Multi-Channel Physical Random Bits Generation Using a Vertical-Cavity Surface-Emitting Laser Under Chaotic Optical Injection

In this work, we propose and experimentally demonstrate a scheme for generating fast physical random bits (PRBs). For such a scheme, the chaotic signal output from an optoelectronic delay loop (OEDL) pumped by a semiconductor laser (SL) under modulated optical feedback is utilized as the chaotic entropy resource, and the m least significant bits (m-LSBs) extraction and local XOR operation are selected as the post-processing methods. Firstly, through analyzing the influences of some typical parameters on the properties of the chaotic signal, the optimized parameter regions for achieving high quality chaotic signals with weak time-delay signatures and broad bandwidths are determined. Secondly, a high quality chaotic signal under optimized parameters is selected as a chaotic entropy resource, which is sampled and transferred to an original digital bit sequence by an 8-bit analog-to-digital converter (ADC) at a rate of 80 GS/s. Finally, through adopting the m least significant bits (m-LSBs) extraction and logical exclusive OR (XOR) operation to process the original digital bit sequence, a PRB at a rate up to 400 Gbits/s can be generated, which has passed all the NIST tests.

Time-delay signature (TDS) and effective bandwidth (EBW) are two key performance indexes to evaluate a chaos signal generated by a laser system including delay-time feedback. In this paper, we propose and simulate a technical scheme to optimize the TDS and EBW of chaotic signal generated by a slave vertical-cavity surface-emitting laser (S-VCSEL) under chaotic optical injection from a master vertical-cavity surface-emitting laser (M-VCSEL), which is subjected to double external-cavity feedback. First, based on the spin-flip model of a VCSEL subjected to two double external-cavity feedback, the time series of two orthogonal polarization components (referred to as X-component (X-PC) and Y-component (Y-PC), respectively) in the M-VCSEL can be obtained. Furthermore, with the help of self-correlation function (SF) analysis method, the TDSs of X-PC and Y-PC can be evaluated. The results show that through selecting suitable system operation parameters, X-PC and Y-PC in the M-VCSEL can simultaneously output chaotic signals with equivalently average intensity and weak TDS. Under optimized operation parameters, the peak values of the SF (σ) of the chaotic signal are 0.20 for X-PC and 0.16 for Y-PC, respectively, and the EBWs of the chaotic signal are 10.72 GHz for X-PC and 10.10 GHz for Y-PC, respectively. The chaotic signals output from the M-VCSEL under optimized operation parameters are injected into the S-VCSEL for further weakening TDS and enhancing EBW. Through examining the evolution rules of TDS and EBW of polarization-resolved chaotic signals in the parameter space composed of injection strength and frequency detuning, the ranges of optimizing injection parameters are determined for achieving two-channel chaotic signals with well suppressed TDS (σ 15 GHz).

Random source is important for the security of key distribution. In this paper, a novel secure key distribution scheme based on unidirectional injection of vertical cavity surface emitting laser (VCSEL) system is proposed. In the proposed scheme, a chaotic signal without time delay signature is generated by a VCSEL subject to unidirectional optical injection, which is regarded as a master laser. The chaotic signal generated by the master VCSEL is further injected into two slave VCSELs to obtain synchronized bandwidth-enhanced chaotic signals. After that, by sampling, quantizing and XOR operation on the two synchronized chaotic signals, two key streams can be obtained. Based on the well-known spin-flip model, the time delay signature of chaotic signals generated by master VCSEL and the synchronization performance between the master VCSELs and two slave VCSELs are numerically investigated in detail. It is shown that by the unidirectional injection, the chaotic outputs can be achieved in the master VCSEL in a wide range of frequency detuning and coupling strength. More importantly, no time delay signature can be observed in the auto correlation function of the chaotic intensity time series generated by the master VCSEL. Besides, we find that high quality synchronization is achieved between the bandwidth-enhanced chaotic signals generated by two slave VCSELs under the common driving of master VCSEL. The synchronization coefficient between two slave VCSELs increases up to 0.99, and the synchronization coefficient between master VCSEL and salve VCSEL is only 0.74. Note that such a high quality synchronization between two slave VCSELs while relatively low quality synchronization between the master and slave VCSEL is conducible to ensuring the security of key distribution. In addition, the effects of tunable parameters on key bit error rate are considered, and two quantization methods are employed for comparison. Numerical simulation results show that the key bit error rate between two legitimate users is as low as 1%, and the key bit error rate between legitimate user and eavesdropper is higher than 10% in the single-threshold case; the bit error rate can even be as low as 10-6 in the double-threshold case. The influence of parameter mismatch on key bit error rate is also discussed, and it is suggested that two salve VCSELs should be finely matched to ensure low bit error rate. Finally, NIST randomness test is performed for the generated key streams. Hence, the proposed scheme enhances the security of key distribution, which is valuable for further developing the chaos communication systems.

We demonstrate a random bit streaming system that uses a chaotic laser as its physical entropy source. By performing real-time bit manipulation for bias reduction, we were able to provide the memory of a personal computer with a constant supply of ready-to-use physical random bits at a throughput of up to 4 Gbps. We pay special attention to the end-to-end entropy source model describing how the entropy from physical sources is converted into bit entropy. We confirmed the statistical quality of the generated random bits by revealing the pass rate of the NIST SP800-22 test suite to be 65 % to 75 %, which is commonly considered acceptable for a reliable random bit generator. We also confirmed the stable operation of our random bit steaming system with long-term bias monitoring.

A new approach for high-speed physical random bit generation (RBG) based on broadband random optoelectronic oscillator (OEO) is proposed and experimentally demonstrated. In this scheme, a broadband random OEO based on Rayleigh scattering (RS) is employed as the entropy source of RBG. Compared with other broadband random OEOs which require an additional pump source, the optical signal output from the laser in the proposed scheme can realize excited Brillouin scattering as well as acting as an optical carrier. Benefiting from the introduction of randomly distributed feedback by RS, which breaks the limitation of the fixed loop length of the conventional chaotic OEO, the signals generated by the proposed broadband random OEO have random characteristics. Meanwhile, the generated signals exhibit wide and flat frequency spectrum characteristics due to the avoidance of semiconductor chaotic laser relaxation oscillations. The experimental results show the proposed RBG technique can generate physical random bits with a rate of up to 500 Gb/s which can fully pass the NIST test.

Vertical-cavity surface-emitting laser (VCSEL) has received much attention due to its high modulation response bandwidth, two linear polarization modes, and easy integration. The fundamental characteristics of lasers can be observed by simple optical feedback. Here, we experimentally investigate the dynamical characteristics in a 1550-nm VCSEL subjected to mirror optical feedback. The distribution of dynamics for different bias currents and feedback strength is in detail unveiled. Four different dynamic routes to laser chaos are observed at different bias currents. As the bias current increases, the route to chaos becomes complex. Apart from the well-known stable state, quasi-periodic state, chaotic state, and two previously reported dynamics switching phenomena, the dynamics switching between intermittently quasi-periodic state and quasi-periodic state is observed at a high bias current. Additionally, the laser chaos at different bias currents is also comparatively studied. The chaos bandwidth can reach 18 GHz. The systematic investigation provides the basis for utilizing the broadband laser chaos and understanding the nonlinear dynamics in VCSELs.

Based on the chaos synchronization between two pairs of corresponding linear polarization modes in two 1550 nm vertical-cavity surface-emitting lasers (1550 nm-VCSELs) subject to optical injection of common chaotic signals, a novel bidirectional and dual-channel long-distance chaos secure communication system is proposed. The chaotic synchronization characteristics, bidirectional dual-channel communication performance, and the influences of the fiber channel on the message transmission are numerically investigated. Results show that, driven by a common chaotic signal generated from a driver VCSEL (D-VCSEL), two pairs of responding linear polarization modes in two response 1550nm-VCSELs (R-VCSELs) can be synchronized completely and isochronally. Meanwhile, the synchronization coefficients between the two pairs of responding linear polarization modes in D-VCSEL and R-VCSELs are low. Based on the high quality chaos synchronization between two pairs of responding linear modes in two R-VCSELs, bidirectional and dual-channel chaos secure communication can be achieved. After adopting a single mode polarization-maintaining fiber (or dispersion-shifted polarization-maintaining fiber), for 2.5 Gbit/s messages, the Q factor of the decryption signals after transmitting 60 km (or 200 km) can be more than 6.

Using two orthogonal polarization mode outputs from a vertical-cavity surface emitting lasers (VCSEL) with double optical feedback as two chaotic carriers, a dual-channel chaos secure communication system is established, and the synchronization and communication performances of such a system are numerically investigated. The results show that under suitable operated condition, the time-delay signatures of two chaotic carriers originating from two linear polarization modes in the T-VCSLE with double optical feedback can be suppressed efficiently. Under the strong injection locking case, high-quality chaos synchronization between two corresponding modes of T-VCSEL and R-VCSEL can be realized by polarization-preserved optical injection from T-VCSEL to R-VCSEL. Moreover, the tolerance of the synchronization quality on the frequency detuning between T-VCSEL and R-VCSEL is enhanced with the increase of the injection strength. Adopting additive chaos modulation encryption scheme, two pieces of 500 Mbit/s encoded message can be hidden efficiently in the two chaotic carriers in the propagation process and can be successfully extracted at the receiver. Although Q factor decreases with the increase of message transmission rate, the values of Q factor for two channels are still larger than 6 for 6 Gbit/s message.

We report on new dynamics in vertical-cavity surface-emitting lasers (VCSELs), which is induced by a polarization preserving optical feedback. Our solitary VCSEL, i.e. without feedback, emits in a single linearly polarized (LP) and fundamental transverse mode. Optical feedback induces multiple polarization switchings in the L-I curve. When the injection current is set close to one of the multiple polarization switching points, the laser system exhibits a random anticorrelated hopping of the two orthogonal LP fundamental modes. Of particular interest is the observation of antiphase oscillations in the two LP modes that occur with a period corresponding to the delay time, and which complement the slow mode-hopping. Moreover, the LP-resolved optical spectra show random frequency hops between ECMs. The laser system is therefore not only bistable between the LP modes, but also multistable between ECMs. A theoretical rate equation approach yields a good qualitative agreement with our experiment. We report similar delay-periodic oscillations complementing a mode hopping in a scalar delay differential equation modeling the motion of a particle in a double well potential. Such a model was recently investigated by Tsimring and Pikovsky, in a very general context. Our results in VCSELs yield the first experimental evidence of delay-periodic oscillations in a bistable physical system with noise, and are therefore thought to be of general interest for many other processes in biology, medicine, etc. that exhibit interaction of noise, delay and bistability.

We demonstrate a physical random bit generation scheme based on a chaotic optoelectronic oscillator with silicon Mach-Zehnder modulator. The randomness of the 320Gbps sequence after two self-delay XOR operations is verified with NIST statistical tests.

We demonstrate physical random bit (PRB) generation from two chaotic optoelectronic oscillators (OEOs) with silicon Mach-Zehnder and microring resonator modulators. The carrier-injection modulation and the beam interference provide the nonlinearity for the OEO. We digitalize the chaotic waveforms from the two OEOs at 40GS/s with 8-bit resolution and use self-delay bitwise exclusive-or operation as a post-processing method. The randomness of the resulting 320Gbps PRB sequences is verified by the National Institute of Standards and Technology Special Publication 800-22 statistical tests. With the progress of silicon photonic circuits, there is a potential to fabricate a monolithic chaotic OEO chip for compact PRB generation.

We introduce a concept of noise robustness in dynamical systems with noise and argue that this concept is essential to guarantee the reliability of physical random bit generators (RBGs). As an example of promising physical RBGs we consider a chaotic laser system and show that it has the property of noise robustness with respect to changes in the temporal correlation of the noise source. Moreover, employing a simple model of tangent space dynamics, we give a theoretical interpretation of the numerical results and in particular show that the Lyapunov exponent determines a theoretical boundary of a noise-robust region in parameter space. These theoretical results are expected to be significant not only for chaotic lasers, but also for a broad class of chaotic dynamical systems with correlated noise.

Two-mode coexistence in 1550-nm vertical-cavity surface-emitting lasers with optical feedback is experimentally investigated in detail. With the increase of the feedback strength, the two-mode coexistence region is enlarged for continually varied current. The feedback delay time has little influence on the two-mode coexistence region distribution under our experimental conditions. Moreover, a mapping of polarization-mode suppression ratio between two linear polarization (LP) modes is presented in the parameter space of the bias current and the feedback strength. In addition, the simultaneous chaos outputs of two LP modes are obtained for a certain two-mode coexistence region.

Photonic generation of wideband chaotic signals with time delay signature elimination is investigated experimentally and numerically based on a semiconductor laser (slave laser) with chaotic optical injection from a master laser. The master laser is subject to moderate optical feedback where the feedback strength and external-cavity length are fixed, while the slave laser stands alone. The experimental results show that wideband chaotic signals with successful time delay concealment can be generated in the slave laser by simply adjusting the coupling strength and frequency detuning between the two lasers. Furthermore, the numerical results are in accordance with the experimental observations. Finally, we propose a simple method for simultaneously generating multiple streams of high-quality chaotic signals using multichaotic lasers, where the time delay is effectively concealed in the autocorrelation function and delayed mutual information calculated from the chaotic time series.

A system is as secure as its weakest link. Current computing systems employ a multiple-layer approach to build a trusted environment. At the bottom of this multi-layer approach is a hardware root of trust which other layers build upon. It is important to assure this root of trust is secure and free from any weakness. Recently there is surge of research topics on hardware security. In this talk we first narrow the topic a bit and outline a more restricted definition of hardware security. Upon this tighter definition we try to explain why it is so hard to defend hardware attacks. We will give example from the recent hardware attacks. We, then, focus on a few topics related to hardware security including hardware Trojans and IC counterfeiting. We argue why it is very unlikely for a reputable foundry such as TSMC to plant them. On IC counterfeiting, there have been work on employing Physically Unclonable Function (PUF) to prevent counterfeiting. In this talk we will attempt to explain the difference between testing of these hardware security elements from testing of standard logic elements. We will also clarify that foundry is in the best position to work with customers directly in building these elements such as Physical Unclonable Functions (PUFs) and Physical Random Bits Generators (PRBGs).