Security-enhanced chaos communication with time-delay signature ...

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Letter

Vol. 41, No. 16 / August 15 2016 / Optics Letters

Security-enhanced chaos communication with time-delay signature suppression and phase encryption CHENPENG XUE, NING JIANG,* YUNXIN LV, CHAO

WANG,

GUILAN LI, SHUQING LIN,

AND

KUN QIU

Key Laboratory of Optical Fiber Sensing and Communications, Ministry of Education, University of Electronic Science and Technology of China, Chengdu 611731, China *Corresponding author: [email protected] Received 16 June 2016; revised 15 July 2016; accepted 17 July 2016; posted 19 July 2016 (Doc. ID 268496); published 2 August 2016

A security-enhanced chaos communication scheme with time delay signature (TDS) suppression and phaseencrypted feedback light is proposed, in virtue of dual-loop feedback with independent high-speed phase modulation. We numerically investigate the property of TDS suppression in the intensity and phase space and quantitatively discuss security of the proposed system by calculating the bit error rate of eavesdroppers who try to crack the system by directly filtering the detected signal or by using a similar semiconductor laser to synchronize the link signal and extract the data. The results show that TDS embedded in the chaotic carrier can be well suppressed by properly setting the modulation frequency, which can keep the time delay a secret from the eavesdropper. Moreover, because the feedback light is encrypted, without the accurate time delay and key, the eavesdropper cannot reconstruct the symmetric operation conditions and decode the correct data. © 2016 Optical Society of America OCIS codes: (060.4510) Optical communications; (060.4785) Optical security and encryption; (140.1540) Chaos; (140.5960) Semiconductor lasers. http://dx.doi.org/10.1364/OL.41.003690

Secure communication based on a chaotic carrier has drawn significant attention for its high-level security on hardware cryptography due to the emergence of experimental chaos encryption [1–3]. Its security mainly relies on the difficulty of identifying the transmitter parameters and the sensitivity of synchronization quality to parameter mismatch. That is, the whole set of structural and operating parameters in the transmitter and receiver play the role of the key. Unfortunately, the time delay of optical feedback in the external cavity semiconductor laser (ECSL) can give rise to an inherent time delay signature (TDS) embedded in the chaos, which has been found to be vulnerable because it can be identified easily using the autocorrelation function (ACF), delayed mutual information (DMI), permutation entropy (PE), and extreme statistics [4–6]. Worse still, if the time delay is identified, 0146-9592/16/163690-04 Journal © 2016 Optical Society of America

the reconstruction of delayed system may be computationally feasible, and for some systems it has been proved successfully by techniques such as artificial neural networks [7,8]. In addition, the dimension of adjustable-parameter (a sort of equivalent to the digital key size) space in the chaos communication is relatively low compared with algorithmic cryptography, and logistically the security is controlled by the optical hardware manufacturer much more than the user. Recently, several schemes for TDS concealment in the chaotic semiconductor laser subject to optical feedback have been proposed [9–12]. Moreover, schemes exploiting the conventional encryption or others to enhance the security of chaos communication also have been reported [13–15]. However, to our knowledge, for the all-optical chaos-based communication, few works take both of them into account to enhance the security of a chaos communication system, which motivates our investigation. To circumvent these drawbacks, we propose to adopt dual fast-phase-modulated feedback to suppress TDS concealment and encrypt the phase of feedback light simultaneously. A schematic illustration of the security-enhanced communication system is shown in Fig. 1. MSL is an ECSL subject to dual optical feedback with independent high-speed phase modulation, which is different from [13]. By this method, not only the TDS in the chaotic carrier can be well suppressed, but the space of the key can be reduplicated, and the encryption efficiency is

Fig. 1. Schematic of the security-enhanced chaos communication system. PM, phase modulator; CIR, circulator; OC, optical coupler; DL, delay line; EDFA, erbium-doped optical fiber amplifier; M, modulator; PD, photodiode; LPF, low-pass filter.

Vol. 41, No. 16 / August 15 2016 / Optics Letters

Letter improved. Here, we consider a key length of 128 bits for each feedback loop, and the phase modulation is performed according to the keys where the bits “1” mean a phase shift of π rad, while the bits “0” mean a phase shift of 0 rad. The transmission data are encrypted into the chaotic carrier, and the modulated chaotic carrier is unidirectionally injected into the SSL at Bob’s end, which is equipped with identical feedback loops and shared keys to the MSL. Due to the injection-locking effects and symmetry operation, high-quality chaos synchronization can be achieved. Consequently, the encrypted data can be recovered by the synchronized decryption. To numerically demonstrate the proposed system, the modified Lang–Kobayashi rate equations are adopted to describe the dynamics of the ECSLs. In terms of the mean field slowly varying complex amplitudes of the electric field E and the carrier number N, these equations are [13,16] pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 E_ M ;S
1  iαG M ;S − γE M ;S  2βN M ;S χ M ;S 2  k in E M t − T  exp−iωM T  iΔωM S t

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Fig. 2. (a) Temporal waveform of MSL and (b) its optical spectrum in decibels. (c) and (d) ACF computed from intensity and phase time series, respectively. (e) and (f) DMI computed from intensity and phase time series, respectively.

 k 1 E M ;S t − τ1  exp−iωM ;S τ1  iφ1   k 2 E M ;S t − τ2  exp−iωM ;S τ2  iφ2 ;

(1)

N_ M ;S
I∕q − γ e N M ;S − G M ;S jE M ;S j2 ;

(2)

where the subscripts M and S represent the MSL and SSL, respectively. G M ;S
gN M ;S − N 0 ∕1  ϵjE M ;S j2  is the optical gain. k1 and k2 (τ1 and τ2 ) represent the feedback strengths (delay time) of the two feedback loops, respectively. φ1 and φ2 are the corresponding phase shifts added by the phase modulators in the feedback loops. k in (T ) is the injection strength (flight time). ω is the central frequency. The frequency detuning between MSL and SSL is defined as ΔωM ;S
ωM − ωS . The other intrinsic parameters include the photon decay rate γ, the linewidth enhancement factor α, the gain saturation coefficient ϵ, the spontaneous emission rate β, the differential gain parameter g, the carrier decay rate γ e , and the transparent carrier number N 0 · I is the operation current. In our simulations, the frequency detuning is set as ΔωM ;S
0 GHz, and the intrinsic parameters of all lasers used in our simulation are assumed to be identical. Their values are set as the typical values reported in [13]. The modulation frequencies in the two feedback loops are fixed to 24 and 25 GHz, respectively. We set the operation current as I
22.05 mA, the feedback strengths of the two feedback loops in MSL are identical and fixed to k 1
k 2
6 ns−1 , and the corresponding time delay τ1
2 ns, τ2
3 ns, which can keep the MSL working in a chaotic regime [see Figs. 2(a) and 2(b)]. The SSL is not only equipped with identical feedback terms but also suffers a unidirectional injection with a strength of kin
100 ns−1 (T
0 ns) from MSL. Moreover, the chaos modulation technology is adopted to encrypt the data [17]. Namely, the data mt are encrypted into the chaotic carrier of the transmitter (Alice) in the manner of jE mod M j
jE M j1  A · mt, where A is the modulation index, and is set to a small value of 0.05 to ensure that the data can be well hidden in the chaotic carrier. The modulated chaotic carrier is transmitted over a section of dispersionshifted fiber (DSF) with a length of 60 km, which is described

by the nonlinear Schrödinger equation (NLSE), as in [18]. The decryption of the data based on the chaos synchronization between the MSL and SSL is described as m 0 t
LPFfjE tr j2 − jE S j2 g, where E tr is the injected signal after fiber propagation, the operation LPF means that the recovered data are filtered by a fifth-order Butterworth low-pass filter with a cutoff frequency equaling to the transmit data bit rate. First, the TDS built-in chaotic carrier is investigated because an evident TDS will leak the time delay of the ECSL in the transmitter and receiver and subsequently reduce the security of the system. To investigate the time delay characteristic, the ACF and DMI of the chaotic carrier are calculated. It turns out that there is no obvious peak and valley in the whole range of the embedded lag time [Figs. 2(c) and 2(d)], which means the TDSs embedded in the intensity and phase of chaos are well suppressed, and eavesdroppers cannot obtain the information of the external-cavity length of MSL and SSL from the chaotic signal. Moreover, it is worth mentioning that the high-speed modulation would lead to a modulation frequency signature in the frequency spectrum of chaos because the effective bandwidth of chaos is limit [see Fig. 2(b)], which may let out the encryption frequency of the key. However, in the proposed scheme, the phase-shift sequence added by the phase modulator is secret and cannot be intercepted by the bandpass filter. Therefore the security can be guaranteed. Furthermore, the influence of modulation frequency on the TDS suppression is shown in Fig. 3. TDS1 and TDS2 present the TDS induced by the time delays τ1 and τ2 and are defined as the peaks in ACF and DMI around the time delays, respectively. The mean lines (triangle curve) and error bars indicate the background mean value and standard deviation of the peaks in ACF and DMI, respectively. With increasing the modulation frequency, the size of TDS stemming from the intensity time series decays can be well suppressed when the modulation frequency is over 25 GHz, while the TDS identified from the phase time series is always weak even with a low modulation frequency. The obvious performance gap of TDS concealment between the intensity and phase time series is attributed to the

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Vol. 41, No. 16 / August 15 2016 / Optics Letters

Fig. 3. TDS suppression versus modulation frequency. (a) and (b) Peak size in ACF computed from the intensity and phase time series, respectively. (c) and (d) Peak size in DMI computed from the intensity and phase time series, respectively.

direct phase variation induced by the high-phase modulation. By the way, we also investigate the TDS suppression performance by calculating the PE from the intensity and phase, and similar results are obtained (not shown for simplicity). Moreover, for the closed-loop chaos synchronization, it takes a relatively long convergence time (about tens of a nanosecond) for the system to resynchronize when a sudden cut in the link between the MSL and SSL occurs [19]. In terms of information security, higher modulation frequency is more significant, as fast phase modulation can enhance the complexity of the phase shift time series during the convergence time. Figure 4(a) shows the synchronization quality of the chaotic carriers before and after the fiber propagation, and Fig. 4(b) presents that of the chaotic carriers of the transmitter and receiver (no data are encrypted). It is clear that the chaotic optical signals are well synchronized due to the injection locking effect and symmetric operation. Under this condition, a system with a transmission rate of 5 Gb∕s is numerically demonstrated. It is clear that the transmission data are well recovered, and an open-eye diagram is achieved [see Figs. 4(c) and 4(d)]. Next, the eavesdropper Eve, trying to decode the data encrypted in the chaos carrier under different scenarios, is taken

Fig. 4. (a) Cross correlation between the chaos in the transmitter and that after the transmission. (b) Cross correlation between the chaos in the transmitter and receiver. (c) Data decryption at the receiver. (d) Corresponding eye diagram.

Letter into consideration to illustrate the effectiveness and superiority of the security-enhanced system. Similarly, a 5 Gb∕s communication system is adopted and investigated. Initially, we consider that Eve tries to break into the system utilizing the direct linear filter (DLF), which is reported as the most straightforward and common method [20]. The intercepted data are obtained by filtering the modulated chaotic carrier with a lowpass filter with a cutoff frequency equaling to the bit rate. As shown in Fig. 5(a), when a small modulation index is adopted, the data can be well hidden in the chaos, and Eve cannot intercept information by this approach. Moreover, the scenario under which Eve tries to decrypt the data by way of synchronization utilization attack also is investigated. Here Eve is equipped with an attack laser that is identical to the lasers of the legal transmitter and receiver but without the structural parameters of the external cavity and the key. The injection strength in the eavesdropper is also fixed as 100 ns−1 . First, we consider the scenario under which Eve knows nothing about the time delay and phase key but tries to attack the system with an open-loop receiver in which the attack laser only suffers a unidirectional injection. As shown in Fig. 5(b), it is obvious that Eve fails to correctly decode the data. Second, the scenarios under which Eve adopts an attack laser with τ1 and τ2 mismatch or only τ2 mismatch are studied [see Figs. 5(c) and 5(d)]. Apparently, the performance of an illegal attack is bad without the accurate time delay of the optical feedback. Because the result for attacking with only τ1 mismatch is similar to that for the case with only τ2 mismatch, it is not shown here. Finally, the roles of phase-encrypted feedback light in the security also are demonstrated in Figs. 5(e) and 5(f ). Apparently, without accurate knowledge of the keys, the data decoded by the illegal attacker are hardly distinguishable with respect to the original data. Figure 6 presents the bit error rates (BER) of legal recovery and illegal interception versus the data rate. Here the BER is calculated by the method reported in [21,22]. The results show that the BER performances degrade gradually with the rise of data rate. However, the BER of illegal interception are much worse than that of the illegal one. It is also indicates that, with a proper high data rate, the BER of illegal interception can be limited at a very low level close to 0.5, while that of the legal recovery can be kept at an acceptable level. When the transmission rate is raised to 5 Gb∕s, BER ∼10−9 can be guaranteed in the legal communication, but the BER of illegal interception is about 0.3.

Fig. 5. (a) Data intercepted by the way of DLF. (b)–(f ) Data intercepted by the way of synchronization utilization, under the scenarios: (b) with open-loop, (c) with τ1 and τ2 mismatch, (d) with only τ2 mismatch, (e) without the keys in both the feedback loops, and (f ) without the key in one of the two feedback loops.

Letter

Vol. 41, No. 16 / August 15 2016 / Optics Letters

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REFERENCES

Fig. 6. rate.

Performance and security of the system versus the data bit

In conclusion, we have proposed and numerically demonstrated a security-enhanced chaos-based communication system with an independent high-speed phase-modulated dual-loop feedback, in which the security not only relies on the difficulty of identifying the emitter parameters but also relies on the privacy of the dynamic symmetric operating conditions (phase-shift time series). It is demonstrated that, due to the dual feedback and high-rate phase modulation, both of the TDSs embedded in the intensity and phase have been well suppressed. Moreover, the phase shifts in the two feedback loops work as keys to encrypt the phase of the feedback light in the transmitter and receiver. Under such a scenario, without the knowledge of the accurate phase shifts or time delays, the eavesdropper cannot intercept the data, and the security of the data transmission is greatly improved. Funding. National Natural Science Foundation of China (NSFC) (61301156, 61471087); Specialized Research Fund for the Doctoral Program of Higher Education of China (20130185120007).

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