On the assumption of mutual independence of jitter realizations in P-TRNG stochastic models

International audienceSecurity in true random number generation in cryptography is based on entropy per bit at the generator output. The entropy is evaluated using stochastic models. Several recent works propose stochastic models based on assumptions related to selected physical analog phenomena such as noise or jittery signal and on the knowledge of the principle of randomness extraction from the obtained analog signal. However, these assumptions simplify often considerably the underlying analog processes, which include several noise sources. In this paper, we present a new comprehensive multilevel approach, which enables to build the stochastic model based on detailed analysis of noise sources starting at transistor level and on conversion of the noise to the clock jitter exploited at the generator level. Using this approach, we can estimate proportion of the jitter coming only from the thermal noise, which is included in the total clock jitter

On the Entropy of Oscillator-Based True Random Number Generators

True random number generators (TRNGs) are essential for cryptographic systems, and they are usually evaluated by the concept of entropy. In general, the entropy of a TRNG is estimated from its stochastic model, and reflected in the statistical results of the generated raw bits. Oscillator-based TRNGs are widely used in practical cryptographic systems due to its elegant structure, and its stochastic model has been studied in different aspects. In this paper, we investigate the applicability of the different entropy estimation methods for oscillator-based TRNGs, including the bit-rate entropy, the lower bound and the approx imate entropy. Particularly, we firstly analyze the two existing stochastic models (one of which is phase-based and the other is time-based), and deduce consistent bit-rate entropy results from these two models. Then, we design an approximate entropy calculation method on the output raw bits of a simulated oscillator-based TRNG, and this statistical calculation result well matches the bit-rate entropy from stochastic models. In addition, we discuss the extreme case of tiny randomness where some methods are inapplicable, and provide the recommendations for these entropy evaluation methods. Finally, we design a hardware verification method in a real oscillator-based TRNG, and validate these estimation methods in the hardware platform

Impact of the Flicker Noise on the Ring Oscillator-based TRNGs

Ring Oscillators (RO) are often used in true random number generators (TRNG). Their jittered clock signal, used as randomness source, originates from thermal and flicker noises. While thermal noise jitter is generally used as the main source of randomness, flicker noise jitter is not due to its autocorrelation. This work aims at qualitatively settling the issue of the influence of flicker noise in TRNGs, as its impact increases in newer technology nodes. For this, we built a RO behavioural model, which generates time series equivalent to a jittered RO signal. It is then used to generate the output of an elementary RO-TRNG. Despite general expectations, the autocorrelation inside the output bit stream is reduced when the amplitude of flicker noise increases. The model shows that this effect is caused by the sampling of the jittered signal by the second oscillator, which hides the behaviour of the absolute jitter, causes resetting of the perceived phase, and suppresses any memory effect. The inclusion of flicker noise as a legitimate noise source can increase the TRNG output bit rate by a factor of four for the same output entropy rate. This observation opens new perspectives towards more efficient stochastic models of the RO-TRNGs

D2.1 - Report on Selected TRNG and PUF Principles

This report represents the final version of Deliverable 2.1 of the HECTOR work package WP2. It is a result of discussions and work on Task 2.1 of all HECTOR partners involved in WP2. The aim of the Deliverable 2.1 is to select principles of random number generators (RNGs) and physical unclonable functions (PUFs) that fulfill strict technology, design and security criteria. For example, the selected RNGs must be suitable for implementation in logic devices according to the German AIS20/31 standard. Correspondingly, the selected PUFs must be suitable for applying similar security approach. A standard PUF evaluation approach does not exist, yet, but it should be proposed in the framework of the project. Selected RNGs and PUFs should be then thoroughly evaluated from the point of view of security and the most suitable principles should be implemented in logic devices, such as Field Programmable Logic Arrays (FPGAs) and Application Specific Integrated Circuits (ASICs) during the next phases of the project

Jitter Estimation with High Accuracy for Oscillator-Based TRNGs

Ring oscillator-based true random number generators (RO-based TRNGs) are widely used to provide unpredictable random numbers for cryptographic systems. The unpredictability of the output numbers, which can be measured by entropy, is extracted from the jitter of the oscillatory signal. To quantitatively evaluate the entropy, several stochastic models have been proposed, all of which take the jitter as a key input parameter. So it is crucial to accurately estimate the jitter in the process of entropy evaluation. However, several previous methods have estimated the jitter with non-negligible error, which would cause the overestimation of the entropy. In this paper, we propose a jitter estimation method with high accuracy. Our method aims at eliminating the quantization error in previous counter-based jitter estimation methods and finally can estimate the jitter with the error smaller than $1\%$. Furthermore, for the first time, we give a theoretical error bound for our jitter estimation. The error bound confirms the $1\%$ error level of our method. As a consequence, our method will signicantly help to evaluate the entropy of RO-based TRNGs accurately. Finally, we present the application of our jitter estimation method on a practical FPGA device and provide a circuit module diagram for on-chip implementation

Hardware design of cryptographic algorithms for low-cost RFID tags

Mención Internacional en el título de doctorRadio Frequency Identification (RFID) is a wireless technology for automatic identification that has experienced a notable growth in the last years. RFID is an important part of the new trend named Internet of Things (IoT), which describes a near future where all the objects are connected to the Internet and can interact between them. The massive deployment of RFID technology depends on device costs and dependability. In order to make these systems dependable, security needs to be added to RFID implementations, as RF communications can be accessed by an attacker who could extract or manipulate private information from the objects. On the other hand, reduced costs usually imply resource-constrained environments. Due to these resource limitations necessary to low-cost implementations, typical cryptographic primitives cannot be used to secure low-cost RFID systems. A new concept emerged due to this necessity, Lightweight Cryptography. This term was used for the first time in 2003 by Vajda et al. and research on this topic has been done widely in the last decade. Several proposals oriented to low-cost RFID systems have been reported in the literature. Many of these proposals do not tackle in a realistic way the multiple restrictions required by the technology or the specifications imposed by the different standards that have arose for these technologies. The objective of this thesis is to contribute in the field of lightweight cryptography oriented to low-cost RFID tags from the microelectronics point of view. First, a study about the implementation of lightweight cryptographic primitives is presented . Specifically, the area used in the implementation, which is one of the most important requirements of the technology as it is directly related to the cost. After this analysis, a footprint area estimator of lightweight algorithms has been developed. This estimator calculates an upper-bound of the area used in the implementation. This estimator will help in making some choices at the algorithmic level, even for designers without hardware design skills. Second, two pseudo-random number generators have been proposed. Pseudorandom number generators are essential cryptographic blocks in RFID systems. According to the most extended RFID standard, EPC Class-1 Gen-2, it is mandatory to include a generator in RFID tags. Several architectures for the two proposed generators have been presented in this thesis and they have been integrated in two authentication protocols, and the main metrics (area, throughput and power consumption) have been analysed. Finally, the topic of True Random Number Generators is studied. These generators are also very important in secure RFID, and are currently a trending research line. A novel generator, presented by Cherkaoui et al., has been evaluated under different attack scenarios. A new true random number generator based on coherent sampling and suitable for low-cost RFID systems has been proposed.La tecnología de Identificación por Radio Frecuencia, más conocida por sus siglas en inglés RFID, se ha convertido en una de las tecnologías de autoidentificación más importantes dentro de la nueva corriente de identificación conocida como Internet de las Cosas (IoT). Esta nueva tendencia describe un futuro donde todos los objetos están conectados a internet y son capaces de identificarse ante otros objetos. La implantación masiva de los sistemas RFID está hoy en día limitada por el coste de los dispositivos y la fiabilidad. Para que este tipo de sistemas sea fiable, es necesario añadir seguridad a las implementaciones RFID, ya que las comunicaciones por radio frecuencia pueden ser fácilmente atacadas y la información sobre objetos comprometida. Por otro lado, para que todos los objetos estén conectados es necesario que el coste de la tecnología de identificación sea muy reducido, lo que significa una gran limitación de recursos en diferentes ámbitos. Dada la limitación de recursos necesaria en implementaciones de bajo coste, las primitivas criptográficas típicas no pueden ser usadas para dotar de seguridad a un sistema RFID de bajo coste. El concepto de primitiva criptográfica ligera fue introducido por primera vez 2003 por Vajda et al. y ha sido desarrollado ampliamente en los últimos años, dando como resultados una serie de algoritmos criptográficos ligeros adecuados para su uso en tecnología RFID de bajo coste. El principal problema de muchos de los algoritmos presentados es que no abordan de forma realista las múltiples limitaciones de la tecnología. El objetivo de esta tesis es el de contribuir en el campo de la criptografía ligera orientada a etiquetas RFID de bajo coste desde el punto de vista de la microelectrónica. En primer lugar se presenta un estudio de la implementación de las primitivas criptográficas ligeras más utilizadas, concretamente analizando el área ocupado por dichas primitivas, ya que es uno de los parámetros críticos considerados a la hora de incluir dichas primitivas criptográficas en los dispositivos RFID de bajo coste. Tras el análisis de estas primitivas se ha desarrollado un estimador de área para algoritmos criptográficos ultraligeros que trata de dar una cota superior del área total ocupada por el algoritmo (incluyendo registros y lógica de control). Este estimador permite al diseñador, en etapas tempranas del diseño y sin tener ningún conocimiento sobre implementaciones, saber si el algoritmo está dentro de los límites de área mpuestos por la tecnología RFID. También se proponen 2 generadores de números pseudo-aleatorios. Estos generadores son uno de los bloques criptográficos más importantes en un sistema RFID. El estándar RFID más extendido entre la industria, EPC Class-1 Gen-2, establece el uso obligatorio de dicho tipo de generadores en las etiquetas RFID. Los generadores propuestos han sido implementados e integrados en 2 protocolos de comunicación orientados a RFID, obteniendo buenos resultados en las principales características del sistema. Por último, se ha estudiado el tema de los generadores de números aleatorios. Este tipo de generadores son frecuentemente usados en seguridad RFID. Actualmente esta línea de investigación es muy popular. En esta tesis, se ha evaluado la seguridad de un novedoso TRNG, presentado por Cherkaoui et al., frente ataques típicos considerados en la literatura. Además, se ha presentado un nuevo TRNG de bajo coste basado en la técnica de muestreo por pares.Programa Oficial de Doctorado en Ingeniería Eléctrica, Electrónica y AutomáticaPresidente: Teresa Riesgo Alcaide.- Secretario: Emilio Olías Ruiz.- Vocal: Giorgio di Natal

All-Silicon-Based Photonic Quantum Random Number Generators

Random numbers are fundamental elements in different fields of science and technology such as computer simulation like Monte Carlo-method simulation, statistical sampling, cryptography, games and gambling, and other areas where unpredictable results are necessary. Random number generators (RNG) are generally classified as “pseudo”-random number generators (PRNG) and "truly" random number generators (TRNG). Pseudo random numbers are generated by computer algorithms with a (random) seed and a specific formula. The random numbers produced in this way (with a small degree of unpredictability) are good enough for some applications such as computer simulation. However, for some other applications like cryptography they are not completely reliable. When the seed is revealed, the entire sequence of numbers can be produced. The periodicity is also an undesirable property of PRNGs that can be disregarded for most practical purposes if the sequence recurs after a very long period. However, the predictability still remains a tremendous disadvantage of this type of generators. Truly random numbers, on the other hand, can be generated through physical sources of randomness like flipping a coin. However, the approaches exploiting classical motion and classical physics to generate random numbers possess a deterministic nature that is transferred to the generated random numbers. The best solution is to benefit from the assets of indeterminacy and randomness in quantum physics. Based on the quantum theory, the properties of a particle cannot be determined with arbitrary precision until a measurement is carried out. The result of a measurement, therefore, remains unpredictable and random. Optical phenomena including photons as the quanta of light have various random, non-deterministic properties. These properties include the polarization of the photons, the exact number of photons impinging a detector and the photon arrival times. Such intrinsically random properties can be exploited to generate truly random numbers. Silicon (Si) is considered as an interesting material in integrated optics. Microelectronic chips made from Si are cheap and easy to mass-fabricate, and can be densely integrated. Si integrated optical chips, that can generate, modulate, process and detect light signals, exploit the benefits of Si while also being fully compatible with electronic. Since many electronic components can be integrated into a single chip, Si is an ideal candidate for the production of small, powerful devices. By complementary metal-oxide-semiconductor (CMOS) technology, the fabrication of compact and mass manufacturable devices with integrated components on the Si platform is achievable. In this thesis we aim to model, study and fabricate a compact photonic quantum random number generator (QRNG) on the Si platform that is able to generate high quality, "truly" random numbers. The proposed QRNG is based on a Si light source (LED) coupled with a Si single photon avalanche diode (SPAD) or an array of SPADs which is called Si photomultiplier (SiPM). Various implementations of QRNG have been developed reaching an ultimate geometry where both the source and the SPAD are integrated on the same chip and fabricated by the same process. This activity was performed within the project SiQuro—on Si chip quantum optics for quantum computing and secure communications—which aims to bring the quantum world into integrated photonics. By using the same successful paradigm of microelectronics—the study and design of very small electronic devices typically made from semiconductor materials—, the vision is to have low cost and mass manufacturable integrated quantum photonic circuits for a variety of different applications in quantum computing, measure, sensing, secure communications and services. The Si platform permits, in a natural way, the integration of quantum photonics with electronics. Two methodologies are presented to generate random numbers: one is based on photon counting measurements and another one is based on photon arrival time measurements. The latter is robust, masks all the drawbacks of afterpulsing, dead time and jitter of the Si SPAD and is effectively insensitive to ageing of the LED and to its emission drifts related to temperature variations. The raw data pass all the statistical tests in national institute of standards and technology (NIST) tests suite and TestU01 Alphabit battery without a post processing algorithm. The maximum demonstrated bit rate is 1.68 Mbps with the efficiency of 4-bits per detected photon. In order to realize a small, portable QRNG, we have produced a compact configuration consisting of a Si nanocrystals (Si-NCs) LED and a SiPM. All the statistical test in the NIST tests suite pass for the raw data with the maximum bit rate of 0.5 Mbps. We also prepared and studied a compact chip consisting of a Si-NCs LED and an array of detectors. An integrated chip, composed of Si p+/n junction working in avalanche region and a Si SPAD, was produced as well. High quality random numbers are produced through our robust methodology at the highest speed of 100 kcps. Integration of the source of entropy and the detector on a single chip is an efficient way to produce a compact RNG. A small RNG is an essential element to guarantee the security of our everyday life. It can be readily implemented into electronic devices for data encryption. The idea of "utmost security" would no longer be limited to particular organs owning sensitive information. It would be accessible to every one in everyday life

Improving Quantum Key Distribution and Quantum Random Number Generation in presence of Noise

The argument of this thesis might be summed up as the exploitation of the noise to generate better noise. More specifically this work is about the possibility of exploiting classic noise to effectively transmit quantum information and measuring quantum noise to generate better quantum randomness. What do i mean by exploiting classical noise to transmit effectively quantum information? In this case I refer to the task of sending quantum bits through the atmosphere in order set up transmissions of quantum key distribution (QKD) and this will be the subject of Chapter 1 and Chapter 2. In the Quantum Communications framework, QKD represents a topic with challenging problems both theoretical and experimental. In principle QKD offers unconditional security, however practical realizations of it must face all the limitations of the real world. One of the main limitation are the losses introduced by real transmission channels. Losses cause errors and errors make the protocol less secure because an eavesdropper could try to hide his activity behind the losses. When this problem is addressed under a full theoretical point of view, one tries to model the effect of losses by means of unitary transforms which affect the qubits in average according a fixed level of link attenuation. However this approach is somehow limiting because if one has a high level of background noise and the losses are assumed in average constant, it could happen that the protocol might abort or not even start, being the predicted QBER to high. To address this problem and generate key when normally it would not be possible, we have proposed an adaptive real time selection (ARTS) scheme where transmissivity peaks are instantaneously detected. In fact, an additional resource may be introduced to estimate the link transmissivity in its intrinsic time scale with the use of an auxiliary classical laser beam co-propagating with the qubits but conveniently interleaved in time. In this way the link scintillation is monitored in real time and the selection of the time intervals of high channel transmissivity corresponding to a viable QBER for a positive key generation is made available. In Chapter 2 we present a demonstration of this protocol in conditions of losses equivalent to long distance and satellite links, and with a range of scintillation corresponding to moderate to severe weather. A useful criterion for the preselection of the low QBER interval is presented that employs a train of intense pulses propagating in the same path as the qubits, with parameters chosen such that its fluctuation in time reproduces that of the quantum communication. For what concern the content of Chapter 3 we describe a novel principle for true random number generator (TRNG) which is based on the observation that a coherent beam of light crossing a very long path with atmospheric turbulence may generate random and rapidly varying images. To implement our method in a proof of concept demonstrator, we have chosen a very long free space channel used in the last years for experiments in Quantum Communications at the Canary Islands. Here, after a propagation of 143 km at an altitude of the terminals of about 2400 m, the turbulence in the path is converted into a dynamical speckle at the receiver. The source of entropy is then the atmospheric turbulence. Indeed, for such a long path, a solution of the Navier-Stokes equations for the {atmospheric flow in which the beam propagates is out of reach. Several models are based on the Kolmogorov statistical theory, which parametrizes the repartition of kinetic energy as the interaction of decreasing size eddies. However, such models only provide a statistical description for the spot of the beam and its wandering and never an instantaneous prediction for the irradiance distribution. These are mainly ruled by temperature variations and by the wind and cause fluctuations in the air refractive index. For such reason, when a laser beam is sent across the atmosphere, this latter may be considered as a dynamic volumetric scatterer which distorts the beam wavefront. We will evaluate the experimental data to ensure that the images are uniform and independent. Moreover, we will assess that our method for the randomness extraction based on the combinatorial analysis is optimal in the context of Information Theory. In Chapter 5 we will present a new approach for what concerns the generation of random bits from quantum physical processes. Quantum Mechanics has been always regarded as a possible and valuable source of randomness, because of its intrinsic probabilistic Nature. However the typical paradigm is employed to extract random number from a quantum system it commonly assumes that the state of said system is pure. Such assumption, only in theory would lead to full and unpredictable randomness. The main issue however it is that in real implementations, such as in a laboratory or in some commercial device, it is hardly possible to forge a pure quantum state. One has then to deal with quantum state featuring some degree of mixedness. A mixed state however might be somehow correlated with some other system which is hold by an adversary, a quantum eavesdropper. In the extreme case of a full mixed state, practically one it is like if he is extracting random numbers from a classical state. In order to do that we will show how it is important to shift from a classical randomness estimator, such as the min-classical entropy H-min(Z) of a random variable Z to quantum ones such as the min-entropy conditioned on quantum side information E. We have devised an effective protocol based on the entropic uncertainty principle for the estimation of the min-conditional entropy. The entropic uncertainty principle lets one to take in account the information which is shared between multiple parties holding a multipartite quantum system and, more importantly, lets one to bound the information a party has on the system state after that it has been measured. We adapted such principle to the bipartite case where an user Alice, A, is supplied with a quantum system prepared by the provider Eve, E, who could be maliciously correlated to it. In principle then Eve might be able to predict all the outcomes of the measurements Alice performs on the basis Z in order to extract random numbers from the system. However we will show that if Alice randomly switches from the measurement basis to a basis X mutually unbiased to Z, she can lower bound the min entropy conditioned to the side information of Eve. In this way for Alice is possible to expand a small initial random seed in a much larger amount of trusted numbers. We present the results of an experimental demonstration of the protocol where random numbers passing the most rigorous classical tests of randomness were produced. In Chapter 6, we will provide a secure generation scheme for a continuos variable (CV) QRNG. Since random true random numbers are an invaluable resource for both the classical Information Technology and the uprising Quantum one, it is clear that to sustain the present and future even growing fluxes of data to encrypt it is necessary to devise quantum random number generators able to generate numbers in the rate of Gigabit or Terabit per second. In the Literature are given several examples of QRNG protocols which in theory could reach such limits. Typically, these are based on the exploitation of the quadratures of the electro-magnetic field, regarded as an infinite bosonic quantum system. The quadratures of the field can be measured with a well known measurement scheme, the so called homodyne detection scheme which, in principle, can yield an infinite band noise. Consequently the band of the random signal is limited only by the passband of the devices used to measure it. Photodiodes detectors work commonly in the GHz band, so if one sample the signal with an ADC enough fast, the Gigabit or Terabit rates can be easily reached. However, as in the case of discrete variable QRNG, the protocols that one can find in the Literature, do not properly consider the purity of the quantum state being measured. The idea has been to extend the discrete variable protocol of the previous Chapter, to the Continuous case. We will show how in the CV framework, not only the problem of the state purity is given but also the problem related to the precision of the measurements used to extract the randomness

Radio Communications

In the last decades the restless evolution of information and communication technologies (ICT) brought to a deep transformation of our habits. The growth of the Internet and the advances in hardware and software implementations modified our way to communicate and to share information. In this book, an overview of the major issues faced today by researchers in the field of radio communications is given through 35 high quality chapters written by specialists working in universities and research centers all over the world. Various aspects will be deeply discussed: channel modeling, beamforming, multiple antennas, cooperative networks, opportunistic scheduling, advanced admission control, handover management, systems performance assessment, routing issues in mobility conditions, localization, web security. Advanced techniques for the radio resource management will be discussed both in single and multiple radio technologies; either in infrastructure, mesh or ad hoc networks