Random Bit Sequence Research Articles

Generating pseudo-random numbers with a Brownian system

We use a deterministic dynamical system that simulates a Brownian movement over time to produce pseudo-random sequences of binary numbers. We show that the used Brownian system has two positive Lyapunov exponents, this characteristic is different of a chaotic system that has only one maximum positive Lyapunov exponent. The implementation of the random number generator uses fixed point arithmetic with numbers with 5 bits for the integer part and 58 bits for the fractional part. The eight least significant bits for each variable of the 3rd order Brownian system are concatenated to form the sequences of random bits. The generated sequences pass all the NIST and TestU01 statistical randomness tests. Furthermore, a hardware design in FPGA of the proposed pseudo-random generator is presented with a throughput equal to 1085.16 Mb/s. For the best of our knowledge, this is the first time a Brownian system is used as the core of a PRNG.

A Novel Strong S-Box Design Using Quantum Crossover and Chaotic Boolean Functions for Symmetric Cryptosystems

In this paper, we propose a new method for drawing a cryptographically strong substitution box using the Lorenz system and quantum genetic algorithm techniques. We used the chaotic function to generate an initial random sequence of bits and the quantum crossover to provide a new and improved substitution box with increased non-linearity. The aim of the proposed algorithm was to generate a strong and secure substitution box that can be utilized in symmetric cryptosystems. The use of chaotic Boolean functions, genetic algorithm techniques, and the quantum crossover helped achieve this goal, and statistical tests further confirmed the randomness and efficiency of the generated substitution box. The results of the statistical test suite showed that the substitution box produced by the proposed algorithm is a “pass” in terms of randomness and has strong cryptographic properties. The tests include a frequency (monobit) test, a frequency test within a block, a linear complexity test, an approximate entropy test, and a cumulative sums test among others. The p-values obtained in the tests indicate that the randomness of the generated substitution box meets the requirements of a cryptographically secure substitution box.

LGTBIDS: Layer-Wise Graph Theory-Based Intrusion Detection System in Beyond 5G

The advancement in wireless communication technologies is becoming more demanding and pervasive. One of the fundamental parameters that limit the efficiency of the network are the security challenges. The communication network is vulnerable to security attacks such as spoofing attacks and signal strength attacks. Intrusion detection signifies a central approach to ensuring the security of the communication network. In this paper, an Intrusion Detection System based on the framework of graph theory is proposed. A Layerwise Graph Theory-Based Intrusion Detection System (LGTBIDS) algorithm is designed to detect the attacked node. The algorithm performs the layer-wise analysis to extract the vulnerable nodes and ultimately the attacked node(s). For each layer, every node is scanned for the possibility of susceptible node(s). The strategy of the IDS is based on the analysis of energy efficiency and secrecy rate. The nodes with the energy efficiency and secrecy rate beyond the range of upper and lower thresholds are detected as the nodes under attack. Further, detected node(s) are transmitted with a random sequence of bits followed by the process of re-authentication. The obtained results validate the better performance, low time computations, and low complexity. Finally, the proposed approach is compared with the conventional solution of intrusion detection.

A Time-Domain Simulation Framework for the Modeling of Jitter in High-Speed Serial Interfaces

We report on the development of a time-domain numerical modeling framework to estimate timing jitter in High-Speed Serial Interfaces (HSSI) including a wide range of effects such as Inter-Symbol Interference (ISI) due to channel dispersion, phase noise of transmitter (TX) and receiver (RX) frequency synthesizers and use of bang-bang phase detector in the Clock and Data Recovery (CDR) loop. Based on the step response of the channel, the numerical model computes the response of the system to a random sequence of bits and provides information in terms of eye diagram, bathtub plot and jitter histogram. Different definitions of jitter are investigated, and for each of them we consider the physical effects that are included, eventually identifying that the most complete definition is based on the time distance between the edges instants defined by the CDR and the crossing points of the sampled signal. We also found that this definition is consistent with the features of the bathtub plot. A channel compliant with the PCIe 4.0 standard is used as test vehicle, including the main equalization strategies. The numerical model is then compared to a simple analytical model for the CDR jitter that can be augmented by including Data-Dependent Jitter (DDJ). An approach to system-level analysis based on proper combination of the above elements is eventually proposed to provide quick although accurate aid to the design of CDRs in HSSIs.

Working with cryptographic key information

It is important to create a cryptographic system such that the encryption system does not depend on the secret storage of the algorithm that is part of it, but only on the private key that is kept secret. In practice, key management is a separate area of cryptography, which is considered a problematic area. This paper describes the main characteristics of working with cryptographic key information. In that, the formation of keys and working with cryptographic key information are stored on external media. The random-number generator for generating random numbers used for cryptographic key generation is elucidated. To initialize the sensor, a source of external entropy, mechanism “Electronic Roulette” (biological random number), is used. The generated random bits were checked on the basis of National Institute of Standards and Technology (NIST) statistical tests. As a result of the survey, the sequence of random bits was obtained from the tests at a value of P≥0.01. The value of P is between 0 and 1, and the closer the value of P is to 1, the more random the sequence of bits is generated. This means that random bits that are generated based on the proposed algorithm can be used in cryptography to generate crypto-resistant keys.

Secret Key Generation From Route Propagation Delays for Underwater Acoustic Networks

With the growing use of underwater acoustic communications and the recent adoption of standards in this field, it is becoming increasingly important to secure messages against eavesdroppers. In this paper, we focus on a physical-layer security solution to generate sequences of random bits (keys) between two devices (Alice and Bob) belonging to an underwater acoustic network (UWAN); the key must remain secret to a passive eavesdropper (Eve) not belonging to the UWAN. Our method is based on measuring the propagation delay of the underwater acoustic channel over multiple hops of the UWAN: this harvests the randomness in the UWAN topology and turns the slow sound propagation in water into an advantage against eavesdropping. Our key generation protocol includes a route discovery handshake, whereby all UWAN devices at intermediate hops accumulate their message processing delays. This enables Alice and Bob to compute the actual propagation delays along each route and to map such information to a sequence of bits. Finally, from these bit sequences, Alice and Bob obtain a secret key. We analyze the performance of the protocol theoretically and assess it via extensive simulations and field experiments.

Random number generator based on semiconductor nanoheterostructures with quantum dots and optical feedback

Subject of study. This study models the generation process of random bit sequences using an array of coupled lasers. It is based on quantum dot (QD) micropillars with optical feedback that is realized via a mirror positioned at some distance from the array. A model of the array of coupled micropillar lasers consists of QD laser rate equations accounting for the global optical feedback. Aim of study. This study aimed to numerically model and analyze a random number generator using an array of coupled lasers based on QD micropillars. Method. The dynamic behavior was modeled through numerical integration of the delayed differential equation system using a semi-implicit Euler method implemented using the Julia programming language. To generate sequences of random bits, an algorithm was used that involved the sampling of the total field intensity of the array, normalization and discretization with 12 bit resolution, conversion of discretized values to bit representation, selection of four less significant bits, and concatenation of the bit values into the final sequence. Main results. The process of generating a sequence of random bits at the rate of 400 Gb/s, which met the criteria of NIST 800-22 statistical tests for the p-value of 0.01 at the sampling rate of total field intensity of the array equal to 100 Gsamples/s and a sequence length of 11,142,860 bits, was modeled. The model of an array of coupled lasers based on QD micropillars with optical feedback was analyzed using bifurcation analysis. The feedback time delay signature was traced in the chaotic signal of the emission intensity. However, it did not affect the quality of the random number generation. Practical significance. The optical feedback resulted in the chaotic generation of an array of lasers based on the QD micropillars, which can be used to generate random numbers.

Using ECG signal as an entropy source for efficient generation of long random bit sequences

Electrocardiogram (ECG) signal produced by the human heart has been investigated as a potential entropy source for cryptographic random bit generation for a long time. The throughput of existing methods remains as the bottleneck for its deployment in practical applications. To overcome this problem, we develop a Bernoulli entropy source by processing a single heartbeat ECG signal to obtain a long random bit sequence (RBS). The proposed method converts the signal into an IID (independent and identically distributed) source of entropy using efficient interpolation and optimization techniques. Several heartbeat signals, obtained from two different databases, were used to test the entropy source generating RBSs with one million bits. The entropy source was evaluated with the latest NIST recommendation for IID source validation and it passed all recommended tests and the average min-entropy obtained from several heartbeat signals of different individuals was close to the perfect entropy value of 1.0. It was also observed that the entropy increases monotonically with the increase of the length of keys. The proposed method can efficiently produce a long RBS for cryptographic applications, such as key generation for one-time pad and image encryption. The method could be further explored to generate a true random number with a personalized signature, which is crucial for information security in the future generation of computing.

True Random Number Generator Based on nondeterministic Device and Multi dimension Chaos Theory

There have been strong links between chaotic theory and cryptographic theory for the last three decades. The characterization of behaviors of the Chaotic system, such as: highly responsive to initial states, mixing attributes, deterministic existence, and often unable to predict long-term returns, allows researchers improve the security of cryptography systems. As a result, there are growing numbers of experiments that have been proposed using chaotic-based random number generators. Furthermore, These proposed generators suffer from minimal key space and those centered on a 1D chaotic map have limited capacity to produce entropy due to their limited number of exponents of Lyapunov (s). Random binary sequence generator producing sequence of bits has been proposed in this paper. The proposed system model consists of two parts that use mouse device data constructively as the basis for the theory of non-determinism and chaos. The chaos theory includes three forms with the mouse cursor coordinates while moving as the initial seeds in this proposed system (1D logistic chaotic system, 2D Hénon system and 3D chaotic system) and combines the values produced in the algorithm. With 1D, 2D Hénon, 3D chaotic maps, the mouse cursor coordinates are treated as an initial random number with post processing to increase the randomness and security of the keys. In the suggested research, there is high key space and a very long time. It is also evident that the developed keys have successful statistical features that require purely random binary sequences that are optimal for use in essential cryptography systems provided by evaluating the results of 16 NIST hardness tests (National Institute of Standards and Technology).

Parity-based, bias-free optical quantum random number generation with min-entropy estimation

We describe the generation of sequences of random bits from the parity of photon counts produced by polarization measurements on a polarization-entangled state. The resulting sequences are bias free, pass the applicable tests in the NIST battery of statistical randomness tests, and are shown to be Borel normal, without the need for experimental calibration stages or postprocessing of the output. Because the photon counts are produced in the course of a measurement of the violation of the Clauser–Horne–Shimony–Holt inequality, we are able to concurrently verify the nonclassical nature of the photon statistics and estimate a lower bound on the min-entropy of the bit-generating source. The rate of bit production in our experiment is around 13 bits/s.

Introduction to Dynamic Stochastic Computing

Stochastic computing (SC) is an old but reviving computing paradigm for its simple data path that can perform various arithmetic operations. It allows for low power implementation, which would otherwise be complex using the conventional positional binary coding. In SC, a number is encoded by a random bit stream of '0's and '1's with an equal weight for every bit. However, a long bit stream is usually required to achieve a high accuracy. This requirement inevitably incurs a long latency and high energy consumption in an SC system. In this article, we present a new type of stochastic computing that uses dynamically variable bit streams, which is, therefore, referred to as dynamic stochastic computing (DSC). In DSC, a random bit is used to encode a single value from a digital signal. A sequence of such random bits is referred to as a dynamic stochastic sequence. Using a stochastic integrator, DSC is well suited for implementing accumulation-based iterative algorithms such as numerical integration and gradient descent. The underlying mathematical models are formulated for functional analysis and error estimation. A DSC system features a higher energy efficiency than conventional computing using a fixed-point representation with a power consumption as low as conventional SC. It is potentially useful in a broad spectrum of applications including signal processing, numerical integration and machine learning.

Применение атаки различения на легковесные блочные шифры, основанные на ARX-операциях

Рассмотрено применение атаки различения на ряд легковесных блочных шифров, основанных на ARX-операциях (сложение по модулю, циклический сдвиг и исключающее ИЛИ). Представлены экспериментальные результаты и теоретические оценки устойчивости легковесных шифров Speck, Simon, Simeck, HIGHT, LEA к атаке различения. Вывод, что семейство шифров Simeck не выдерживает эту атаку, сделан на основе прогнозов, полученных путем экстраполяции экспериментальных данных. The distinguishing attack on modern lightweight ARX-based block ciphers was applied. Distinguishing attack is any form of cryptanalysis on data encrypted by a cipher that allows an attacker distinguishing the encrypted data from random data. Purpose. Modern symmetric-key ciphers must be designed to be immune to such an attack. The purpose of the work was to estimate the resistance of lightweight ciphers Speck, Simon, Simeck, HIGHT, and LEA to a distinguishing attack. Methodology. We note that these ciphers are iterated block ciphers. It is means that they transform blocks of plain text into blocks of cipher text by using the cyclically repeated invertible function known as the round function where each iteration is to be referred as a round. We have experimentally found a maximum number of rounds where encrypted data looked like random bit-sequence by using statistical test “Book Stack”. Then we extrapolated the theoretical length required for a successful distinguishing attack on cipher with full-number rounds by a polynomial of a low degree. Note that cryptography attack is considered as successful if the length of the encrypted sequence is less than the length 2K (K — key size). Originality/value. Our experiments and estimations show, that Simeck with 48bit block size and 96-bit key size is not immune to distinguishing attack. We recommended increasing the number of rounds by 15–20% in order to improve the reliability of the Simeck 48/96.

Is Natural Language a Perigraphic Process? The Theorem about Facts and Words Revisited.

As we discuss, a stationary stochastic process is nonergodic when a random persistent topic can be detected in the infinite random text sampled from the process, whereas we call the process strongly nonergodic when an infinite sequence of independent random bits, called probabilistic facts, is needed to describe this topic completely. Replacing probabilistic facts with an algorithmically random sequence of bits, called algorithmic facts, we adapt this property back to ergodic processes. Subsequently, we call a process perigraphic if the number of algorithmic facts which can be inferred from a finite text sampled from the process grows like a power of the text length. We present a simple example of such a process. Moreover, we demonstrate an assertion which we call the theorem about facts and words. This proposition states that the number of probabilistic or algorithmic facts which can be inferred from a text drawn from a process must be roughly smaller than the number of distinct word-like strings detected in this text by means of the Prediction by Partial Matching (PPM) compression algorithm. We also observe that the number of the word-like strings for a sample of plays by Shakespeare follows an empirical stepwise power law, in a stark contrast to Markov processes. Hence, we suppose that natural language considered as a process is not only non-Markov but also perigraphic.

Random Number Generation From Intermittent Optical Chaos

We propose a method to generate physical random numbers based on intermittent optical chaos. Intermittent chaotic output is produced in a semiconductor laser subjected to optical feedback embedded in a photonic integrated circuit. This dynamics is characterized by a temporal waveform organized in a succession of laminar regions of low amplitude and bursts of high amplitude. The temporal randomness ruling the alternation of successive laminar regions and bursts is used as an entropy source to generate sequences of random bits. We compare the performances of the exclusive OR and reverse methods implemented in the bit generation process and evaluate the quality of the random bits with the Rabbit test of TestU01 for different bit sequences lengths.

Generalized Elias schemes for efficient harvesting of truly random bits

The problem of generating a sequence of true random bits (suitable for cryptographic applications) from random discrete or analog sources is considered. A generalized version, including vector quantization, of the classical approach by Elias for the generation of truly random bits is introduced, and its performance is analyzed, both in the finite case and asymptotically. The theory allows us to provide an alternative proof of the optimality of the original Elias’ scheme. We also consider the problem of deriving random bits from measurements of a Poisson process and from vectors of iid Gaussian variables. The comparison with the scheme of Elias, applied to geometric-like non-binary vectors, originally based on the iso-probability property of permutations of iid variables, confirms the potential of the generalized scheme proposed in our work.

Deterministic Randomness Extraction from Generalized and Distributed Santha--Vazirani Sources

A Santha--Vazirani (SV) source is a sequence of random bits where the conditional distribution of each bit, given the previous bits, can be partially controlled by an adversary. Santha and Vazirani show that deterministic randomness extraction from these sources is impossible. In this paper, we study the generalization of SV sources for nonbinary sequences. We show that unlike the binary setup of Santha and Vazirani, deterministic randomness extraction in the generalized case is sometimes possible. In particular, if the adversary has access to $s$ “nondegenerate” dice that are $c$-sided and can choose one die to throw based on the previous realizations of the dice, then deterministic randomness extraction is possible if $s<c$. We present a necessary condition and a sufficient condition for the possibility of deterministic randomness extraction. These two conditions complement each other in the nondegenerate cases. Next, we turn to a distributed setting. In this setting the SV source consists of a random sequence of pairs $(a_1, b_1), (a_2, b_2), \ldots$ distributed between two parties, where the first party receives $a_i$'s and the second one receives $b_i$'s. The goal of the two parties is to extract common randomness without communication. Using the notion of maximal correlation, we prove a necessary condition and a sufficient condition for the possibility of common randomness extraction from these sources. Based on these two conditions, the problem of common randomness extraction essentially reduces to the problem of randomness extraction from (nondistributed) SV sources. This result generalizes results of Gács and Körner, and Witsenhausen about common randomness extraction from independently and identically distributed sources to adversarial sources.

Random number generation from spontaneous Raman scattering

We investigate the generation of random numbers via the quantum process of spontaneous Raman scattering. Spontaneous Raman photons are produced by illuminating a highly nonlinear chalcogenide glass (As2S3) fiber with a CW laser at a power well below the stimulated Raman threshold. Single Raman photons are collected and separated into two discrete wavelength detuning bins of equal scattering probability. The sequence of photon detection clicks is converted into a random bit stream. Postprocessing is applied to remove detector bias, resulting in a final bit rate of ∼650 kb/s. The collected random bit-sequences pass the NIST statistical test suite for one hundred 1 Mb samples, with the significance level set to α=0.01. The fiber is stable, robust and the high nonlinearity (compared to silica) allows for a short fiber length and low pump power favourable for real world application.

Gambling with Superconducting Fluctuations

Physical, hardware-based random-number generators (RNGs) are keenly sought for numerous applications, including secure communication. The authors show how a Josephson junction or superconducting nanowire can act as a coin with tunable probability, generating a random sequence of bits by remaining in the zero-voltage superconducting state (``heads'') or switching to the normal state (``tails'') in response to current pulses. This solid-state RNG is simple and compact for straightforward on-chip integration, and with optimization a bit rate above 1 Gb/s is anticipated.

Two approaches for ultrafast random bit generation based on the chaotic dynamics of a semiconductor laser

This paper reports the experimental investigation of two different approaches to random bit generation based on the chaotic dynamics of a semiconductor laser with optical feedback. By computing high-order finite differences of the chaotic laser intensity time series, we obtain time series with symmetric statistical distributions that are more conducive to ultrafast random bit generation. The first approach is guided by information-theoretic considerations and could potentially reach random bit generation rates as high as 160 Gb/s by extracting 4 bits per sample. The second approach is based on pragmatic considerations and could lead to rates of 2.2 Tb/s by extracting 55 bits per sample. The randomness of the bit sequences obtained from the two approaches is tested against three standard randomness tests (ENT, Diehard, and NIST tests), as well as by calculating the statistical bias and the serial correlation coefficients on longer sequences of random bits than those used in the standard tests.

A New Randomness Test for Bit Sequences

Generating sequences of random numbers or bits is a necessity in many situations (cryptography, modeling, simulations, etc…). Those sequences must be random in the sense that their behavior should be unpredictable. For example, the security of many cryptographic systems depends on the generation of unpredictable values to be used as keys. Since randomness is related to the unpredictable property, it can be described in probabilistic terms, studying the randomness of a sequence by means of a hypothesis test. A new statistical test for randomness of bit sequences is proposed in the paper. The created test is focused on determining the number of different fixed length patterns that appear along the binary sequence. When 'few' distinct patterns appear in the sequence, the hypothesis of randomness is rejected. On the contrary, when 'many' different patterns appear in the sequence, the hypothesis of randomness is accepted.The proposed can be used as a complement of other statistical tests included in suites to study randomness. The exact distribution of the test statistic is derived and, therefore, it can be applied to short and long sequences of bits. Simulation results showed the efficiency of the test to detect deviation from randomness that other statistical tests are not able to detect. The test was also applied to binary sequences obtained from some pseudorandom number generators providing results in keeping with randomness. The proposed test distinguishes by fast computation when the critical values are previously calculated.