Statistical Test Suite Research Articles

True Random Number Generation Using Latency Variations of FRAM

True random number generation (TRNG) plays an important role in security applications and protocols. In this article, we propose an effective technique to generate a robust true random number using emerging, energy-efficient, nonvolatile, consumer-off-the-shelf (COTS) ferroelectric random access memory (FRAM) chips. In the proposed method, we extract inherent randomness from internal ferroelectric capacitors by exploiting latency variation across cells within FRAM. Hardware results and subsequent National Institute of Standards and Technology (NIST) statistical test suite (STS) testing indicate that the proposed latency-based TRNG is robust over a wide range of operating conditions at speeds of 6.23 Mb/s using COTS, silicon FRAM chips from Cypress Semiconductor Corporation.

Multivariate analysis of cooking pots from elite and “commoner” contexts at Yanshi Shangcheng: implications for the politics of daily life and development of ceramic technology in the early Bronze Age of northern China

In this study, we investigate how ceramics used in domestic contexts may have differed between elites and “commoners” at Yanshi Shangcheng, a walled settlement from the early Shang (Erligang) period of northern China. Marked social stratification is evident at the site, particularly in the form of differential architecture and the layout of the settlement, which had an inner “palace” district and an outer lower status area. We inquire into whether social difference infused the sphere of daily life and daily cuisine at this early Bronze Age settlement. We performed a suite of statistical tests on two types of grayware cooking pots, guan jars and li tripods, from elite and lower status contexts, including a permutation-based modified multivariate analysis of variance (MANOVA), univariate tests, and a test of the homogeneity of multivariate dispersions. We tested variables related to main stages in the pottery production sequence, including clay preparation, vessel construction, and vessel firing. Pottery data, such as characteristics of the fabric, measurements of thickness, rim diameter, color, and hardness, were recorded at the site visually and with the aid of a hand lens and various measurement devices. Results indicate significant aspects of heterogeneity related to thickness, hardness, pot size, surface texture, and color. Results also indicate little difference in variables related to clay preparation methods. Possible explanations for the differences are explored, including developments in firing conditions and selection of higher quality pieces for elites. The statistical techniques developed herein could be applied to a range of artifactual types to investigate questions of difference.

An Integrated TRNG-PUF Architecture Based on Photovoltaic Solar Cells

This article presents an integrated true random number generator (TRNG) and physically unclonable function (PUF) architecture using photovoltaic (PV) solar cells. We illustrate that the PV solar cell sensor response can be engineered into dynamic (TRNG) and static responses (PUF). The proposed prototype uses the iterative Von Neumann postprocessing scheme to produce random bits with 34% better throughput compared to a single Von Neumann operation. The random bit quality was checked by statistical test suites from the National Institute of Science and Technology and achieves an average p-value of 0.45 at all variations in light intensity. The PUF response achieves 92.13% reliability and 50.91% uniformity. The integrated TRNG-PUF architecture is beneficial for resource-constrained cyber-physical system.

A Distant Fast Radio Burst Associated with Its Host Galaxy by the Very Large Array

Abstract We present the discovery and subarcsecond localization of a new fast radio burst (FRB) by the Karl G. Jansky Very Large Array (VLA) and realfast search system. The FRB was discovered on 2019 June 14 with a dispersion measure of 959 . This is the highest DM of any localized FRB and its measured burst fluence of 0.6 Jy ms is less than nearly all other FRBs. The source is not detected to repeat in 15 hr of VLA observing and 153 hr of CHIME/FRB observing. We describe a suite of statistical and data quality tests we used to verify the significance of the event and its localization precision. Follow-up optical/infrared photometry with Keck and Gemini associate the FRB with a pair of galaxies with mag. The false-alarm rate for radio transients of this significance that are associated with a host galaxy is roughly . The two putative host galaxies have similar photometric redshifts of , but different colors and stellar masses. Comparing the host distance to that implied by the dispersion measure suggests a modest ( ) electron column density associated with the FRB environment or host galaxy/galaxies.

Pseudo Random Binary Sequence Based on Cyclic Difference Set

With the increasing reliance on technology, it has become crucial to secure every aspect of online information where pseudo random binary sequences (PRBS) can play an important role in today’s world of Internet. PRBS work in the fundamental mathematics behind the security of different protocols and cryptographic applications. This paper proposes a new PRBS namely MK (Mamun, Kumu) sequence for security applications. Proposed sequence is generated by primitive polynomial, cyclic difference set in elements of the field and binarized by quadratic residue (QR) and quadratic nonresidue (QNR). Introduction of cyclic difference set makes a special contribution to randomness of proposed sequence while QR/QNR-based binarization ensures uniformity of zeros and ones in sequence. Besides, proposed sequence has maximum cycle length and high linear complexity which are required properties for sequences to be used in security applications. Several experiments are conducted to verify randomness and results are presented in support of robustness of the proposed MK sequence. The randomness of proposed sequence is evaluated by popular statistical test suite, i.e., NIST STS 800-22 package. The test results confirmed that the proposed sequence is not affected by approximations of any kind and successfully passed all statistical tests defined in NIST STS 800-22 suite. Finally, the efficiency of proposed MK sequence is verified by comparing with some popular sequences in terms of uniformity in bit pattern distribution and linear complexity for sequences of different length. The experimental results validate that the proposed sequence has superior cryptographic properties than existing ones.

One-Dimensional Pseudo-Chaotic Sequences Based on the Discrete Arnold’s Cat Map Over ℤ₃ᵐ

In this brief we employ the discrete Arnold’s cat map over the integer ring <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathbb {Z}_{3^{m}}$ </tex-math></inline-formula> to construct one-dimensional pseudo-chaotic sequences. We analyze their period properties using the properties of the Fibonacci sequence over <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathbb {Z}_{3^{m}}$ </tex-math></inline-formula> and show that they have twice the period of the sequences generated by the logistic map over <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathbb {Z}_{3^{m}}$ </tex-math></inline-formula> recently proposed. Moreover, we investigate the pseudo-chaotic properties of the proposed sequences in the context of pseudo-chaos. Finally, these sequences are employed to design a pseudo-random number generator and a statistical analysis with the NIST statistical test suite is performed.

Дослідження статистичних характеристик модифікованого алгоритму BBS із залежністю від поточного та попереднього значення послідовності

У системах захисту інформації широкого застосування набув генератор Блюма-Блюма-Шуба (BBS), який базується на використанні односторонньої функції факторизації, та належить до криптостійких. У роботі досліджено характеристики запропонованого автором модифікованого алгоритму BBS із залежністю від поточного та попереднього значення послідовності, зокрема, період повторення та статистичні характеристики вихідної послідовності залежно від параметрів генератора. Дослідження проведено з використанням тестів NIST і порівняно із класичним алгоритмом BBS. З'ясовано, що період повторення класичного алгоритму BBS для малих значень ключа, від 5 до 10 бітів, становить не більше ніж 20 % від його значення. Ця тенденція зберігається на ключах більшого розміру, від 15 до 21 бітів, де період повторення для вибраних початкових установок не перевищує 5,56 %. Період повторення модифікованого алгоритму BBS для ключів від 5 до 10 бітів у середньому становить 200 % від значення ключа. Така поведінка зберігається для вибіркових початкових установок для ключів від 15 до 21 бітів, період повторення яких в середньому становить 351 %. Дослідження статистичних характеристик пакетом статистичних тестів NIST проведено на згенерованих послідовностях із 109 бітів для ключів завдовжки від 29 до 31 бітів. Встановлено, що статистичні портрети для класичного алгоритму є не задовільними, зокрема, статистичні портрети для 31-бітного ключа мають до 5 незадовільних результатів із 188 тестів. Статистичні портрети для модифікованого алгоритму BBS є задовільними для ключів від 30 до 31 бітів, але не є задовільними для 29-бітного ключа – мають по одному незадовільному результату. Отже, модифікований алгоритм BBS має кращі значення періоду повторення та статистичні портрети порівняно із класичним алгоритмом, що дає змогу використовувати ключі меншої довжини при генеруванні послідовності, які вимагають менше ресурсів системи, оскільки операція піднесення до квадрату за модулем більш ресурсозатратна, ніж операція додавання. Подальші дослідження будуть зосереджені на апаратну реалізацію модифікованого алгоритму BBS та порівняння використаних ресурсів системи із реалізацією класичного алгоритму BBS.

A Compact Low-Voltage True Random Number Generator Based on Inkjet Printing Technology

Printed electronics (PE) is a fast-growing field with promising applications in wearables, smart sensors, and smart cards, since it provides mechanical flexibility, and low-cost, on-demand, and customizable fabrication. To secure the operation of these applications, true random number generators (TRNGs) are required to generate unpredictable bits for cryptographic functions and padding. However, since the additive fabrication process of the PE circuits results in high intrinsic variations due to the random dispersion of the printed inks on the substrate, constructing a printed TRNG is challenging. In this article, we exploit the additive customizable fabrication feature of inkjet printing to design a TRNG based on electrolyte-gated field-effect transistors (EGFETs). We also propose a printed resistor tuning flow for the TRNG circuit to mitigate the overall process variation of the TRNG so that the generated bits are mostly based on the random noise in the circuit, providing a true random behavior. The simulation results show that the overall process variation of the TRNGs is mitigated by 110 times, and the generated bitstream of the tuned TRNGs passes the National Institute of Standards and Technology - Statistical Test Suite. For the proof of concept, the proposed TRNG circuit was fabricated and tuned. The characterization results of the tuned TRNGs prove that the TRNGs generate random bitstreams at the supply voltage of down to 0.5 V. Hence, the proposed TRNG design is suitable to secure low-power applications in this domain.

SEPAR: A New Lightweight Hybrid Encryption Algorithm with a Novel Design Approach for IoT

This paper presents a new hybrid encryption algorithm with 16-bit block size and a 128-bit initialization vector, referred to as SEPAR, and it is suitable for IoT devices. The design idea of this algorithm combines pseudorandom permutation and pseudorandom generator functions. This smart integration causes resistance improvement against common cryptographic attacks meanwhile leads to cipher speed increment. Investigation of security analysis on the algorithm and results of the NIST statistical test suit proves its resistance against common cryptographic attacks as linear and differential cryptanalysis. Furthermore, efficient software implementation of SEPAR is presented on 8, 16 and 32-bit platforms. Compared to BORON cipher, SEPAR provides 42.22% throughput improvement on 32-bit ARM CPU. Also, for 8-bit and 16-bit microcontroller, SEPAR provides 87.91% and 98.01% performance improvements compared to present, respectively.

Generating True Random Numbers Based on Multicore CPU Using Race Conditions and Chaotic Maps

A true random number generator (TRNG) is proposed, harvesting entropy from multicore CPUs to generate non-deterministic outputs. The entropy source is the unpredictable sequence of thread access when parallel threads attempt to access the same memory location, known as race condition or data races. Although prior work using the same entropy source exists, they either have low efficiency or insufficient security analysis. The novelty of this work lies in its use of chaotic networks capable of extracting entropy while postprocessing outputs simultaneously. These networks are formulated by coupling chaotic maps in the form of chaotic coupled map lattices which have the capability to amplify minor uncertainties, leading to better performance as compared to other CPU-based TRNGs. We first perform experiments to depict the unpredictable nature of thread access due to race conditions through entropy and scale index analysis. Next, the proposed generator is scrutinized based on a standardized set of evaluation criteria which includes the use of multiple statistical test suites followed by an analysis of its non-deterministic property. We also perform an in-depth entropy analysis of the generator’s outputs and measure its degree of non-periodicity. Results indicate that the proposed chaos-based TRNG is fast, evenly distributed, and is secure enough for applications that have high security requirements.

Cryptographically Secure Pseudo-Random Number Generator IP-Core Based on SHA2 Algorithm.

In the context of growing the adoption of advanced sensors and systems for active vehicle safety and driver assistance, an increasingly important issue is the security of the information exchanged between the different sub-systems of the vehicle. Random number generation is crucial in modern encryption and security applications as it is a critical task from the point of view of the robustness of the security chain. Random numbers are in fact used to generate the encryption keys to be used for ciphers. Consequently, any weakness in the key generation process can potentially leak information that can be used to breach even the strongest cipher. This paper presents the architecture of a high performance Random Number Generator (RNG) IP-core, in particular a Cryptographically Secure Pseudo-Random Number Generator (CSPRNG) IP-core, a digital hardware accelerator for random numbers generation which can be employed for cryptographically secure applications. The specifications used to develop the proposed project were derived from dedicated literature and standards. Subsequently, specific architecture optimizations were studied to achieve better timing performance and very high throughput values. The IP-core has been validated thanks to the official NIST Statistical Test Suite, in order to evaluate the degree of randomness of the numbers generated in output. Finally the CSPRNG IP-core has been characterized on relevant Field Programmable Gate Array (FPGA) and ASIC standard-cell technologies.

Key Generation based on Henon map and Lorenz system

Securing information has been the most significant process for communication and data store. Orderly to secure information such as data authentication, data integrity, and confidentiality must be verified based on algorithms of cryptography. Where, the most important part of any encryption algorithms is the key which specifies if the system is strong enough or not. The proposal of this paper is a new method to generate keys based on two kinds of chaos theory in order to improve the security of cryptographic algorithms. The base of this proposal is to investigate a new method for generating random numbers by using the 3D Lorenz system and 2D Henon map. The newly generated keys have successfully passed the National Institute of Standards and Technology (NIST) statistical test suite

Enhancing the security of AES through small scale confusion operations for data communication

With the advent of computers, networks, distributed systems and wireless data transfer technologies, data communication is subjected to potential threats and hence needs to be protected. Advanced Encryption Standard (AES) is an efficient encryption algorithm used for secure wireless communication, but its security is under threat due to different forms of theoretical and practical attacks such as linear cryptanalysis, differential cryptanalysis, boomerang attack, truncated differentials, hybrid attacks, related-key distinguishing attack, and side channel attacks. This work is focused on reducing the attacks by increasing the complexity of cryptanalysis through small scale variations in the shift row transformation and key expansion unit of the AES algorithm. The proposed small scale variations in the linear layer of the cipher unit and in the word column of key expansion unit enhances confusion during encryption. The inherent diffusion property of the algorithm along with the proposed confusion characteristics allows us to increase the overall security of the algorithm. The confusion and diffusion characteristics of the modified algorithm are found to be higher in terms of balance, Strict Avalanche Criterion and bit independence criteria. The AES variants are also tested using NIST-800-22 statistical test suite for random number generators, the small scale variations made in the architecture provides a higher degree of randomness in the ciphertext thus increasing cryptanalysis complexity. This paper also proposes an obfuscation control unit that allows on-demand selection of the three AES variants resulting in a variable encrypting pattern for a plaintext-key pair thus adding more bottlenecks to the adversaries.

True Random Number Generation From Commodity NVM Chips

In this article, we propose a novel technique to generate true random numbers (TRNs) using off-the-shelf non-volatile memory (NVM) chips. In particular, we illustrate a TRN generator (TRNG) extraction methodology from two types of NVM technologies: 1) emerging resistive NVM, and 2) charge-based NOR flash. We exploit the variability in programming latency while performing write and erase operations. The main causes of such effects can be attributed to the switching-time variability of the NVM devices and second-order effects, such as peripheral CMOS variability and circuit parasitics. Through multiple experiments, we show that dominant variability contribution arises from NVM switching-time distributions. In order to increase the quality of randomness, we propose an XOR-based post-processing technique. In the proposed methodology, latency values are first extracted from multiple locations on the chip followed by the application of post-processing technique. The randomness of the generated bitstream is evaluated using NIST SP 800-22 statistical test suite, and all the 15 tests are passed with encouraging P-values. We validated the proposed NVM-based TRNG for a wide range of operational temperatures (−40 °C to +85 °C). Utilization of the existing NVM chips and no requirement of additional specialized hardware make the proposed TRNG technique highly advantageous and cost-effective.

Entropy evaluation of white chaos generated by optical heterodyne for certifying physical random number generators

The entropy of white chaos is evaluated to certify physical random number generators. White chaos is generated from the electric subtraction of two optical heterodyne signals of two chaotic outputs in semiconductor lasers with optical feedback. We use the statistical test suites of NIST Special Publication 800-90B for the evaluation of physical entropy sources of white chaos with an eight-bit resolution. The minimum value of entropy is 2.1 for eight most significant bits data. The entropy of white chaos is enhanced from that of the chaotic output of the semiconductor lasers. We evaluate the effect of detection noise and distinguish between the entropy that originates from the white chaos and the detection noise. It is found that the entropy of five most significant bits originates from white chaos. The minimum value of entropy is 1.1 for five most significant bits data, and it is considered that the entropy can be obtained at at least one bit per sample.

LoRa-Based Physical Layer Key Generation for Secure V2V/V2I Communications.

In recent years, Vehicle-to-Vehicle (V2V) and Vehicle-to-Infrastructure (V2I) communication brings more and more attention from industry (e.g., Google and Uber) and government (e.g., United States Department of Transportation). These Vehicle-to-Everything (V2X) technologies are widely adopted in future autonomous vehicles. However, security issues have not been fully addressed in V2V and V2I systems, especially in key distribution and key management. The physical layer key generation, which exploits wireless channel reciprocity and randomness to generate secure keys, provides a feasible solution for secure V2V/V2I communication. It is lightweight, flexible, and dynamic. In this paper, the physical layer key generation is brought to the V2I and V2V scenarios. A LoRa-based physical key generation scheme is designed for securing V2V/V2I communications. The communication is based on Long Range (LoRa) protocol, which is able to measure Received Signal Strength Indicator (RSSI) in long-distance as consensus information to generate secure keys. The multi-bit quantization algorithm, with an improved Cascade key agreement protocol, generates secure binary bit keys. The proposed schemes improved the key generation rate, as well as to avoid information leakage during transmission. The proposed physical layer key generation scheme was implemented in a V2V/V2I network system prototype. The extensive experiments in V2I and V2V environments evaluate the efficiency of the proposed key generation scheme. The experiments in real outdoor environments have been conducted. Its key generation rate could exceed 10 bit/s on our V2V/V2I network system prototype and achieve 20 bit/s in some of our experiments. For binary key sequences, all of them pass the suite of statistical tests from National Institute of Standards and Technology (NIST).

Pseudorandom Number Generator (PRNG) Design Using Hyper-Chaotic Modified Robust Logistic Map (HC-MRLM)

Robust chaotic systems, due to their inherent properties of mixing, ergodicity, and larger chaotic parameter space, constitute a perfect candidate for cryptography. This paper reports a novel method to generate random numbers using modified robust logistic map (MRLM). The non-smooth probability distribution function of robust logistic map (RLM) trajectories gives an un-even binary distribution in randomness test. To overcome this disadvantage in RLM, control of chaos (CoC) is proposed for smooth probability distribution function of RLM. For testing the proposed design, cryptographic random numbers generated by MRLM were vetted with National Institute of Standards and Technology statistical test suite (NIST 800-22). The results showed that proposed MRLM generates cryptographically secure random numbers (CSPRNG).

Generation of Highly Nonlinear and Dynamic AES Substitution-Boxes (S-Boxes) Using Chaos-Based Rotational Matrices

This work reports a novel chaos-based affine transformation generation method, which is based on rotational matrices to design strong key-based S-boxes. Chaotic logistic map’s nonlinear trajectories are used to generate rotational matrices under given design conditions. Thus, the inherent logic is to generate key-based S-boxes, as strong as AES S-box, in terms of cryptographic properties using chaos in affine transformation. The randomness of chaotic sequences is tested using the National Institute of Standard and Technology (NIST) Statistical Test Suit (STS) 800–22 that validates the generated sequences for S-box design. The results show that methodology adapted to design proposed key-based dynamic S-boxes entails near-optimal cryptographic properties so that proposed S-boxes are as stronger as AES S-box.

XORSHIFTUL+: A Novel Hybrid Random Number Generator for Internet Of Things And Wireless Sensor Network Applications

There are an increasing number of lightweight devices such as smart cards, radio frequency identification (RFID) tags, wireless sensor nodes and devices associated with the Internet of Things (IoT) concept, all of which need effective and lightweight security structures. One of the basic elements used in authentication protocols is the nonce values that are generated by PRNGs. Also random numbers are used for encryption process in secure communication. Proposed PRNG has demonstrated great suitability for devices with limited resources in terms of performance, resource usage and randomness. This generator is tested with NIST statistical test suite (NIST STS), which is one of the most comprehensive randomness test tools. It is also implemented, tested on wireless identification and sensing platform (WISP) passive RFID tag and compared with well-known PRNGs. As a result of the comparisons, it has better results than its rivals.

KBC: Multiple Key Generation using Key Block Chaining

Cryptography is an important aspect of securing communications, however, the encryption scheme may be known to the attacker(s). Hence, the key can be rewarded as a crucial part of any cryptographic algorithm. With the symmetric key, researchers have developed chaining concepts where the output of one operation becomes an input to the next one. Such concept of modes of operation (Cipher Block Chaining) is integrated in this article to generate multiple key blocks. The generated keys can be provided to an individual block of plaintext for any encryption technique as per the requirements. The proposed Key Block Chaining (KBC) approach can also be referred to as a key derivation approach. The basic concepts of Advanced Encryption Standard and Message Authentication Code have also been incorporated in the proposed model to introduce randomness, and thereby, ensuring security as well as robustness. To assess the randomness of the sequence of generated keys, KBC is implemented and tested using the National Institute of Standards and Technology statistical test suite and reasonable randomness has been successfully achieved. Possible variations and key points of the proposed approach along with statistical analysis and significance of our work have been discussed.