Random Bits Research Articles

Construction of a New 2D Hyperchaotic Map with Application in Efficient Pseudo-Random Number Generator Design and Color Image Encryption

This paper proposes a new two-dimensional discrete hyperchaotic system and utilizes it to design a pseudo-random number generator (PRNG) and an efficient color image encryption algorithm. This hyperchaotic system has very complex dynamic properties and can generate highly random chaotic sequences. The complex hyperchaotic characteristics of the system are confirmed via bifurcation diagram, chaotic attractor, Lyapunov exponents, correlation analysis, approximate entropy and permutation entropy. Compared with some traditional discrete chaotic systems, the new chaotic system has a larger range of chaotic parameters and more complex hyperchaotic characteristics, making it more suitable for application in information encryption. The proposed PRNG can generate highly random bit sequences that can fully pass all NIST testing items. The proposed color image encryption algorithm achieves cross-channel permutation and diffusion of pixels in parallel. These strategies not only greatly improve the encryption speed of color images, but also enhance the security level of cipher images. The simulation experiments and security analysis results show that the algorithm has strong robustness against differential attacks, statistical attacks and interference attacks, and has good application potential in real-time secure communication applications of color images.

Random number generation using spontaneous symmetry breaking in a Kerr resonator.

We demonstrate an all-optical random number generator based on spontaneous symmetry breaking in a coherently driven Kerr resonator. Random bit sequences are generated by repeatedly tuning a control parameter across a symmetry-breaking bifurcation that enacts random selection between two possible steady-states of the system. Experiments are performed in a fiber ring resonator, where the two symmetry-broken steady-states are associated with orthogonal polarization modes. Detrimental biases due to system asymmetries are suppressed by leveraging a recently discovered self-symmetrization phenomenon that ensures the symmetry-breaking dynamics act as an unbiased coin toss, with a genuinely random selection between the two available steady-states. We optically generate bits at a rate of 3 MHz without post-processing and verify their randomness using the National Institute of Standards and Technology and Dieharder statistical test suites.

Composably secure device-independent encryption with certified deletion

We study the task of encryption with certified deletion (ECD) introduced by Broadbent and Islam (2020), but in a device-independent setting: we show that it is possible to achieve this task even when the honest parties do not trust their quantum devices. Moreover, we define security for the ECD task in a composable manner and show that our ECD protocol satisfies conditions that lead to composable security. Our protocol is based on device-independent quantum key distribution (DIQKD), and in particular the parallel DIQKD protocol based on the magic square non-local game, given by Jain, Miller and Shi (2020). To achieve certified deletion, we use a property of the magic square game observed by Fu and Miller (2018), namely that a two-round variant of the game can be used to certify deletion of a single random bit. In order to achieve certified deletion security for arbitrarily long messages from this property, we prove a parallel repetition theorem for two-round non-local games, which may be of independent interest.

Reconfigurable Physically Unclonable Functions Based on Nanoscale Voltage‐Controlled Magnetic Tunnel Junctions

AbstractWith the fast growth of the number of electronic devices on the internet of things (IoT), hardware‐based security primitives such as physically unclonable functions (PUFs) have emerged to overcome the shortcomings of conventional software‐based cryptographic technology. Existing PUFs exploit manufacturing process variations in a semiconductor foundry technology. This results in a static challenge–response behavior, which can present a long‐term security risk. This study shows a reconfigurable PUF based on nanoscale magnetic tunnel junction (MTJ) arrays that uses stochastic dynamics induced by voltage‐controlled magnetic anisotropy (VCMA) for true random bit generation. A total of 100 PUF instances are implemented using 10 ns voltage pulses on a single chip with a 10 × 10 MTJ array. The unipolar nature of the VCMA mechanism is exploited to stabilize the MTJ state and eliminate bit errors during readout. All PUF instances show entropy close to one, inter‐Hamming distance close to 50%, and no bit errors in 104 repeated readout measurements.

Pseudo random number generator based on vertical-cavity surface-emitting lasers under current modulation embedded in microcontroller

This paper explores the dynamics, microcontroller validation of a vertical-cavity surface-emitting laser (VCSEL) under current modulation (CM) and employs it to model a process of pseudo-random number generator (PRNG). Solitary VCSEL has three equilibrium points whose stabilities depend on the direct current density. VCSEL under CM (VCSELCM) experiences antimonotonicity, chaotic bubble attractor as well as chaotic attractor. A microcontroller implementation of VCSELCM is used to establish the dynamical behaviors spotted in VCSELCM during the numerical simulations. Lastly, the chaotic characteristics depicted by the VCSELCM are used to design a process of PRNG. The generated random bits are validated successfully by a standard statistical tool set by the National Institute of Standards and Technology (NIST-800–22).

Formally Verified Samplers from Probabilistic Programs with Loops and Conditioning

We present Zar: a formally verified compiler pipeline from discrete probabilistic programs with unbounded loops in the conditional probabilistic guarded command language (cpGCL) to proved-correct executable samplers in the random bit model. We exploit the key idea that all discrete probability distributions can be reduced to unbiased coin-flipping schemes. The compiler pipeline first translates cpGCL programs into choice-fix trees, an intermediate representation suitable for reduction of biased probabilistic choices. Choice-fix trees are then translated to coinductive interaction trees for execution within the random bit model. The correctness of the composed translations establishes the sampling equidistribution theorem: compiled samplers are correct wrt. the conditional weakest pre-expectation semantics of cpGCL source programs. Zar is implemented and fully verified in the Coq proof assistant. We extract verified samplers to OCaml and Python and empirically validate them on a number of illustrative examples.

Colour image encryption based on hybrid bit-level scrambling, ciphering, and public key cryptography

This paper proposes an image encryption technique using three stages algorithms based on hyper-chaotic maps. In the first scenario, bit-level scrambling (BLS) using a 2D coupled chaotic map (2D-CCM) is used to encrypt the bits of the basic colour image. In the second strategy, the scrambled bit level is XORed with pseudo random bit generator (PRBG). The PRBG is designed using a combination of chaotic maps, including, logistic map (LM), sine map (SM), 5D chaotic map (5D-CM), enhanced quadratic map (EQM), and 2D henon SM (2D-HSM). The pubic key based on the Chebyshev polynomial chaotic map is used as the final phase of the encryption algorithms. The performance analysis of the proposed image encryption technique is validated through various criteria such as fundamental space analysis, correlation coefficient, entropy, the number of pixels changes rate (NPCR), and unified average-changing intensity (UACI). Also, the obtained results are compared with other recent studies. The simulation results demonstrated that the proposed technique has robust security and it provides the image with high protection against various attacks.

MRNG: Accessing Cosmic Radiation as an Entropy Source for a Non-Deterministic Random Number Generator.

Privacy and security require not only strong algorithms but also reliable and readily available sources of randomness. To tackle this problem, one of the causes of single-event upsets is the utilization of a non-deterministic entropy source, specifically ultra-high energy cosmic rays. An adapted prototype based on existing muon detection technology was used as the methodology during the experiment and tested for its statistical strength. Our results show that the random bit sequence extracted from the detections successfully passed established randomness tests. The detections correspond to cosmic rays recorded using a common smartphone during our experiment. Despite the limited sample, our work provides valuable insights into the use of ultra-high energy cosmic rays as an entropy source.

An innovative approach based on optimization for the determination of initial conditions of continuous-time chaotic system as a random number generator

Security has been one of the important problems in the processing, storage and transmission of information. The transfer of information to virtual environments with technological developments has made it necessary to examine the concept of security with different dimensions. Data security can be achieved to a great extent by using randomly generated unpredictable bit sequences in encryption. In this study, approximately 1,000,000 random bits were generated for use in computer science. The Mode2(x) method and the unpredictable nature of chaotic systems are used for random number generation. With this hybrid structure used in the study, it is aimed to gain a different perspective to future studies. However, it is known that the sensitivity of chaotic systems to initial conditions is very high. The most important contribution of the study to the literature is that the initial conditions were determined using optimization algorithms. In this study, Particle Swarm Optimization (PSO) and Ant Colony Optimization (ACO) were used to calculate the initial conditions. To the authors' knowledge, this is the first study to use optimization to determine initial conditions for continuous-time chaotic systems. NIST SP 800-22 Statistical Test Suite was used to analyze the reliability of the generated random bits. It was seen that the proposed method passed all statistical tests successfully (100 %). Histogram and floating frequency analysis were used for the analysis of random numbers obtained from the generated bits. Histogram plots showed uniform distribution. It is seen that there is a homogeneous distribution in the sliding frequency analysis.

A 200 kb/s 36 µw True Random Number Generator Based on Dual Oscillators for IOT Security Application

As a module of the internet of things (IOT) information security system, the true random number generator (TRNG) plays an important role in overall performance. In this paper, a low-power TRNG based on dual oscillators is proposed. Two high-frequency cross-coupled oscillators are used to generate high-jitter clock signals, and then the SR latch with power supply below standard power supply voltage is adopted to process the oscillator output to maintain its metastability and increase jitter. The circuit is realized by an SMIC 180 nm 1P6M mixed-signal process. The experimental results show that when power supply voltage is 1.8 V, the circuit outputs a random number bit rate of 200 kb/s, the core area is 0.0039 mm2, and the power consumption is only 36 µw. The output random sequences can pass the NIST SP 800-22 test.

An Energy Efficient and High Performance Modified Trng based Two Phase Multi Bit Per Cycle Ring Oscillator for IoT Applications

The modified TRNG (true random number generator) is mainly focused due to minimize the power wasted by the superfluous oscillations at higher frequency operations. To boost fan-out condition, random bits are collected from both phases of the slow ROs (Ring oscillators), and the fast RO is only engaged during the brief transition time difference between two slow ROs that are symmetrically built. In order to lower the power consumption of the suggested design, the slow jittery ROs are implemented utilising current starved inverters (CSI) biassed in the weak inversion zone. By decreasing the transistors' drain current and oscillation frequency, their jitter amplitudes are made more pronounced. The quickest three-stage RO quantizes the narrow jittery pulse produced by the differential pair of slow ROs. By counting the number of oscillatory cycles of the quick RO, a gigahertz dynamic toggled D flip-flop counter may be used to extract two random bits from each phase of the jittery ROs. The proposed TRNG is fabricated in a standard 45 nm using 1V supply of CMOS process.

Finite-horizon distributed set-membership filtering with dynamical bias and DoS attacks under binary encoding schemes

In this work, we cope with the design issue of finite-horizon distributed set-membership filters concerning a set of time-varying systems (TVSs) over sensor networks (SNs). The system to be discussed is suffering from dynamical bias and unknown but bounded noise. The binary encoding schemes (BESs) are utilized in the data transmission through SNs from neighbors to the intelligent sensor nodes, which exhibit robustness to some degree due to usage of the binary data. Both random bit errors caused by channel noises and denial of service (DoS) attacks reflecting network vulnerability are considered that may arise and lead to signal distortion in the transmission process of the binary bit string. In the framework of adopting BESs, our aim is to realize the distributed set-membership filtering for TVSs over SNs limited by dynamical bias and DoS attacks. Sufficient conditions, relying on the solvability of a class of recursive linear matrix inequalities, are obtained for the presence of the expected time-varying distributed set-membership filters. Furthermore, an additional optimization issue is constructed to find the minimal ellipsoids (on the basis of matrix trace) to obtain the best filtering performance. Eventually, a numerical simulation instance is provided to verify the availability of the presented design strategy of finite-horizon distributed set-membership filters.

Realization of a source-device-independent quantum random number generator secured by nonlocal dispersion cancellation

Quantum random number generators (QRNGs) can provide genuine randomness by exploiting the intrinsic probabilistic nature of quantum mechanics, which play important roles in many applications. However, the true randomness acquisition could be subjected to attacks from untrusted devices involved or their deviations from the theoretical modeling in real-life implementation. We propose and experimentally demonstrate a source-device-independent QRNG, which enables one to access true random bits with an untrusted source device. The random bits are generated by measuring the arrival time of either photon of the time–energy entangled photon pairs produced from spontaneous parametric downconversion, where the entanglement is testified through the observation of nonlocal dispersion cancellation. In experiment, we extract a generation rate of 4 Mbps by a modified entropic uncertainty relation, which can be improved to gigabits per second by using advanced single-photon detectors. Our approach provides a promising candidate for QRNGs with no characterization or error-prone source devices in practice.

A 2.22 Mb/s True Random Number Generator Based on a GeTex Ovonic Threshold Switching Memristor

True random number generators (TRNGs) based on threshold switching memristors emerge as a building block for secure electronics. However, the throughputs reported in previous studies have a stark gap with the requirements of practical applications (>1 Mb/s). Here, we implement a high-speed TRNG with a GeTe <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</sub> ovonic threshold switching (OTS) memristor. The TRNG throughput reaches 2.22 Mb/s for a single cell, which is 2.2 times faster than the prior state-of-the-art threshold-switching-based TRNG. In addition, the TRNG endurance of 2×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">9</sup> bits was achieved, and the random bits passed 12 tests in the National Institute of Standards and Technology statistical test suite. Our results demonstrated that the OTS-based TRNG could provide a high–throughput and highly secure solution for edge applications.

Secured computed tomography scanner using a random bit.

Patient data in current computed tomography scanner machines are transferred through several communication channels, such as WiFi, to the mobile channel platform. Therefore, patient information is an important security concern. Medical imaging must be protected using various methods. The current hardware-dependent method for generating random bits exhibits predictable or inconvenient physical characteristics. Therefore, a more flexible random-bit generation technique is to be devised. We propose a deterministic random bit generation algorithm that uses a mathematical periodic function. After randomizing the image using the proposed random bit, the performance is analyzed and compared with that of the processed image. The random bit generation method using a mathematical algorithm shows higher entropy than the random bit generated by hardware.

Development of a High Min-Entropy Quantum Random Number Generator Based on Amplified Spontaneous Emission.

We present the theory, architecture, and performance characteristics of a quantum random number generator (QRNG) which operates in a PCI express form factor-compatible plug-and-play design. The QRNG relies on a thermal light source (in this case, amplified spontaneous emission), which exhibits photon bunching according to the Bose-Einstein (BE) statistics. We demonstrate that 98.7% of the unprocessed random bit stream min-entropy is traceable to the BE (quantum) signal. The classical component is then removed using a non-reuse shift-XOR protocol, and the final random numbers are generated at a 200 Mbps rate and shown to pass the statistical randomness test suites FIPS 140-2, Alphabit, SmallCrush, DIEHARD, and Rabbit of the TestU01 library.

Pseudo random number generator based on memristive Helmholtz snap oscillator with two lines of equilibria embedded in microcontroller

This paper explores the dynamics and electronic validations of a memristive Helmholtz snap oscillator (MHSO), employing it to model a process of pseudo-random number generator (PRNG). The MHSO depicts two lines of Hopf bifurcation is associated with one of the equilibrium domains while the other region of equilibrium points is always unstable. Extreme multistability features, hidden complex attractors, antimonotonicity equilibrium points. Characterizing the stability of the equilibrium domains, period-3-oscillations and chaotic hidden attractors coexisting, chaotic bubbles, and hidden attractors are generated in MHSO for particular values of parameters. Electronic validations of MHSO based on OrCAD-PSpice software and microcontroller reveal that OrCAD-PSpice and microcontroller dynamics agree well with the dynamics achieved by numerical simulations. Lastly, the chaotic characteristics depicted by the MHSO are used to design a process of PRNG. The generated random bits are validated successfully by a standard statistical tool set by the National Institute of Standards and Technology (NIST-800-22).

Medical image encryption based on RNG with an autonomous piecewise damping Josephson junction jerk oscillator embedded in FPGA

This paper explore the dynamics, Field Programmable Gate Array (FPGA) validation of an autonomous piecewise damping Josephson junction jerk oscillator (APDJJJO) and uses it to protect medical images based on random number generator (RNG). APDJJJO is derived from a piecewise damping Josephson junction (JJ) model and has either no equilibrium points or two unstable equilibrium points. One-scroll chaotic hidden attractor, one-scroll sovereign complex attractor, periodic and one-scroll complex self-driven attractors coexisting, and bistable limit cycles are found in APDJJJO during the investigation based on numerical simulations. Additionally, the FPGA validation of the APDJJJO shows similar complex characteristics to those obtained during the investigation via numerical simulations. Lastly, the chaotic characteristics depicted by the APDJJJO are used to design a RNG for the encryption of medical images. The generated random bits are validated successfully by standard statistical tool set by the National Institute of Standards and Technology (NIST-800-22). Encryption algorithm is developed to secure a medical image by exploring the unpredicted bits generated. The safety and performances analysis are done to prove the robustness and efficiency of the image encryption algorithm.

Numerical and experimental investigation of a dispersive optoelectronic oscillator for chaotic time-delay signature suppression.

Chaos generation from a novel single-loop dispersive optoelectronic oscillator (OEO) with a broadband chirped fiber Bragg grating (CFBG) is numerically and experimentally investigated. The CFBG has much broader bandwidth than the chaotic dynamics such that its dispersion effect rather than filtering effect dominates the reflection. The proposed dispersive OEO exhibits chaotic dynamics when sufficient feedback strength is guaranteed. Suppression of chaotic time-delay signature (TDS) is observed as the feedback strength increases. The TDS can be further suppressed as the amount of grating dispersion increases. Without compromising bandwidth performance, our proposed system extends the parameter space of chaos, enhances the robustness to modulator bias variation, and improves TDS suppression by at least five times comparing to the classical OEO. Experimental results qualitatively agree well with numerical simulations. In addition, the advantage of dispersive OEO is further verified by experimentally demonstrating random bit generation with tunable rate up to 160 Gbps.

Experimental cheat-sensitive quantum weak coin flipping

As in modern communication networks, the security of quantum networks will rely on complex cryptographic tasks that are based on a handful of fundamental primitives. Weak coin flipping (WCF) is a significant such primitive which allows two mistrustful parties to agree on a random bit while they favor opposite outcomes. Remarkably, perfect information-theoretic security can be achieved in principle for quantum WCF. Here, we overcome conceptual and practical issues that have prevented the experimental demonstration of this primitive to date, and demonstrate how quantum resources can provide cheat sensitivity, whereby each party can detect a cheating opponent, and an honest party is never sanctioned. Such a property is not known to be classically achievable with information-theoretic security. Our experiment implements a refined, loss-tolerant version of a recently proposed theoretical protocol and exploits heralded single photons generated by spontaneous parametric down conversion, a carefully optimized linear optical interferometer including beam splitters with variable reflectivities and a fast optical switch for the verification step. High values of our protocol benchmarks are maintained for attenuation corresponding to several kilometers of telecom optical fiber.