NIST Test Suite Research Articles

Novel Randomized Placement for FPGA Based Robust ROPUF with Improved Uniqueness

The physical unclonable functions (PUFs) are used to provide software as well as hardware security for the cyber-physical systems. They have been used for performing significant cryptography tasks such as generating keys, device authentication, securing against IP piracy, and to produce the root of trust as well. However, they lack in reliability metric. We present a novel approach for improving the reliability as well as the uniqueness of the field programmable gated arrays (FPGAs) based ring oscillator PUF and derive a random number, consuming very small area (< 1%) concerning look-up tables (LUTs). We use frequency profiling method for distributing frequency variations in ring oscillators (RO), spatially placed all across the FPGA floor. We are able to spot suitable locations for RO mapping, which leads to enhanced ROPUF reliability. We have evaluated the proposed methodology on Xilinx -7 series FPGAs and tested the robustness against environmental variations, e.g. temperature and supply voltage variations, simultaneously. The proposed approach achieves significant improvement (i) in uniqueness value upto 49.90%, within 0.1% of the theoretical value (ii) in the reliability value upto 99.70%, which signifies that less than 1 bit flipping has been observed on average, and (iii) in randomness, signified by passing NIST test suite. The response generated through the ROPUF passes all the applicable relevant tests of NIST uniformity statistical test suite.

Periodic template tests: A family of statistical randomness tests for a collection of binary sequences

In this work, we classify all templates according to their periods and for each template we evaluate the exact probabilities using generating functions. Afterwards, we propose a new family of statistical randomness tests, that is periodic template tests, for a collection of binary sequences. We apply these tests to the outputs of AES, SHA-3, SHA-2 family, SHA-1 and MD5 and the binary expansion of π and 2, and biased non-random data to test the power of new tests. Moreover, we give the probabilities for all templates for the overlapping template matching test in the NIST test suite. Afterwards, we analyse the power of templates and compare the periodic template tests with NIST overlapping template test.

Quantum systems for Monte Carlo methods and applications to fractional stochastic processes

Random numbers are a fundamental and useful resource in science and engineering with important applications in simulation, machine learning and cyber-security. Quantum systems can produce true random numbers because of the inherent randomness at the core of quantum mechanics. As a consequence, quantum random number generators are an efficient method to generate random numbers on a large scale. We study in this paper the applications of a viable source of unbiased quantum random numbers (QRNs) whose statistical properties can be arbitrarily programmed without the need for any post-processing and that pass all standard randomness tests of the NIST and Dieharder test suites without any randomness extraction. Our method is based on measuring the arrival time of single photons in shaped temporal modes that are tailored with an electro-optical modulator. The advantages of our QRNs are shown via two applications: simulation of a fractional Brownian motion, which is a non-Markovian process, and option pricing under the fractional SABR model where the stochastic volatility process is assumed to be driven by a fractional Brownian motion. The results indicate that using the same number of random units, our QRNs achieve greater accuracy than those produced by standard pseudo-random number generators. Moreover, we demonstrate the advantages of our method via an increase in computational speed, efficiency, and convergence.

Pseudo-random number generators based on the Collatz conjecture

In this research, we have studied the applicability of the Collatz Conjecture to pseudo-random number generators (PRNG). The research was motivated by the simplicity of the Collatz function, which makes it attractive as a potential PRNG. We have experimented with several candidate PRNGs based on the trajectory property of the Collatz function and the Collatz graph. The NIST Test Suite (SP 800-22) was used to evaluate the statistical randomness of the output of our PRNGs. In addition, we utilized a method to rank each PRNG by quality of random output. The test results have demonstrated that two of our PRNGs pass the NIST Test Suite, and that there is no significant statistical difference between the outputs of our PRNGs to that of the Mersenne Twister, the built-in PRNG in Python 3.7. To the best of our knowledge, our algorithms are the first to successfully utilize properties of the Collatz function to generate random numbers. Additionally, we have proved that one of our PRNGs generates uniformly distributed output with a period of 232. Finally, we have found that two of our PRNGs perform on par with the Mersenne Twister algorithm. Because our algorithms pass the NIST Test Suite, they are suitable for usage in certain cryptographic applications as well as simulations.

CSRO-Based Reconfigurable True Random Number Generator Using RRAM

In this paper, we propose a high-speed (kilohertz–megahertz), reconfigurable current starved ring oscillator (CSRO)-based true random number generator (TRNG) design. The proposed TRNG exploits the intradevice stochastic variations in resistive RAM switching parameters and random telegraph noise (RTN). We demonstrate the effect of RTN on the jitter of CSRO oscillations. We also propose a methodology to reconfigure the TRNG to generate new random numbers. The proposed 10-bit TRNG is validated by NIST test suite for randomness in the data stream. Energy/bit is 22.8 fJ for generation, and the speed of random data generation is 6 MHz. Security vulnerabilities and countermeasures of the proposed TRNG are also investigated.

Pseudo Random Bits’ Generator Based on Tent Chaotic Map and Linear Feedback Shift Register

The unforeseeable demand for secure paradigm cannot be fulfilled by the arbitrary sequence generated by the linear feedback shift register, which means the generated sequence can’t meet satisfy the unpredictable demand for secure paradigm. Tent chaotic equation combined with the linear property of Linear Feedback Shift Register (LFSR) has resulted in a novel arbitrary sequence generator having a lengthier and composite structure. An analysis of the LFSR output sequence’s architecture when combined with Tent map has revealed similar conformity compared to the homologous set of the individual linear constituents. Furthermore, to ensure the reliability of using the proposed Pseudo Random Number Generator (PRNG) in secure algorithms, the generated output bits sequence has been subjected to statistical analysis by NIST test suite and the result of the generated sequence confirm the efficiency of the proposed generator. The speed of the proposed generator and the security in terms of key space has been evaluated which give a robustness against different attacks.

Checking the quality of approximation of [formula omitted]-values in statistical tests for random number generators by using a three-level test

Statistical tests of pseudorandom number generators (PRNGs) are applicable to any type of random number generators and are indispensable for evaluation. While several practical packages for statistical tests of randomness exist, they may suffer from a lack of reliability: for some tests, the amount of approximation error can be deemed significant. Reducing this error by finding a better approximation is necessary, but it generally requires an enormous amount of effort. In this paper, we introduce an experimental method for revealing defects in statistical tests by using a three-level test proposed by Okutomi and Nakamura. In particular, we investigate the NIST test suite and the test batteries in TestU01, which are widely used statistical packages. Furthermore, we show the efficiency of several modifications for some tests.

YRBS coding with logistic map – a novel Sanskrit aphorism and chaos for image encryption

The role of image encryption in secure communication of confidential images is quite significant and novel schemes to encrypt images always have a demand in the scientific research community. DNA coding has found a noteworthy position in various earlier proposed image encryption schemes because of its simple but effective diffusion capabilities. Similar to the DNA coding, novel coding technique based on an aphorism present in the Sanskrit literature has been utilized in this image encryption work. The utility of Sanskrit sūtra ‘yamātārājabhānasalagam (YRBS)’ for performing scrambling, substitution and cyclic bit shifting promises the usage of this scheme as a part of various image encryption solutions. In this approach, YRBS coding has been employed along with simple one dimensional logistic map for encrypting 256 × 256 grayscale test images. The suggested scheme possesses a keyspace of 4.3769 × 1046 and average correlation figures of −0.00021, −0.00021, −0.00015 in horizontal, vertical and diagonal directions respectively when applied on ten test images. The encrypted pixels passed the NIST Test suite and this approach also offers a good resistance to chosen cipher text attack which was a challenge in DNA coding.

Design And Analysis of Analog TRNG Using Sample and Hold Circuit

Implementation of analog True random number generators is inevitable in almost all the security applications and encryption protocols nowadays. Although many digital True Random Number Generators are available, we proposed a method of random number generation using analog module of mixed signals. In actual fact generation of True Random Numbers is by utilizing the sample and hold circuit which is controlled by another random clock source, and a post processing circuit for generation of unpredictable binary sequence of numbers. The primary input source is an analog signal, essentially highly random noise from the external environment. The high unpredictability, less resource and simple circuit design are some highlights of the proposed work. Finally, the randomness is evaluated using NIST test suites and results are plotted and analyzed.

8-Bit Quantizer for Chaotic Generator With Reduced Hardware Complexity

This article describes how nowadays, data is widely transmitted over the internet in the real time. Wherever the transmission or storage is required, security is needed. High speed processing hardware machine with reduced complexity are used for the security of the data, that are transmitted in real time. The information which is to be secure are encoded by pseudorandom key. Chaotic numbers are used in place of a pseudorandom key. The generated chaotic values are analogous in nature, these analog values are digitized to generate encryption key like 8-bit, 16-bit, 32-bit. To generate an 8-bit key, an 8-bit quantizer is required. The design of 8-bit quantizer requires 256 levels which needs lot of complex hardware to implement. In this article, an 8-bit quantizer is designed with reduced complexity, where hardware requirement is reduced by more than 12 times. Without compromising the randomness of the sequence generated. To increase the randomness and confusion timed hop random selection is used. The randomness of the sequence generated by the chaotic generators is analyzed by NIST test suite, to test for its randomness.

A homodyne detector integrated onto a photonic chip for measuring quantum states and generating random numbers

Optical homodyne detection has found use as a characterisation tool in a range of quantum technologies. So far implementations have been limited to bulk optics. Here we present the optical integration of a homodyne detector onto a silicon photonics chip. The resulting device operates at high speed, up 150 MHz, it is compact and it operates with low noise, quantified with 11 dB clearance between shot noise and electronic noise. We perform on-chip quantum tomography of coherent states with the detector and show that it meets the requirements for characterising more general quantum states of light. We also show that the detector is able to produce quantum random numbers at a rate of 1.2 Gbps, by measuring the vacuum state of the electromagnetic field and applying off-line post processing. The produced random numbers pass all the statistical tests provided by the NIST test suite.

Programmable quantum random number generator without postprocessing.

We demonstrate a viable source of unbiased quantum random numbers whose statistical properties can be arbitrarily programmed without the need for any postprocessing such as randomness distillation or distribution transformation. It is based on measuring the arrival time of single photons in shaped temporal modes that are tailored with an electro-optical modulator. We show that quantum random numbers can be created directly in customized probability distributions and pass all randomness tests of the NIST and Dieharder test suites without any randomness extraction. The min-entropies of such generated random numbers are measured close to the theoretical limits, indicating their near-ideal statistics and ultrahigh purity. Easy to implement and arbitrarily programmable, this technique can find versatile uses in a multitude of data analysis areas.

Hardware implementation of pseudo-random number generators based on chaotic maps

We show the usefulness of bifurcation diagrams to implement a pseudo-random number generator (PRNG) based on chaotic maps. We provide details on the selection of the best parameter values to obtain high entropy and positive Lyapunov exponent from the bifurcation diagram of four chaotic maps, namely: Bernoulli shift map, tent, zigzag, and Borujeni maps. The binary sequences obtained from these maps are analyzed to implement a PRNG both in software and in hardware. The software implementation is realized using 32 and 64 bits microprocessor architectures, and with floating point and fixed point computer arithmetic. The hardware implementation is done by using a field-programmable gate array (FPGA) architecture. We developed a serial communication interface between the PRNG on the FPGA and a personal computer to obtain the generated sequences. We validate the randomness of the generated binary sequences with the NIST test suite 800-22-a both in floating point and fixed point arithmetic. At the end, we show that those chaotic maps are suitable to implement a PRNG but according to the hardware resources, the one based on the Bernoulli shift map is better. In addition, another advantage is that the required initial value for the sequences can be within the whole interval $$[-1,1]$$ , including its bounds.

Improving randomness characterization through Bayesian model selection

Random number generation plays an essential role in technology with important applications in areas ranging from cryptography to Monte Carlo methods, and other probabilistic algorithms. All such applications require high-quality sources of random numbers, yet effective methods for assessing whether a source produce truly random sequences are still missing. Current methods either do not rely on a formal description of randomness (NIST test suite) on the one hand, or are inapplicable in principle (the characterization derived from the Algorithmic Theory of Information), on the other, for they require testing all the possible computer programs that could produce the sequence to be analysed. Here we present a rigorous method that overcomes these problems based on Bayesian model selection. We derive analytic expressions for a model’s likelihood which is then used to compute its posterior distribution. Our method proves to be more rigorous than NIST’s suite and Borel-Normality criterion and its implementation is straightforward. We applied our method to an experimental device based on the process of spontaneous parametric downconversion to confirm it behaves as a genuine quantum random number generator. As our approach relies on Bayesian inference our scheme transcends individual sequence analysis, leading to a characterization of the source itself.

NIST Syndromic Surveillance Test Suite 2015 Edition

ObjectiveThe NIST Syndromic Surveillance Test Suite for 2015 EditionONC certification testing was published in February 2016. Keyinformation related to the purpose, development, and use of thisconformance test tool is provided via snapshots on a poster.IntroductionDetails about the ONC 2015 Edition certification criteria forSyndromic Surveillance and the related NIST Test Suite wereexplained previously. We now provide an overview and keyinformation regarding updates to the Test Suite and how it is designedto be used.MethodsSnapshots are provided on a poster and are used by the presenterto explain the steps involved in developing the NIST SyndromicSurveillance Test Suite 2015 Edition, to show key features of andupdates to the Test Suite, and to illustrate the relationship of the TestSuite to various releases of the PHIN Messaging Guide for SyndromicSurveillance.ResultsThe NIST Syndromic Surveillance Test Suite for 2015 EditionONC certification testing was published in February 2016. As thetarget stakeholders began using it and providing feedback, this tooland associated documentation were updated. The Test Suite is beingused by test labs for ONC certification testing of health informationtechnologies, by developers in preparation for certification testing,and ultimately by public health jurisdictions for on-boarding ofprovider organizations that need to submit surveillance data.ConclusionsAutomated conformance test tools enable validation of healthinformation technologies’ ability to support the requirementspublished in the PHIN Messaging Guide for Syndromic Surveillance.Having this standard and the means to validate conformance helpsdrive the industry toward the level of interoperability needed topromote efficient reporting and utilization of syndrome-based publichealth surveillance information.

On the independence of statistical randomness tests included in the NIST test suite

Random numbers and random sequences are used to produce vital parts of cryptographic algorithms such as encryption keys and therefore the generation and evaluation of random sequences in terms of randomness are vital. Test suites consisting of a number of statistical randomness tests are used to detect the nonrandom characteristics of the sequences. Construction of a test suite is not an easy task. On one hand, the coverage of a suite should be wide; that is, it should compare the sequence under consideration from many different points of view with true random sequences. On the other hand, an overpopulated suite is expensive in terms of running time and computing power. Unfortunately, this trade-off is not addressed in detail in most of the suites in use. An efficient suite should avoid use of similar tests, while still containing sufficiently many. A single statistical test gives a measure for the randomness of the data. A collection of tests in a suite give a collection of measures. Obtaining a single value from this collection of measures is a difficult task and so far there is no conventional or strongly recommended method for this purpose. This work focuses on the evaluation of the randomness of data to give a unified result that considers all statistical information obtained from different tests in the suite. A natural starting point of research in this direction is to investigate correlations between test results and to study the independences of each from others. It is started with the concept of independence. As it is complicated enough to work even with one test function, theoretical investigation of dependence between many of them in terms of conditional probabilities is a much more difficult task. With this motivation, in this work it is tried to get some experimental results that may lead to theoretical results in future works. As experimental results may reflect properties of the data set under consideration, work is done on various types of large data sets hoping to get results that give clues about the theoretical results. For a collection of statistical randomness tests, the tests in the NIST test suite are considered. Tests in the NIST suite that can be applied to sequences shorter than 38,912 bits are analyzed. Based on the correlation of the tests at extreme values, the dependencies of the tests are found. Depending on the coverage of a test suite, a new concept, the coverage efficiency of a test suite, is defined, and using this concept, the most efficient, the least efficient, and the optimal subsuites of the NIST suite are determined. Moreover, the marginal benefit of each test, which also helps one to understand the contribution of each individual test to the coverage efficiency of the NIST suite, is found. Furthermore, an efficient subsuite that contains five statistical randomness tests is proposed.

New statistical randomness tests: 4-bit template matching tests

For cryptographic algorithms, secret keys should be generated randomly as the security of the system depends on the key and therefore generation of random sequences is vital. Randomness testing is done by means of statistical randomness tests. In this work, we show that the probabilities for the overlapping template matching test in the NIST test suite are only valid for a specific template and need to be recalculated for the other templates. We calculate the exact distribution for all 4-bit templates and propose new randomness tests, namely template matching tests. The new tests can be applied to any sequence of minimum length 5504 whereas the overlapping template matching test in the NIST test suite can only be applied to sequences of minimum length $10^6$. Moreover, we apply the proposed tests to biased nonrandom data and observe that the new tests detect the nonrandom behavior of the generator even for a bias of $0.001$, whereas the template matching tests in NIST cannot detect that bias.

A quantum random number generator implementation with polarized photons

In this letter, we present an implementation of a random number generator based on photon polarization superposition. We prepare photons in a superposition state of vertical and horizontal polarizations, let them pass through a polarizing beamsplitter and set two detectors at each path to get a 50–50 chance of finding the photon at each detector. We present the results of the NIST test suite for random number generators for our binary sequence of approximately 1.4 × 107 bits and analyze the different p -values obtained to statistically assess its randomness. In doing so, we use von Neumann’s algorithm for bias removal and briefly explain how the statistical tests work.

A switched‐capacitor skew‐tent map implementation for random number generation

SummaryPiecewise linear one‐dimensional maps have been proposed as the basis for low‐power analog and mixed‐signal true random number generators (TRNGs). Recent research has moved towards conceiving maps that operate robustly under the consideration of parameter variations. In this paper, we introduce an oscillator circuit mapping a low‐complexity map known as the skew‐tent. This oscillator is employed as the basis for a TRNG scheme. Simulation results in TSMC 0.18 μm validate the chaotic oscillator and the randomness of the TRNG scheme is verified with the NIST test suite 800‐22. Copyright © 2016 John Wiley &amp; Sons, Ltd.

(Invited) Silicon Nanostructures: A Versatile Material for Photonics

The increased control over nanoscale materials structuring is reshaping a number of applications and technologies at a fast pace. Semiconducting materials are playing an increasingly important role and Silicon is so far the most investigated one thanks to its broad availability and its fundamental role in microelectronics. Despite all its favorable properties, a major drawback of silicon is the lack of an efficient light emission mechanism that prevents its use in active photonics. Quantum size effects has been demonstrated a viable strategy to overcome this limit and to achieve light emission from silicon nanostructures. Si nanostructures are well controlled and can be tuned to achieve the desired properties, often exploiting the mature CMOS technological platform. Simultaneously several synthetic strategies have been developed in order to fabricate silicon quantum dots from chemical synthesis. Silicon chemistry is (rather) well known and permits to synthesize nanoparticles and to functionalize their surface using a broad number of reactions. Such flexibility allows for the grafting of both organic and inorganic species onto the Si QDs surface, to add functionalities and to protect the nanoparticle from their natural oxidations that, in turn, quenches the photoluminescence properties. Thus, despite the initial research was focused on the possibility to fabricate inorganic light sources that might rival with III-V or II-VI semiconductors. More recently a large research effort has been devoted to the use of Silicon nanostructures in biological-related applications. In such research topics Silicon has several properties take renders it an ideal candidate: it is considered a biocompatible material; it is readily dissolved in biological environment without releasing toxic byproducts; its red and tunable luminescence make it an interesting fluorescent tag able to exploit the tissue transparency window. During the presentation I will make a brief review of the fabrications methods proposed so far and I will discuss in details some of the recent research activities performed in our group in ICT- as well as in bio-related topics, all sharing the common denominator of Si QDs as active optical element. About the ICT-related topics I will discuss two applications of Si QDS. The first is about the use of Si QDs in quantum technologies. Data encryption and cryptography are core technologies hidden in our daily life and their importance is constantly growing. We have developed a robust physical random number generator that exploits Si QDs as a random bit source. The preliminary results are promising and the random sequences pass the standard NIST test suite. Furthermore the system is fully compatible with CMOS technology and can be scaled up to achieve large bit-rate generation. The second case in point is about the large optical nonlinearities possessed by Si QDs and their exploitation to develop integrated photonic devices. As a bio-related application I will discuss how nanostructured silicon microparticles can be used as fluorescent tags and are successfully up-taken by human dendritic cells without stimulating apoptosis up to a very large concentration. Porous silicon micro-particles (micro-pSi) with size in the range of 1-10 um are functionalized obtaining an interface that exposes either positive or negative charges at neutral pH. Their porous structure enables their use as drug carriers. Moreover, the surface modification stabilizes their intense photoluminescence and suggests their use for simultaneous imaging and drug delivery. The few cases discussed underline the great potentialities of Silicon nanostructures in different technologies and suggest its possible implementation as a functional interface between organic and inorganic systems.