, parameters include not only the internal laser parameters but also the additional hardware parameters of random modulation.
Fig. 5. Effects of parameter mismatch on laser synchronization. Mismatch between (a) modulation delay and (b) modulation depth in both users. The modulation depth of IMB is fixed on 1.7.
Figure 6 further show the synchronization characteristics of continuous shift-keying in our proposed scheme. The upper gray and black overlapping temporal waveforms represent the modulation signals MA and MB generated by Alice and Bob, respectively. The corresponding control codes CA and CB are inscribed in the upper and lower of modulation signals, respectively. The middle blue and red overlapping temporal waveforms PA and PB are the corresponding laser outputs. The connected dotted line at the bottom is the short-time cross correlation of PA and PB, computed with a data length of 1.1 ns (1/10 of time slot T). It can be found that the CC value is around 0.93 within CA = CB, but decreases to about 0.23 when CA ≠ CB. Therefore, after exchanging and comparing CA and CB, Alice and Bob can validate the laser synchronization in time slots upon CA = CB. In Fig. 6(b), a complete keying time slot is displayed and clearly shows the lasers transition from non-synchronization to synchronization, as well as from synchronization to non-synchronization. The difference of the normalized temporal waveforms PA and PB is plotted in the middle. According to a 10-µs experimental CC value curve, most of them are less than 1.1 ns. In Fig. 6(b), a complete keying time slot is displayed and clearly shows the transition from non-synchronization to synchronization, as well as from synchronization to non-synchronization. According to the experimental CC value curve, a stable laser synchronization recovery time is less than 1.1 ns. The actual laser synchronization recovery time is determined by laser’s response time to the drive light, which is less than 1.1 ns. In the scheme of switching laser synchronization, it is significantly shorter compared to the reported optical-feedback laser configuration [22–24]. The synchronization remains stable within each calculation point, allowing for a minimum keying time slot of two times the synchronization recovery time. In principle the duration time can be shortened and its limit is the synchronization recovery time. When the key successfully extracted, even if Eve manages to forge a matched laser system, the random modulation and parameter shift keying ensure the information security of laser entropy source. Moreover, assuming that Eve forges two laser systems running in parallel, our proposed scheme still has a sensitive modulation delay as a physical parameter and allows for changes in parameters of random sequence S0 and S1 to encrypt the system. In summary, as long as Eve’s hardware manufacturing capacity do not significantly surpass those of legitimate users, the proposed key distribution scheme remains secure.
Fig. 6. (a) Shift-keying modulation waveforms (upper) with their control codes and corresponding laser outputs (middle) of Alice and Bob. The sliding short time cross correlation curve is plotted at the bottom with a calculation length of 1.1 ns. (b) The enlarged view of a keying time slot.
3.2 Key generation rate
Now we use the shift-keying laser waveforms for key generation. The secure key generation rate Rgen in this scheme is estimated as follows [22,23]:
Fig. 7. BER and the key generation rate of Alice and Bob. (a) BER as a function of the threshold coefficients C+ of Alice and Bob in comparison to Eve intercepting and quantizing the drive signal. (b) The key generation rate according to Eq. (3) with sampling rate at 90 Mb/s and 11.42 Gb/s, respectively. The BER is calculated with 0.25 million retained bits.
Robust dual-threshold quantization [22,23] is used to extract bits from laser waveforms. This method can effectively reduce BER and be expressed by the following formula:
Figure 7(b) shows the key generation rate as a function of the threshold coefficients C + . According to Eq. (3), the maximum secure key generation rate Rgen is 20.11 Mb/s when sampling rate Rsamp = 90 Mb/s (i.e., only one bit extraction per keying time slot), corresponding to C+ = 0.50, r = 0.50 and BER = 1.68 × 10−3. When C+ decreases, the increasing BER of Alice and Bob leads to a rapid decrease of the key generation rate.
To fully utilize the complex laser dynamics, the upper limit of sampling rate Rsamp is typically determined using the National Institute of Standards and Technology (NIST) Special Publication 800-22 statistical test suite [34]. The random performance of the quantization bit stream is considered satisfactory when passing all the 15 test items. Each test item is performed using 1000 samples of 1-Mbit sequence. A logical XOR between the quantization bit stream and its 39.1-ns-delay duplicate is executed to eliminate the weak periodicity. All P-values should be greater than 0.0001 and the proportions should fall in the confidence interval of 0.99 ± 0.0094392. Figure 8 shows the test reports of quantization bit stream using a sampling rate Rsamp = 11.42 Gb/s, corresponding to key generation rate Rgen = 2.55 Gb/s (see Fig. 7(b)). In this case, multiple bits can be extracted during each time slot T. NIST results indicate that the proposed scheme performs well in high-speed key generation. To ensure the randomness, a sampling rate of 11.42 Gb/s is used, which is much smaller than the signal bandwidth (as shown in Fig. 2(b)). Note that due to the lower bandwidth of our oscilloscope compared to the actual bandwidth (as shown in Fig. 2(b)), it is equivalent to apply electrical filter to the laser outputs. Therefore, the actual allowable sampling rate can be even higher. All the results suggest that our generated bits are statistically independent and meet the needs of rigorous communication criteria.
Fig. 8. NIST test results. P-value (left column) and proportion (right column) of all the 15 test items.
4. Conclusion
In conclusion, we propose and experimentally demonstrate a physical-layer key distribution scheme based on commonly-driven laser synchronization with random modulation of drive light. The random modulation operates in the electrical domain and successfully scrambles the drive light, ultimately achieving on-off synchronization of lasers. We experimentally achieve information-theoretic secure key distribution between legitimate users using random control codes and matched physical hardware systems. The proposed random modulation reduces the correlation between the drive light and response laser outputs to 0.27 and introduces additional hardware parameters, which enhances the security of the key distribution. In addition, we demonstrate a low synchronization-recovery time in lasers of less than 1.1 ns, in support of a high-speed key distribution of up to 2.55 Gb/s in the proposed scheme. All optics can be available commercial devices and the random modulation can be completed using integrated circuits, which will improve the robustness and practicability of the scheme. Our experiments present a promising approach for future integrated high-speed key distribution that is resistant against computational attacks and interception attacks, serving as an intermediary solution between algorithms and QKD.
Funding
National Key Research and Development Program of China (2020YFB1806401); National Natural Science Foundation of China (61927811, 62035009, U22A2087); Program for Guangdong Introducing Innovative and Enterpreneurialeams.
Disclosures
The authors declare no conflicts of interest.
Data availability
The data that support the plots in this study are available from the corresponding author upon reasonable request.
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