Random Number Streams Research Articles

The Cost of Randomness in Evolutionary Algorithms: Crossover Can Save Random Bits.

Evolutionary algorithms make countless random decisions during selection, mutation and crossover operations. These random decisions require a steady stream of random numbers. We analyze the expected number of random bits used throughout a run of an evolutionary algorithm and refer to this as the cost of randomness. We give general bounds on the cost of randomness for mutation-based evolutionary algorithms using 1-bit flips or standard mutations using either a naive or a common, more efficient implementation that uses Θ(logn) random bits per mutation. Uniform crossover is a potentially wasteful operator as the number of random bits used equals the Hamming distance of the two parents, which can be up to n. However, we show for a (2+1) Genetic Algorithm that is known to optimize the test function ONEMAX in roughly (e/2)nlnn expected evaluations, twice as fast as the fastest mutation-based evolutionary algorithms, that the total cost of randomness during all crossover operations on ONEMAX is only Θ(n). A more pronounced effect is shown for the common test function JUMPk, where there is an asymptotic decrease both in the number of evaluations and in the cost of randomness. Consequently, the use of crossover can reduce the cost of randomness below that of the fastest evolutionary algorithms that only use standard mutations.

Toward robust image encryption based on chaos theory and DNA computing

Due to the significant importance of image security for various users, there is an ongoing need to develop innovative algorithms to enhance this security. Image security typically involves encryption techniques. This study has tackled the challenge of creating an efficient, secure, and resilient image cipher by using pixel-swapping techniques at both DNA and decimal levels. The swapping methods include four different approaches that involve randomly selecting pixel pairs to swap with adjacent pixels—either left, right, upper, or lower—based on random numbers generated by a chaotic map. Specifically, the 2D Tinkerbell chaotic map was used to generate the necessary random numbers for diffusion and confusion processes in the encryption. Additionally, through careful arithmetic operations, two more random number streams were derived from the main streams produced by the chaotic map. Thorough performance analyses and computer simulations have shown that this image cipher is robust, secure, and resilient against various threats, making it suitable for practical applications. Notably, the cipher achieved a very high information entropy value of 7.9975, indicating its effectiveness in encryption.

FOPBIE: Multi-image cipher based on the random walk of fleet of pawns on the large hypothetical chessboard and chaotic system.

In the last two decades or so, a large number of image ciphers have been written. The majority of these ciphers encrypt only one image at a time. Few image ciphers were written which could encrypt multiple images in one session. The current era needs speedy multiple image ciphers to address its varied needs in different settings. Motivated by this dictation, the current study has ventured to write a multi-image cipher based on the fleet of pawns walking in the large hypothetical chessboard. This walk of pawns on the chessboard has been ingeniously linked with transferring the pixels from the plain image to the scrambled image. The confusion effects have been realized through the XOR operation between the scrambled image and the key image. The plaintext sensitivity has been incorporated by embedding the SHA-384 hash codes of the given large combined plain image. Moreover, the Henon map has been employed to spawn the streams of random numbers. Besides, Blum Blum Shub random number generator has been used to further cement the security of the proposed cipher. We got a computational time of 0.2278 seconds and an encryption throughput of 5.5782 MBit/seconds by using the four images with a size of 256×256. Apart from that, the information entropy gained is 7.9993. Lastly, the cipher has been subjected to an array of validation metrics to demonstrate its aversion to the myriad threats from the cryptanalysis savvy. We contend that the proposed work has great potential for some real-world applications.

5-bit all-optical quantum random number generator based on a time-multiplexed optical parametric oscillator.

Random numbers are of critical importance in many applications, including secure communication, photonics computing and cryptography. Due to the non-deterministic nature of the quantum processes, a degenerate optical parametric oscillator (DOPO) constitutes a solution to produce true randomness. Nevertheless, one of the existing challenges for DOPO in this field is bit sequence scalability. Here, we experimentally report on the generation of 5-bit random number streams in a time-multiplexed femtosecond DOPO system. A multi-pass cell is added to elongate the OPO cavity to scale up the bit sequences. To this end, for a ∼15 m long all free space OPO cavity, resonating 5 signal pulses with a repetition rate of 50 MHz is demonstrated. The above-threshold binary phase nature originates from vacuum fluctuations of a DOPO ensuring the randomness of the system. The phase state of the output is characterized by the interference pattern between the output pulses and the fundamental pump pulses. Different bit sequences are presented here by turning on and off the OPO. Conditional probability is performed to verify the randomness of the output for 1200 bits. Our scheme provides a new direction for an all-optical random number generator.

Random Telegraph Noise-Based True Random Number Generator for Fully Integrated Systems

Generating streams of true random numbers is a critical component of many electronic and information systems. The design of fully integrated, area and power efficient true random number generators (TRNGs) is a challenge. We propose a fully integrated, lightweight implementation that uses the random telegraph noise (RTN) of standard MOSFET as entropy source. It is not analog-intensive, and without traditional post-processing algorithms, the generated random bit sequence passes the National Institute of Standards and Technology (NIST) tests.

Random Number Generation With a Hybrid Conjugated Polymer Memristor

A two-terminal memristor was constructed from electrochemically doped poly(4-(6-(9H-carbazol-9-yl)hexyl)-4H-dithieno[3,2-b:2’,3’-d]pyrrole) (pC6DTP) and employed as a random number generator (RNG). The polymer exhibited a conductive nature that was dependent on its voltage history that was theorized to be due to two synergistic percolation mechanisms: one associated with the pendant electroactive heterocyclic rings and one associated with the polymer backbone conjugation. The generated random number (RN) stream was evaluated for “randomness” with select tests from NIST SP 800–22 Rev. 1a testing protocol, which indicated that the bitstream was classified as random as generated without any postprocessing, while the energy required to generate a bit was ca. 0.67 pJ.

Prediction of Defects in the Structure of Non-Metallic Heterogeneous Materials

Heterogeneous media can be represented as specially organized heterogeneous materials. The complex process of forming heterogeneous materials and media as systems is realized by gradually transitioning from one state to another. The presence of many one-time transformations of space-time structures causes the latter. When simulating damage such as cracks and fractures in products made of non-metallic heterogeneous materials, which consists of “assigning” the place of damage to the product at a specific moment in time, neither the method of random selection from the previously compiled list of “dangerous” places, nor the method of transfer to the object can be used, which is modeled, the results of field and operational tests of other products of a similar class or even other products of the same class. Therefore, it is proposed to use a combined method of obtaining a stream of quasi-random numbers, that is, a stream of random numbers that are “modulated” by information about defects in the structure of the material of the product, which was obtained because of field tests of the products or during their operation.

Statistical Characteristics Improvement of a Hardware Random Number Generator by a Software Method

As a source of random numbers, hardware random number generators are often used, the operation of which is based on randomly changing parameters of various physical processes. The statistical characteristics of such generators do not always allow their use in the field of information security. To improve the statistical characteristics, various software tools for processing the output data of the generator are used. The purpose of this work is to study the possibility to improve the statistical characteristics of a hardware random number generator by software. The investigated hardware random number generator is based on the ND103L noise diode and has a random digital sequence of binary numbers at the output. To improve the statistical characteristics, the output stream of random numbers was processed using a software method based on the calculation of high-order finite differences. This method would allow one to get a more symmetrical distribution of random numbers, as well as increase the speed of their generation. After processing, the data from the generator under study have better statistical characteristics, which is confirmed by the NIST and Diehard tests, and the generation rate has also increased by more than 5 times. The results of this work may be useful to developers of hardware random number generators who need to improve the performance of the generator.

A chaotic image encryption scheme based on multi-directional confusion and diffusion operations

A careful perusal of the literature regarding the image encryption algorithms indicates that many research articles based on pixel swapping operations in the horizontal and vertical orientations, have been published. This study ventures to develop a yet another sophisticated algorithm by extending the swapping operations along the diagonal–antidiagonal directions. Besides, unlike the previous studies, the confusion and diffusion operations over the pixels of the given input plain image have been crafted in a parallel fashion. This work has employed a 4D chaotic system to spawn the streams of random numbers. The initial values and the system parameters have been made dependent over the given plain image in order to inject the plaintext sensitivity in the proposed cipher. As a modus operandi of the proposed encryption algorithm, a non-intersecting pair of row and column is selected randomly with the same arbitrary length and swapped/XORed according to the value dictated by the random numbers. The same operations have been carried out for the non-intersecting pair of diagonal and anti-diagonal. The reason for selecting the non-intersecting pair stems from the fact that intersecting pairs cause to lose the precious pixels data which questions the potential invertibility feature of the proposed algorithm. To demonstrate the improved efficiency, ability to withstand the varied attacks by the cryptanalysis savvy, and prospects for some real-world application, the algorithm has been subjected to a comprehensive set of evaluation metrics.

A Novel Grayscale Image Encryption Scheme Based on the Block-Level Swapping of Pixels and the Chaotic System.

Hundreds of image encryption schemes have been conducted (as the literature review indicates). The majority of these schemes use pixels as building blocks for confusion and diffusion operations. Pixel-level operations are time-consuming and, thus, not suitable for many critical applications (e.g., telesurgery). Security is of the utmost importance while writing these schemes. This study aimed to provide a scheme based on block-level scrambling (with increased speed). Three streams of chaotic data were obtained through the intertwining logistic map (ILM). For a given image, the algorithm creates blocks of eight pixels. Two blocks (randomly selected from the long array of blocks) are swapped an arbitrary number of times. Two streams of random numbers facilitate this process. The scrambled image is further XORed with the key image generated through the third stream of random numbers to obtain the final cipher image. Plaintext sensitivity is incorporated through SHA-256 hash codes for the given image. The suggested cipher is subjected to a comprehensive set of security parameters, such as the key space, histogram, correlation coefficient, information entropy, differential attack, peak signal to noise ratio (PSNR), noise, and data loss attack, time complexity, and encryption throughput. In particular, the computational time of 0.1842 s and the throughput of 3.3488 Mbps of this scheme outperforms many published works, which bears immense promise for its real-world application.

Gull's Theorem Revisited.

In 2016, Steve Gull has outlined has outlined a proof of Bell’s theorem using Fourier theory. Gull’s philosophy is that Bell’s theorem (or perhaps a key lemma in its proof) can be seen as a no-go theorem for a project in distributed computing with classical, not quantum, computers. We present his argument, correcting misprints and filling gaps. In his argument, there were two completely separated computers in the network. We need three in order to fill all the gaps in his proof: a third computer supplies a stream of random numbers to the two computers representing the two measurement stations in Bell’s work. One could also imagine that computer replaced by a cloned, virtual computer, generating the same pseudo-random numbers within each of Alice and Bob’s computers. Either way, we need an assumption of the presence of shared i.i.d. randomness in the form of a synchronised sequence of realisations of i.i.d. hidden variables underlying the otherwise deterministic physics of the sequence of trials. Gull’s proof then just needs a third step: rewriting an expectation as the expectation of a conditional expectation given the hidden variables.

Post Quantum Cryptographic Keys Generated with Physical Unclonable Functions

Lattice and code cryptography can replace existing schemes such as elliptic curve cryptography because of their resistance to quantum computers. In support of public key infrastructures, the distribution, validation and storage of the cryptographic keys is then more complex for handling longer keys. This paper describes practical ways to generate keys from physical unclonable functions, for both lattice and code-based cryptography. Handshakes between client devices containing the physical unclonable functions (PUFs) and a server are used to select sets of addressable positions in the PUFs, from which streams of bits called seeds are generated on demand. The public and private cryptographic key pairs are computed from these seeds together with additional streams of random numbers. The method allows the server to independently validate the public key generated by the PUF, and act as a certificate authority in the network. Technologies such as high performance computing, and graphic processing units can further enhance security by preventing attackers from making this independent validation when only equipped with less powerful computers.

Laser-based generation of random numbers

Optoelectronics The security of our digital networks is underpinned by the ability to generate streams of random numbers or bits. As networks expand in an ever-connected way, the challenge is to increase the generation rate of the random numbers to keep pace with demand. Kim et al. designed a chip-scale laser diode that generates random bits at an ultrahigh rate (see the Perspective by Fischer and Gauthier). By tailoring the geometry of the cavity, they were able to exploit the spatiotemporal interference of many lasing modes to generate picosecond-scale emission intensity fluctuations in space and time, producing ultrafast random bit streams in parallel. Such a device will find a wide range of applications requiring an ultrafast, compact, robust, and energy-efficient random bit generator. Science , this issue p. [948][1]; see also p. [889][2] [1]: /lookup/doi/10.1126/science.abc2666 [2]: /lookup/doi/10.1126/science.abg5445

Massively parallel ultrafast random bit generation with a chip-scale laser.

Random numbers are widely used for information security, cryptography, stochastic modeling, and quantum simulations. Key technical challenges for physical random number generation are speed and scalability. We demonstrate a method for ultrafast generation of hundreds of random bit streams in parallel with a single laser diode. Spatiotemporal interference of many lasing modes in a specially designed cavity is introduced as a scheme for greatly accelerated random bit generation. Spontaneous emission, caused by quantum fluctuations, produces stochastic noise that makes the bit streams unpredictable. We achieve a total bit rate of 250 terabits per second with off-line postprocessing, which is more than two orders of magnitude higher than the current postprocessing record. Our approach is robust, compact, and energy-efficient, with potential applications in secure communication and high-performance computation.

A novel gray scale image encryption scheme based on pixels’ swapping operations

Design principles for image encryption schemes abound in the literature. Among these schemes, few were built upon the philosophy of swapping of the pixels in the given input image. Swapping is a very straightforward and a naive approach for image scrambling. We believe that fuller potential of swapping has not been realized yet. In this work, a novel image encryption scheme is being presented through the swapping of pixel values of the given gray scale input image. The 5D multi-wing hyperchaotic system rendering five key streams of random numbers have been used in the proposed cipher. After the gray scale image is input, its pixels are swapped randomly. The random numbers given through the first two key streams jointly determine the address of the first pixel to be swapped with the second pixel whose address is determined by the random numbers given through the third and fourth key streams. In this way, the pixels of the given image are swapped abundantly. The selection of both the pixels for swapping is purely arbitrary and random in character having no restriction of linearity and sequentiality as was done by other schemes previously. To create the diffusion effects, an XOR operation is carried out between this scrambled image and the key image formed through the fifth stream of random numbers given by the chaotic system. SHA-384 hash codes have been used in the proposed scheme to embed the plaintext sensitivity. The simulation and the extensive security analyses carried out at the end expressly portray the good security effects and the potential for the real world application of the reported scheme.

A Novel and Efficient 3D Multiple Images Encryption Scheme Based on Chaotic Systems and Swapping Operations

Single image encryption schemes are not efficient enough when a bunch of images is to be encrypted in some real-world setting. To overcome this problem, an efficient and secured multiple images encryption scheme is proposed in this study using two chaotic maps and simple row and column swapping operations in a 3D image space. The N input images are piled to make a 3D image. To confuse the given pixel data, two images are chosen randomly from this pile. The randomly chosen two rows from the two randomly chosen images are swapped with each other. In the same way, two randomly chosen columns are swapped with each other. The operation of randomly chosen two images, two rows, and two columns have been iterated an arbitrary number of times to throw the confusion effects in the pixels data. Intertwining Logistic Map (ILM) and Improved Piecewise Linear Chaotic Map (MPWLCM) have been used to get the four streams of random numbers. The three streams of the former map have been used to create the confusion effects, whereas the fourth stream of random numbers given by the latter map has been used for the diffusion effects. SHA-256 hash codes have been used to throw the plaintext sensitivity in the proposed cipher. Besides, a 256-bit user key has been employed to increase the key space. Both the simulation and the exhaustive security analyses carried out at the end vividly prove the security, resistance to the varied attacks, and the real-world applicability of the proposed cipher.

DNA Strands Level Scrambling Based Color Image Encryption Scheme

In the past, many image encryption schemes have been developed through the swapping operations at the different levels of granularity. These levels span bits, Deoxyribonucleic acid (DNA) molecules, pixels, blocks of pixels. In this study, a new scheme for the encryption of color images based on the DNA strands level scrambling (DNASLS) and chaotic system has been proposed. After a color image is input, it is decomposed into the red, green and blue components. After it, these components are merged to form a big single image. Intertwining logistic map (ILM) has been used for the random data which generates three streams of random numbers. These streams have been further manipulated in such a way that nine streams are spawned out of them. One stream out of these nine streams has been used for the generation of a key image. Two streams have been used to DNA-encode the big single image and the key image. Afterwards, the strands of DNA-encoded single image are swapped with each other. Four streams determine the addresses of two DNA encoded pixels for the selection. A yet another stream is being used to select a particular strand from the DNA strands. To create the diffusion effects, an XOR operation has been done between the DNA encoded image after the swapping of strands and the DNA encoded key image. Finally, the last and ninth stream has been used to decode the DNA-encoded pixels into the decimal form. Purely random numbers with no inter-dependence have been employed in the entire encryption process. The effects of plaintext sensitivity have been achieved through the incorporation of Secure Hash Algorithm-256 or SHA-256 hash codes. In the end, the experiment and the security analysis have been performed. The results of the validation metrics like information entropy(7.9973), average key sensitivity(99.61%) and mean absolute error(84.7158) demonstrate the security, defiance to the number of attacks and a potential for real world application of the proposed image cipher.

МОДЕЛЮВАННЯ НЕСИМЕТРИЧНО РОЗПОДІЛЕНИХ ПРОЦЕСІВ

The article deals with the problems of modeling asymmetrically distributed stochastic processes and assessing the quality of the modeling process based on the use of the Pearson chi-square criterion. The problems that arise in each individual case of modeling are identified. As a method of generating an output stream of random numbers distributed according to a given law of probability distribution, the method of inverse functions is proposed, and as a generator of the input stream, it is proposed to use a stream generated by the Mersenne generator. The analysis of research methods and evaluation of computer models of stochastic processes is given and the choice of a nonparametric research method based on histograms is substantiated. Suggestions on the choice of their main parameters are provided: the size of the interval for separating the statistical set of values of the output stream of the model and the number of such intervals, calculated on the basis of the size of the statistical sample. It is shown that the quality of statistical material significantly affects the success of modeling. In the case of an asymmetric nature of the distribution of the model's output stream, the accuracy of calculating the chi-square exponent is significantly affected by those values that fall into the extreme intervals of the histogram. It is shown that the reason for this is the incommensurability of their values with the values in the central part of the histogram and this is a separate modeling problem, as a solution to which there can be filtering of the statistical set, preceding the determination of the quality indicator. The sequence of procedures for forming a model of a stochastic process and processing the results of calculating the parameters of the histogram is determined.

Chaotic laser voltage: An electronic entropy source

The chaotic terminal voltage dynamics of a semiconductor laser subjected to external optical feedback are utilized to directly generate electronic random number streams with minimal post-processing at rates of 40–120 Gb/s, thus obviating the need for optical-to-electrical conversion and facilitating integration with high-speed computers and devices. Furthermore, a comparison of the terminal voltage to the optical intensity being utilized as entropy sources is performed. It is shown that the voltage dynamics have an inherently larger entropy, a reduction in delay signature, and a more suitable distribution for generating random bit streams.

Self-balanced real-time photonic scheme for ultrafast random number generation

We propose a real-time self-balanced photonic method for extracting ultrafast random numbers from broadband randomness sources. In place of electronic analog-to-digital converters (ADCs), the balanced photo-detection technology is used to directly quantize optically sampled chaotic pulses into a continuous random number stream. Benefitting from ultrafast photo-detection, our method can efficiently eliminate the generation rate bottleneck from electronic ADCs which are required in nearly all the available fast physical random number generators. A proof-of-principle experiment demonstrates that using our approach 10 Gb/s real-time and statistically unbiased random numbers are successfully extracted from a bandwidth-enhanced chaotic source. The generation rate achieved experimentally here is being limited by the bandwidth of the chaotic source. The method described has the potential to attain a real-time rate of 100 Gb/s.