Fast random bit generation with a single chaotic laser subjected to optical feedback

A semiconductor laser with distributed feedback from a fiber Bragg grating (FBG) is investigated for random bit generation (RBG). The feedback perturbs the laser to emit chaotically with the intensity being sampled periodically. The samples are then converted into random bits by a simple postprocessing of self-differencing and selecting bits. Unlike a conventional mirror that provides localized feedback, the FBG provides distributed feedback which effectively suppresses the information of the round-trip feedback delay time. Randomness is ensured even when the sampling period is commensurate with the feedback delay between the laser and the grating. Consequently, in RBG, the FBG feedback enables continuous tuning of the output bit rate, reduces the minimum sampling period, and increases the number of bits selected per sample. RBG is experimentally investigated at a sampling period continuously tunable from over 16 ns down to 50 ps, while the feedback delay is fixed at 7.7 ns. By selecting 5 least-significant bits per sample, output bit rates from 0.3 to 100 Gbps are achieved with randomness examined by the National Institute of Standards and Technology test suite.

This paper reports the experimental investigation of two different approaches to random bit generation based on the chaotic dynamics of a semiconductor laser with optical feedback. By computing high-order finite differences of the chaotic laser intensity time series, we obtain time series with symmetric statistical distributions that are more conducive to ultrafast random bit generation. The first approach is guided by information-theoretic considerations and could potentially reach random bit generation rates as high as 160 Gb/s by extracting 4 bits per sample. The second approach is based on pragmatic considerations and could lead to rates of 2.2 Tb/s by extracting 55 bits per sample. The randomness of the bit sequences obtained from the two approaches is tested against three standard randomness tests (ENT, Diehard, and NIST tests), as well as by calculating the statistical bias and the serial correlation coefficients on longer sequences of random bits than those used in the standard tests.

Chaotic semiconductor laser is a good candidate for secure communication and high-speed true random bit generator, for its characteristics of broad bandwidth and prominent unpredictability. Based on the synchronization property and true random bit generation characteristic of chaotic semiconductor lasers, physical secure key distribution is available. In this work, we majorly show three key distribution schemes stemming from synchronized chaotic semiconductor lasers or chaos-based key exchange protocol. The numerical results demonstrate that the security of the chaos-synchronization-based key distribution scheme can be physically enhanced by adopting dynamic synchronization scheme or encrypted key generation, and that of key distribution with chaos-based key exchange protocol is dependent on the security of the exchange protocol and finally determined by the difficulty of regeneration the chaos system accurately.

Security and privacy problems in communication systems and social media platforms where digital image/video are shared almost always, have attracted researchers interest on information security. Starting from this point of view, a novel one-dimensional chaotic maps based pseudo random bit generator is proposed to make a significant contribution to the literature about protection of personal data in any network. Electronic circuit realizations of Logistic and Tent maps as entropy source are designed on Orcad-Pspice environment and state variables are inputted to novel post-processor algorithm. The rest of main blocks of proposed pseudo random bit generator design are built up fixed-point binary conversion algorithm, XOR processor and H function post-processor. The generated pseudo random bit series are tested by using NIST 800.22 statistical test suite and applied to color image encryption in order to show the effectiveness of proposed design. Cryptanalysis processes such as histogram, NPCR-UACI and correlation analysis are demonstrated. Analysis results show that the proposed design can be used successfully in many secure communication and media transmission applications.

Chaotic laser generated by semiconductor lasers has been attached great importance in areas of secure communication, random number generation, and optical sensing. This article mainly reviews the research progress in the performance improvement of chaotic laser, including bandwidth enhancement and time‐delay signature suppression. First, the methods of chaotic laser generation and the existing problems are briefly introduced. Then, innovative methods for the optimization of chaotic characteristics are analyzed and discussed. The integrated chaotic semiconductor lasers are also discussed. At last, avenues for the development trends and future applications of chaotic semiconductor lasers are prospected.

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.

Chapter 3 - Random Number Generation

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.

There is a wide range of problems devoted to the possibility of traversing the maze by finite automatons. They can differ as the type of maze (it can be any graph, even infinite), and the automata themselves or their number. In particular, a finite state machine can have a memory (store) or a random bit generator. In the future, we will assume that the robot — is a finite automaton with a random bit generator, unless otherwise stated. In addition, in this system, there can be stones-an object that the finite state machine can carry over the graph, and flags-an object whose presence the finite state machine can only observe. This topic is of interest due to the fact that some of these problems are closely related to problems from probability theory and computational complexity. This paper continues to address some of the open questions posed in Ajans’s thesis: traversal by a robot with a random bit generator of integer spaces in the presence of a stone and a subspace of [4] flags. Such problems help to develop the mathematical apparatus in this area, in addition, in this work we investigate the almost unexplored behavior of a robot with a random number generator. It is extremely important to transfer combinatorial methods developed by A. M. Raigorodsky in the problems of this topic. This work is devoted to the maze traversal by a finite automaton with a random bit generator. This problem is part of the actively developing theme of traversing the maze by various finite automata or their teams, which is closely related to problems from the theory of complexity of calculations and probability theory. In this work it is shown what dimensions a robot with a generator of random bits, and you can get around stone integer space with flag subspace. In this paper, we will study the behavior of a finite automaton with a random bit generator on integer spaces. In particular, it is proved that the robot bypasses Z 2 and cannot bypass Z 3 ; the c ++ robot bypasses Z 4 and cannot bypass Z 5 ; a robot with a stone and a flag bypasses Z 6 and cannot bypass Z 7 ; a robot with a stone and a flag plane bypasses Z 8 and cannot bypass Z 9 .

A robust true random number generator (TRNG), able to assure high quality output at different working conditions, is an attractive solution in secure communication application, because it increases resilience against possible external attacks. Among different TRNGs, quantum RNGs (QRNG) represent a good candidate for such systems, because of their compactness, low cost and performance [1–6]. They typically consist of a source of photons, such as an attenuated LED, coupled to a detector with single photon capability (SPAD). Many works in the literature have used a single detector [1–4] for random bit extraction. These devices are characterized by a limited bit rate [1], which can be increased by exploiting the arrival time of photons at the cost of circuit and system complexity [2–4]. Recent works [5–6] proposed to implement an array of detectors based on SPAD working in parallel thus extending the speed of QRNG up to 5 Gb/s [5]. Despite the high bit rate, the main drawback of [5] is the strong dependence of each pixel bias on the impinging light intensity which forces the system to work only for a narrow range of photon flux that poses several constraints on the design of the final QRNG system, e.g. the need of a feedback control loop to maintain a constant flux of photons, and of a uniform distribution of light over the entire sensor. Moreover, it is impractical to implement algorithms for bit extraction to all detectors of the array because of different responses and mismatches among SPADs.

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.

Communication security that depends on chaos can be considered as a new approach which provides protection and security of communications and maintains confidentiality because Chaos theory can be implemented in cryptosystem successfully. A stream cipher, on the other hand, is a type of symmetric cryptosystem in which the plaintext is divided into small entities known as characters. The key in stream cipher is typically generated by a random bit generator. Many key stream generators employ linear feedback shift registers (LFSRs). LFSR systems are made up of a group of LFSR units and a combining function (CF) unit. The plaintext is encrypted one bit at a time. The key is fed into a random bit generator, which produces a long series of binary signals. This "key-stream" k is then combined with plaintext m, typically via a bit-wise XOR (Exclusive-OR modulo 2 addition), to produce the ciphertext stream, which employs the same random bit generator and seed. In this paper we will introduce a new stream cipher keygenerator which using a hybrid between chaotic and combination of Linear Feedback Shift Registers (LFSR's). The proposed generator can be used to protect different types of data files (text, image, audio and video). Many kinds of tests are applied to specifying the goodness of the proposed keygenerator. The results of testing prove the efficiency of the suggested system.

The cryptographic security provided by various techniques of random number generator (RNG) construction is one of the developing research areas today. Among various types of RNG, the true random bit generator (TRBG) can be considered as the most unpredictable and most secure because its randomness seed is generated from chaotic sources. This paper proposes a design of TRBG model based on double-scroll attractors circuits with GST memristor. After implementation and simulation of the chaotic circuit with GST memristor emulator, the chaotic behavior of the output voltage and inductor current were received. Moreover, their dependence on the input voltage revealed the close to double-scroll form. The randomness generated from the proposed circuit was tested by analysis of the Fast Fourier Transform (FFT) and Lyapunov exponents of the output voltage.

We propose and implement a simple and compact quantum random number generation (QRNG) scheme based on the quantum phase fluctuations of a DFB laser. The distribution probability of the experimentally measured data fits well with the simulation result, got from the theoretical model we established. Min-entropy estimation and Toeplitz-hashing randomness extractor are used to obtain the final random bit. The proposed approach has advantages not only in simple structure but also in high random bit generation rate. As a result, 502 Gbits/s random bits generation speed can be obtained, which is much higher than previous similar schemes. This approach offers a possibility to promote the practical application of QRNG.

Much scientific work has focused on the generation of random numbers as well as the distribution of said random numbers for use as a cryptographic key. However, emphasis is often placed on one of the two to the exclusion of the other, but both are often simultaneously important. Here we present a simple hybrid free-space link scheme for both the generation and secure distribution of (pseudo-)random numbers between two remote parties, drawing the randomness from the stochastic nature of atmospheric turbulence. The atmosphere is simulated using digital micro-mirror devices for efficient, all-digital control. After outlining one potential algorithm for extracting random numbers based on finding the centre-of-mass (COM) of turbulent beam intensity profiles, the statistics of our experimental COM measurements is studied and found to agree well with the literature. After implementing the scheme in the laboratory, Alice and Bob are able to establish a string of correlated random bits with an 84% fidelity. Finally, we make a simple modification to the original setup in an attempt to thwart the hacking attempts of an eavesdropper, Eve, who has access to the free-space portion of the link. We find that the fidelity between Eve’s key and that of Alice/Bob is 54%, only slightly above the theoretical minimum. Atmospheric turbulence could hence be leveraged as an added security measure, rather than being seen as a drawback.