Randomness quantification in spontaneous emission

Data encryption is a way to increase security of data by using cryptographic keys generated from random numbers. Random Number generator (RNG), which produces such numbers, is classified as True Random Number Generator (TRNG) or Pseudorandom Number generator (PRNG). The first one uses physical phenomena to generate random numbers whereas the second one uses deterministic systems. A commonly used deterministic system in PRNG applications is the logistic map, a nonlinear system that under certain operating ranges becomes chaotic. However, the logistic map alone does not generate satisfactory random sequence because the sequence generated is not uniformly distributed, and it does not have good results in statistical tests, such as the NIST test suite. To solve this problem, this paper proposes an implementation in Field Programmable Gate Array (FPGA) of a PRNG, which uses the k – logistic map concept, discarding the most significant k decimal digits of an underlying orbit generated from the traditional logistic map equation. The results from synthesis and simulations show that the designed circuit is a low-cost and a high efficiency RNG solution.

Dr Zhang Yixin of Nanjing University, China, talks about the work behind the paper ‘Portable true random number generator for personal encryption application based on smartphone camera’, page 1841. Dr Zhang Yixin My major was more related to radio communication as an undergraduate. About eight years ago, I started a PhD at Nanjing University, that was the beginning of my research in optical. In 2011, I joined NTRC at Nanyang Technological University in Singapore as a postdoctoral research fellow. The lab had just begun a joint military project on unconditional encrypted optical communication. That is where my current research work really began. Two years later I returned to Nanjing University as a lecturer and my current main field of research is single photon level optical signal detection and its applications, such as the true random number generator (TRNG) based on photon distribution. True random numbers are the key to secure communication, even if quantum technology is included. A TRNG based on an off-the-shelf image sensor, rather than a thousands-of-dollars photon counter, would be much more attractive for portable personal encryption applications, such as E-payment, privacy call and cryptographic data transmission on a smartphone or laptop. In the near future, the security level of personal devices has to be enhanced with new encryption technology to stand against the technological advances of eavesdroppers; this is the goal of our current project. Present TRNGs are mainly based on specialised, expensive hardware like single photon detectors, chaotic lasers and radioactive nuclei, which are more suited to commercial or academic applications than personal usage. We present a portable TRNG configuration simply based on the camera of a smartphone. The randomness of the output bit sequence has been proved with NIST tests, and all necessary processing functions could be fully integrated within Android software in the near future. This approach offers a promising solution for portable personal encryption, since no equipment is needed except the smartphone itself. Back in my PhD days, working on micro-structure imaging, our group confirmed by experiment that in certain conditions, shot noise other than thermal noise can dominate the overall noise characteristics of a high-sensitivity CCD image sensor. Commonly speaking, shot noise of photocurrent is believed to be a quantum process and true random number could be generated accordingly. However, the performance of image sensors on smartphones were not as good then. Two or three years later, I saw a picture taken by my colleague's latest phone, and thought maybe it was time to realise the portable TRNG with smartphone camera. I see two main trends in recent TRNG research. The first is realising higher bit rates; speeds of gigabits per second were reported several years ago. The second is looking for new physical random phenomena that are more reliable. Arguments have always existed on whether chaotic process is as random as quantum process. However, I believe that the integration of TRNGs is very likely to be the main topic in the future. TRNGs are still too big and expensive for most practical applications. Integration of optics and electronics components on a single chip is necessary for portable and low-cost TRNGs. Meanwhile, TRNGs only solve the random number generation problem, a communication protocol which employs true random numbers as secret keys for encryption also needs to be developed. Here at the Institute of Optical Communication Engineering at Nanjing, my group will try to improve the Android App for TRNGs to automatically adapt to different types of smartphone, since the camera setting is essential to the overall performance of output random bits. We are also working on high-speed single photon counting technology based on avalanche photodiodes to improve the detection speed if higher rates are required. Another research area we are involved in is fibre optical sensing, with the goal of locating eavesdroppers in time, while they are intercepting optical signals from fibre communication links. Probe pulse coding based on TRNGs will be used for the improvement of measuring speed, spatial resolution and dynamic range.

The subject matter of the article is pseudo-random number generators. Random numbers play the important role in cryptography. Using not secure pseudo-random number generators is a very common weakness. It is also a fundamental resource in science and engineering. There are algorithmically generated numbers that are similar to random distributions but are not random, called pseudo-random number generators. In many cases the tasks to be solved are based on the unpredictability of random numbers, which cannot be guaranteed in the case of pseudo-random number generators, true randomness is required. In such situations, we use real random number generators whose source of randomness is unpredictable random events. Quantum Random Number Generators (QRNGs) generate real random numbers based on the inherent randomness of quantum measurements. The goal is to develop a mathematical model of the generator, which generates fast random numbers at a lower cost. At the same time, a high level of randomness is essential. Through quantum mechanics, we can obtain true numbers using the unpredictable behavior of a photon, which is the basis of many modern cryptographic protocols. It is essential to trust cryptographic random number generators to generate only true random numbers. This is why certification methods are needed which will check both the operation of the device and the quality of the random bits generated. The goal of the research is also to develop the model of a hybrid semi self-testing certification method for quantum random number generators (QRNG). The tasks to be solved are to create the mathematical model of a random number generator, which generates the fast random numbers at a lower cost. To create the mathematical model of a hybrid semi self-testing certification method for quantum random number generators. To integrate a hybrid semi self-testing certification method to the hybrid random number generator. the methods used are mathematical optimization and simulation. The following results were obtained: we present the improved hybrid quantum random number generator, which is based on QRNG, which uses the time of arrival of photons. The model of a hybrid semi self-testing certification method for quantum random number generators (QRNG) is offered in the paper. This method combines different types of certification approaches and is rather secure and efficient. Finally, the hybrid certification method is integrated into the model of the new quantum random number generator. Conclusions. The scientific novelty of the results obtained is as follows: 1. The hybrid quantum random number generator is offered, which is based on QRNG, which uses the time of the arrival of photons. It uses the simple version of the detectors with few requirements. The hybrid QRNG produces more than one random bit per the detection of each photon. It is rather efficient and has a high level of randomness. 2. The hybrid semi self-testing certification method for quantum random number generators (QRNG) is offered. The Self-testing, as well as device-independent quantum random number generation methods, are analyzed. The advantages and disadvantages of both methods are identified. Based on the result the hybrid method is offered. 3. The hybrid semi self-testing certification method for quantum random number generators is integrated into the offered model of the quantum random number generator. The paper analyzes its security and efficiency. The paper offers to use the new random number generator in the crypto-schemes.

Exploiting Random Chemistry for Digital Security

Random number generators are of paramount importance in numerous fields. Under certain well-defined adversarial settings, True Random Number Generators (TRNGs) are more secure than their computational (pseudo) random number generator counterparts. TRNGs are also known to be more efficiently implemented on hardware platforms where, for various applications, efficiency in terms of electronic cost factors is critical. In this manuscript, we first provide an evaluation of robustness and reliability of efficient time-domain-based TRNG implementation over FPGA platform. In particular, we demonstrate sensitivities which imply a TRNG construction which is not agnostic to electronic-design-automation tools and to the level of designers’ know-how. This entails a large amount of effort and validation to make the designs robust, as well as requires a high degree of complexity from non-trivial FPGAs flows. This motivates the second part of the manuscript, where we propose an ASIC-based implementation of the TRNG, along with the optimization steps to enhance its characteristics. The optimized design improves the randomness-throughput by 42× for the same entropy level described in previous works, and it can provide maximal entropy level of 0.985 with 7× improvement in randomness throughput over the raw samples (no pre-processing). The proposed design simultaneously provides a reduced energy of 0.1 (mW/bit) for the same entropy level as previous works, and 1.06 (mW/bit) for the higher entropy flavor, and a lower area utilization of 0.000252 (mm2) on a 65 nm technology evaluation, situating it in the top-class of the discuss ratings. This leads to the quantitative question of the gain in electronic cost factors over ASIC TRNGs, and the minimum Cost Per Bit/Source possible to date. Finally, we exemplify a TRNG versus PRNG cost-extrapolation for security architects and designers, targeting an ASIC scenario feeding a lightweight encryption core.

The entropy or randomness source is an essential ingredient in random number generation. Quantum random number generators generally require well modeled and calibrated light sources, such as a laser, to generate randomness. With uncharacterized light sources, such as sunlight or an uncharacterized laser, genuine randomness is practically hard to be quantified or extracted owing to its unknown or complicated structure. By exploiting a recently proposed source-independent randomness generation protocol, we theoretically modify it by considering practical issues and experimentally realize the modified scheme with an uncharacterized laser and a sunlight source. The extracted randomness is guaranteed to be secure independent of its source and the randomness generation speed reaches 1 Mbps, three orders of magnitude higher than the original realization. Our result signifies the power of quantum technology in randomness generation and paves the way to high-speed semi-self-testing quantum random number generators with practical light sources.

The basis of encryption techniques is random number generators (RNGs). The application areas of cryptology are increasing in number due to continuously developing technology, so the need for RNGs is increasing rapidly, too. RNGs can be divided into two categories as pseudorandom number generator (PRNGs) and true random number generator (TRNGs). TRNGs are systems that use unpredictable and uncontrollable entropy sources and generate random numbers. During the design of TRNGs, while analog signals belonging to the used entropy sources are being converted to digital data, generally comparators, flip-flops, Schmitt triggers, and ADCs are used. In this study, a computer-controlled new and flexible platform to find the most appropriate system parameters in ADC-based TRNG designs is designed and realized. As a sample application with this new platform, six different TRNGs that use three different outputs of Zhongtang, which is a continuous time chaotic system, as an entropy source are designed. Random number series generated with the six designed TRNGs are put through the NIST800–22 test, which has the internationally highest standards, and they pass all tests. With the help of the new platform designed, ADC-based high-quality TRNGs can be developed fast and also without the need for expertise. The platform has been designed to decide which entropy source and parameter are better by comparing them before complex embedded TRNG designs. In addition, this platform can be used for educational purposes to explain how to work an ADC-based TRNG. That is why it can be utilized as an experiment set in engineering education, as well.

The success of any cryptographic algorithm lies in the unpredictability& irreproducibility of random number generation. For implementing the cryptographic algorithms it should be integrated within a single chip. Hence a random number generator which produces unpredictable random numbers as well as occupying less area is the essential one. In this work, random numbers are generated based on sampling two oscillator frequencies. Jitters and phase noise's usually considered as disturbance signals. Here the time when they appear in the oscillators is the main thing to generate random numbers. However, when these algorithms are implemented in smart cards they have to produce the same result throughout its life. But actually there are some issues to reproduce the same number due to aging. In this paper, an efficient method is proposed to mitigate the effects of aging in TRNGs. Here, a tetrahedral oscillator-based true random number generator (TRNG) is presented and the issues about aging which affect the random key generated by the TRNG are addressed. So we proposed an aging resistant tetrahedral oscillator concept to mitigate the impact of aging in the key generator. The performance of the proposed random number generator is measured by statistical tests. This TRNG is used as a private key generator for cryptographic algorithm and its operation is programmed and the simulations have been done by ModelSim-Altera6.4a (Quartus-II 9.0) starter Edition. To prove the proposed tetrahedral aging-resistant oscillator operation it is designed in TANNER EDA tool v14.1 (S-Edit Schematic Editor). By varying the supply voltage and transistor channel width and length, it is visible that the effects of run-time stress is mitigated which affect the lifetime of the oscillator in TRNG.

True random number generators (TRNGs) are crucial components for the security of cryptographic systems. In contrast to pseudo--random number generators (PRNGs), TRNGs provide higher security by extracting randomness from physical phenomena. To evaluate a TRNG, statistical properties of the circuit model and raw bitstream should be studied. In this article, a model for the beat frequency detector--based high-speed TRNG (BFD-TRNG) is proposed. The parameters of the model are extracted from the experimental data of a test chip. A statistical analysis of the proposed model is carried out to derive mean and variance of the counter values of the TRNG. Our statistical analysis results show that mean of the counter values is inversely proportional to the frequency difference of the two ring oscillators (ROSCs), whereas the dynamic range of the counter values increases linearly with standard deviation of environmental noise and decreases with increase of the frequency difference. Without the measurements from the test data, a model cannot be created; similarly, without a model, performance of a TRNG cannot be predicted. The key contribution of the proposed approach lies in fitting the model to measured data and the ability to use the model to predict performance of BFD-TRNGs that have not been fabricated. Several novel alternate BFD-TRNG architectures are also proposed; these include parallel BFD, cascade BFD, and parallel-cascade BFD. These TRNGs are analyzed using the proposed model, and it is shown that the parallel BFD structure requires less area per bit, whereas the cascade BFD structure has a larger dynamic range while maintaining the same mean of the counter values as the original BFD-TRNG. It is shown that 3.25 M and 4 M random bits can be obtained per counter value from parallel BFD and parallel-cascade BFD, respectively, where M counter values are computed in parallel. Furthermore, the statistical analysis results illustrate that BFD-TRNGs have better randomness and less cost per bit than other existing ROSC-TRNG designs. For example, it is shown that BFD-TRNGs accumulate 150% more jitter than the original two-oscillator TRNG and that parallel BFD-TRNGs require one-third power and one-half area for same number of random bits for a specified period.

Random numbers are at the heart of diverse fields, ranging from simulations of stochastic processes to classical and quantum cryptography. The requirement for true randomness in these applications has motivated various proposals for generating random numbers based on the inherent randomness of quantum systems. The generation of true random numbers with arbitrarily defined probability distributions is highly desirable for applications, but it is very challenging. Here we show that single-photon quantum walks can generate multi-bit random numbers with on-demand probability distributions, when the required “coin” parameters are found with the gradient descent (GD) algorithm. Our theoretical and experimental results exhibit high fidelity for various selected distributions. This GD-enhanced single-photon system provides a convenient way for building flexible and reliable quantum random number generators. Multi-bit random numbers are a necessary resource for high-dimensional quantum key distribution.

The true random number generators (TRNGs) have received extensive attention\nbecause of their wide applications in information transmission and encryption.\nThe true random numbers generated by TRNG are typically applied to the\nencryption algorithm or security protocol of the information security core.\nRecently, TRNGs have also been employed in emerging stochastic computing\nparadigm for reducing power consumption. Roughly speaking, TRNG can be divided\ninto circuits-based, e.g., oscillator sampling or directly noise amplifying;\nand quantum physics-based, e.g., photoelectric effect. The former generally\nrequires a large area and has a large power consumption, whereas the latter is\nintrinsic random but is more difficult to implement and usually requires\nadditional post-processing circuitry. Very recently, magnetic skyrmion has\nbecome a promising candidate for implementing TRNG because of their nanometer\nsize, high stability, and intrinsic thermal Brownian motion dynamics. In this\nwork, we propose a TRNG based on continuous skyrmion thermal Brownian motion in\na confined geometry at room temperature. True random bitstream can be easily\nobtained by periodically detecting the relative position of the skyrmion\nwithout the need for additional current pulses. More importantly, we implement\na probability-adjustable TRNG, in which a desired ratio of 0 and 1 can be\nacquired by adding an anisotropy gradient through voltage-controlled magnetic\nanisotropy (VCMA) effect. The behaviors of the skyrmion-based TRNG are verified\nby using micromagnetic simulations. The National Institute of Standards and\nTechnology (NIST) test results demonstrate that our proposed random number\ngenerator is TRNG with good randomness. Our research provides a new perspective\nfor efficient TRNG realization.\n

Recent advances in information security requires strong keys which are randomly generated. Most of the keys are generated by the softwares which use software-based random number generators. However, implementing a True Random Number Generator (TRNG) without using a hardware-supported platform is not reliable. In this paper, a biometric authentication system using a FPGA-based TRNG to produce a private key that encrypts the face template of a person is presented. The designed hardware can easily be mounted on standard or embedded PC via its PCI interface to produce random number keys. Random numbers forming the private key is guaranteed to be true because it passes a two-level randomness test. The randomness test is evaluated first on the hardware then on the PC by applying the full NIST test suite. The whole system implements an AES-based encryption scheme to store the person's secret safely. Assigning a private key which is generated by our TRNG guarantees a unique and truly random password. The system stores the Wavelet Fourier-Mellin Transform (WFMT) based face features in a database with an index number that might be stored on a smart or glossary card. The objective of this study is to present a practical application integrating any biometric technology with a hardware-implemented TRNG.

Two FPGA-based (field programmable gate array) implementations of random number generators intended for embedded cryptographic applications are presented. The first is a true random number generator (TRNG) which employs oscillator phase noise, and the second is a bit serial implementation of a Blum Blum Shub (BBS) pseudorandom number generator (PRNG). Both designs are extremely compact and can be implemented on any FPGA of PLD device. They were designed specifically for use as FPGA-based cryptographic hardware cores. The TRNG and PRNG were tested using the NIST and Diehard random number test suites.

This work presents two significant contributions from the perspectives of quantum random number generator (QRNG) manufacturers and users. For manufacturers, the conventional method of assessing the quantumness of single-photon-based QRNGs through mean and variance comparisons of photon counts is statistically unreliable due to finite sample sizes. Given the sub-Poissonian statistics of single photons, confirming the underlying distribution is crucial for validating a QRNG's quantumness. We propose a more efficient two-fold statistical approach to ensure the quantumness of optical sources with the desired confidence level. Additionally, we demonstrate that the output of QRNGs from exponential and uniform distributions exhibit similarity under device noise, deriving corresponding photon statistics and conditions for $\epsilon$-randomness.

From the user's perspective, the fundamental parameters of a QRNG are quantumness, efficiency (random entropy and random number generation rate), and cost. Our analysis reveals that these parameters depend on three factors, namely, expected photon count per unit time, external reference cycle duration, and detection efficiency. A lower expected photon count enhances entropy but increases cost and decreases the generation rate. A shorter external reference cycle boosts entropy but must exceed a minimum threshold to minimize timing errors, with minor impacts on cost and rate. Lower detection efficiency enhances entropy and lowers cost but reduces the generation rate. Finally, to validate our results, we perform statistical tests like NIST, Dieharder, AIS-31, ENT etc. over the data simulated with different values of the above parameters. Our findings can empower manufacturers to customize QRNGs to meet user needs effectively.

In this paper we address the use of Neural Networks (NNs) for the assessment of the quality and hence safety of several Random Number Generators (RNGs), focusing both on the vulnerability of classical Pseudo Random Number Generators (PRNGs), such as Linear Congruential Generators (LCGs) and the RC4 algorithm, and extending our analysis to non-conventional data sources, such as Quantum Random Number Generators (QRNGs) based on Vertical-Cavity Surface-Emitting Laser (VCSEL). Among the results found, we have classified the generators based on the capability of the NN to distinguish between the RNG and a Golden Standard RNG (GSRNG). We show that sequences from simple PRNGs like LCGs and RC4 can be distinguished from the GSRNG. We also show that sequences from LCG on elliptic curves and VCSEL-based QRNG can not be distinguished from the GSRNG even with the biggest long-short term memory or convolutional neural networks (CNNs) that we have considered. We underline the fundamental role of design decisions in enhancing the safety of RNGs. The influence of network architecture design and associated hyper-parameters variations was also explored. We show that longer sequence lengths and CNNs are more effective for discriminating RNGs against the GSRNG. Moreover, in the prediction domain, the proposed model is able to deftly distinguish between the raw data of our QRNG and data from the GSRNG exhibiting a cross-entropy error of 0.52 on the test data-set used. All these findings reveal the potential of NNs to enhance the security of RNGs, while highlighting the robustness of certain QRNGs, in particular the VCSEL-based variants, for high-quality random number generation applications.