Pseudorandom Vectors Research Articles

Utilizing a pseudo-random Linear Congruential Generator (LCG) S-Box for encoding color images through genetic crossover

This article introduces a novel algorithm crafted for encrypting color images. The algorithm leverages chaotic principles and harnesses fresh substitution tables derived from independent linear congruence generators. These generators are dynamically sized based on pseudo-random vectors used in this technology. The proposed method initiates with the original image, vectorization, employing selected chaotic maps. The primary goal revolves around implementing a genetic operator tailored for image encryption, who integrates an enhanced Vigenère technique, incorporating novel confusion and diffusion functions derived from the previously established substitution tables. To gauge the effectiveness of this approach, numerous color images of varying dimensions and formats underwent testing using our algorithm. The yielded outcomes are both promising and gratifying, furnishing heightened security against recognized attacks.

On the distribution of pseudorandom vectors generated by elliptic curves

In the present paper, the distribution of pseudorandom vectors, derived from a specific set of rational points on elliptic curves over finite fields, is studied by estimating its discrepancy based on the system of Walsh functions and exponential sums over elliptic curves. It turns out these pseudorandom vectors have good behaviors, such as uniform distribution and strong pseudorandomness. Moreover, we apply the incomplete sum to the elliptic curve version of sum-product and Sárközy problems.

Pseudorandom vector generation using elliptic curves and applications to Wiener processes

In this paper we present, using the arithmetic of elliptic curves over finite fields, an algorithm for the efficient generation of a sequence of uniform pseudorandom vectors in high dimensions, that simulates a sample of a sequence of i.i.d. random variables, with values in the hypercube [0,1]d with uniform distribution. As an application, we obtain, in the discrete time simulation, an efficient algorithm to simulate, uniformly distributed sample path sequence of a sequence of independent standard Wiener processes. This could be employed for use, in the full history recursive multi-level Picard approximation method, for numerically solving the class of semilinear parabolic partial differential equations of the Kolmogorov type.

Моделирование пассивных помех в РЛС с цифровой антенной решеткой

The problem of imitation modeling of passive interference is considered in the context of devel-oping algorithms for space-time processing of broadband signals in a radar system with a digital antenna array. Spectral and correlation characteristics of passive noise are discussed in the frame-work of Gaussian, polynomial (fractional rational) and exponential models. Due to the broadband nature of probing signals, the formation of the antenna array directional pattern is carried out by controlling the time delays of oscillations arriving at the array elements, which is implemented in the frequency domain through complex weighting factors. Modeling of passive interference as a sta-tionary complex random process is performed in discrete "slow" time, with each complex vector of samples being spaced from neighboring vectors by the value of the repetition period of the probing pulses. The known method for modeling passive interference based on a shaping recursive filter is unsuitable for use in the case of an interference spectrum other than rational. The method for model-ing the vector of correlated samples using the Cholesky expansion of the noise covariance matrix is inapplicable when the correlation coefficient is close to one. A method is proposed for modeling masking extended passive interference of a wide class based on filtering a sequence of complex pseudo-random vectors in the frequency domain with the use of a fast Fourier transform.

Hardware Optimizations of Dense Binary Hyperdimensional Computing: Rematerialization of Hypervectors, Binarized Bundling, and Combinational Associative Memory

Brain-inspired hyperdimensional (HD) computing models neural activity patterns of the very size of the brain’s circuits with points of a hyperdimensional space, that is, with hypervectors . Hypervectors are D -dimensional (pseudo)random vectors with independent and identically distributed (i.i.d.) components constituting ultra-wide holographic words: D =10,000 bits, for instance. At its very core, HD computing manipulates a set of seed hypervectors to build composite hypervectors representing objects of interest. It demands memory optimizations with simple operations for an efficient hardware realization. In this article, we propose hardware techniques for optimizations of HD computing, in a synthesizable open-source VHDL library, to enable co-located implementation of both learning and classification tasks on only a small portion of Xilinx UltraScale FPGAs: (1) We propose simple logical operations to rematerialize the hypervectors on the fly rather than loading them from memory. These operations massively reduce the memory footprint by directly computing the composite hypervectors whose individual seed hypervectors do not need to be stored in memory. (2) Bundling a series of hypervectors over time requires a multibit counter per every hypervector component. We instead propose a binarized back-to-back bundling without requiring any counters. This truly enables on-chip learning with minimal resources as every hypervector component remains binary over the course of training to avoid otherwise multibit components. (3) For every classification event, an associative memory is in charge of finding the closest match between a set of learned hypervectors and a query hypervector by using a distance metric. This operator is proportional to hypervector dimension ( D ), and hence may take O( D ) cycles per classification event. Accordingly, we significantly improve the throughput of classification by proposing associative memories that steadily reduce the latency of classification to the extreme of a single cycle. (4) We perform a design space exploration incorporating the proposed techniques on FPGAs for a wearable biosignal processing application as a case study. Our techniques achieve up to 2.39× area saving, or 2,337× throughput improvement. The Pareto optimal HD architecture is mapped on only 18,340 configurable logic blocks (CLBs) to learn and classify five hand gestures using four electromyography sensors.

Low Delay Sparse and Mixed Excitation CELP Coders for Wideband Speech Coding

Code Excited Linear Prediction (CELP) algorithms are proposed for compression of speech in 8 kHz band at switched or variable bit rate and algorithmic delay not exceeding 2 msec. Two structures of Low-Delay CELP coders are analyzed: Low-delay sparse excitation and mixed excitation CELP. Sparse excitation is based on MP-MLQ and multilayer models. Mixed excitation CELP algorithm stems from the narrowband G.728 standard. As opposed to G.728 LD-CELP coder, mixed excitation codebook consists of pseudorandom vectors and sequences obtained with Long-Term Prediction (LTP). Variable rate coding consists in maximizing vector dimension while keeping the required speech quality. Good speech quality (MOS=3.9 according to PESQ algorithm) is obtained at average bit rate 33.5 kbit/sec.

Primitive transformation shift registers over finite fields

Linear feedback shift registers (LFSRs) are widely used cryptographic primitives for generating pseudorandom sequences. Here, we consider systems which are efficient generalizations of LFSRs and produce pseudorandom vector sequences. We study problems related to the cardinality, existence and construction of these systems and give certain results in this direction.

A New Cryptosystem of Color Image Using a Dynamic-Chaos Hill Cipher Algorithm

The conventional symmetric Hill cipher encryption algorithm, applied for data encryption, presents several disadvantages. However, a drawback of the conventional algorithm is known to be vulnerable to plain-text attack. Another setback, it does not hide all features of the image with homogeneous background and finally, the difficulty of finding the inverse of the key matrix. To overcome these problems, in this paper, we propose an improvement of the Hill cipher algorithm. The principle consists in using an affine transformation provided by a three-order invertible matrix and a dynamic translation vector. This vector is dynamically transformed at each iteration by an affine transformation composed of a chaotic matrix T, not necessarily invertible, and a pseudo random translation vector Y. This improvement overcomes the linearity problem of Hill’s classic method. In addition, computational complexity can be reduced by simplifying the inverse matrix search process at the time of decryption. This inverse lies only in the search for the modular inverse of a single element of the matrix in the ring Z/256Z. The proposed scheme overcomes the disadvantages of the conventional Hill cipher, especially, the images with strong homogenous zones. The proposed algorithm guarantees a better quality of security and encryption.

Calculations Involving the Multivariate Normal and Multivariate t Distributions with and without Truncation

In this article, we present a set of commands and Mata functions to evaluate different distributional quantities of the multivariate normal distribution and a particular type of noncentral multivariate t distribution. Specifically, their densities, distribution functions, equicoordinate quantiles, and pseudo–random vectors can be computed efficiently, in either the absence or the presence of variable truncation.

Spectral test of the MIXMAX random number generators

An important statistical test on the pseudo-random number generators is called the spectral test. The test is aimed at answering the question of distribution of the generated pseudo-random vectors in dimensions d that are larger than the genuine dimension of a generator N. In particular, the default MIXMAX generators have various dimensions: N=8,17,240 and higher. Therefore the spectral test is important to perform in dimensions d > 8 for N=8 generator, d > 17 for N=17 and d > 240 for N=240 generator. These tests have been performed by L’Ecuyer and collaborators. When d > N the vectors of the generated numbers fall into the parallel hyperplanes and the distances between them can be larger than the genuine “resolution” of the MIXMAX generators, which is l=2−61. The aim of this article is to further study the spectral properties of the MIXMAX generators, to investigate the dependence of the spectral properties of the MIXMAX generators as a function of their internal parameters and in particular their dependence on the parameter m. We found that the best spectral properties are realized when m is between 224 and 236, a range which is inclusive of the value of the N=17 generator. We also provide the alternative parameters for the generators, N=8 and N=240 with m in this optimized range.

Robust topology optimization for continuum structures with random loads

PurposeThis paper aims to tackle the challenge topic of continuum structural layout in the presence of random loads and to develop an efficient robust method.Design/methodology/approachAn innovative robust topology optimization approach for continuum structures with random applied loads is reported. Simultaneous minimization of the expectation and the variance of the structural compliance is performed. Uncertain load vectors are dealt with by using additional uncertain pseudo random load vectors. The sensitivity information of the robust objective function is obtained approximately by using the Taylor expansion technique. The design problem is solved using bi-directional evolutionary structural optimization method with the derived sensitivity numbers.FindingsThe numerical examples show the significant topological changes of the robust solutions compared with the equivalent deterministic solutions.Originality/valueA simple yet efficient robust topology optimization approach for continuum structures with random applied loads is developed. The computational time scales linearly with the number of applied loads with uncertainty, which is very efficient when compared with Monte Carlo-based optimization method.

Nonlinear vectorial primitive recursive sequences

We discuss nonlinear vectorial primitive recursive sequences. First we consider the nonlinearly filtered multiple-recursive matrix generator for producing pseudorandom vectors based on some nonlinear schemes and give lower bounds for their componentwise linear complexity. Moreover, we obtain certain results concerning the jump multiple-recursive matrix generator and establish that sequences generated by them have better period and componentwise linear complexity as compared to usual multiple-recursive matrix generator sequences. We also include analogous results for transformation shift registers for generating pseudorandom vectors.

A note on the multiple-recursive matrix method for generating pseudorandom vectors

The multiple-recursive matrix method for generating pseudorandom vectors was introduced by Niederreiter (1993). We propose an algorithm for finding an efficient primitive multiple-recursive matrix method. Moreover, for improving the linear complexity, we introduce a tweak on the contents of the primitive multiple-recursive matrix method.

Digital inversive vectors can achieve polynomial tractability for the weighted star discrepancy and for multivariate integration

We study high-dimensional numerical integration in the worst-case setting. The subject of tractability is concerned with the dependence of the worst-case integration error on the dimension. Roughly speaking, an integration problem is tractable if the worst-case error does not grow exponentially fast with the dimension. Many classical problems are known to be intractable. However, sometimes tractability can be shown. Often such proofs are based on randomly selected integration nodes. Of course, in applications, true random numbers are not available and hence one mimics them with pseudorandom number generators. This motivates us to propose the use of pseudorandom vectors as underlying integration nodes in order to achieve tractability. In particular, we consider digital inverse vectors and present two examples of problems, the weighted star discrepancy and integration of Hölder continuous, absolute convergent Fourier and cosine series, where the proposed method is successful.

Effective Method for Constructing Pseudo-Random Vectors Uniformly Distributed in Cone

In this paper we propose an algorithm for efficient production of pseudo-random vectors uniformly distributed in an n-dimensional cone. The method shows higher efficiency compared to the process of elimination in the case of large dimensions. The results of computer experiments confirm the theoretical construct.

Sparse Frequency Waveform Design for Radar-Embedded Communication

According to the Tag application with function of covert communication, a method for sparse frequency waveform design based on radar-embedded communication is proposed. Firstly, sparse frequency waveforms are designed based on power spectral density fitting and quasi-Newton method. Secondly, the eigenvalue decomposition of the sparse frequency waveform sequence is used to get the dominant space. Finally the communication waveforms are designed through the projection of orthogonal pseudorandom vectors in the vertical subspace. Compared with the linear frequency modulation waveform, the sparse frequency waveform can further improve the bandwidth occupation of communication signals, thus achieving higher communication rate. A certain correlation exists between the reciprocally orthogonal communication signals samples and the sparse frequency waveform, which guarantees the low SER (signal error rate) and LPI (low probability of intercept). The simulation results verify the effectiveness of this method.

An Information-Theoretic Security Evaluation of a Class of Randomized Encryption Schemes

Randomized encryption techniques, where randomness is used for security enhancement, are considered. We focus on the case where the encrypted data experiences noise, e.g., is transmitted over a noisy channel, within the encoding-encryption paradigm, where the data is first encoded for error correction, before being encrypted for security. We assume that the ciphertext is subject to a corruption equivalent to its transmission through a binary symmetric channel with known probability of error. The enhanced security is based on a dedicated wire-tap channel coding that introduces extra randomness, combined with that of the communication channel noise. The encryption is based on a block-by-block modulo 2 addition between an encoded message vector and a pseudorandom vector. The goal is to enhance the protection of the secret key employed in the encryption algorithm. Security evaluations of the model are performed employing an information-theoretic approach. Assuming both a passive and an active attacker, we show that there is a threshold before which the wire-tap encoder guarantees an information-theoretic security (during which the equivocation of the secret key is increased), and after which the uncertainty reduces, entering a regime in which a computational security analysis is needed for estimating the complexity resistance against the secret key recovery.

Empirical distributions of statistics of correlation analysis for protected information CDMA-systems

It is noted in the paper that the multivariate normal distribution is not always a proper model to describe the actually observed signatures. For a number of statistics that are used in testing the hypotheses regarding the observed multi-dimensional variables it is shown that in the case of laws that differ from the multivariate normal distribution in a fairly wide range, significant changes in marginal distributions of statistics do not occur. Empirical distributions of statistics data are well described by the limiting laws obtained in the classical correlation analysis on the assumption of normality of the observed vector. It is shown that based on the correlation analysis results the conclusions can be made on the existence and nature of functional dependence or the preference of the particular regression model for description of the object under the study. The necessity to have the ability to model pseudo-random vectors under the laws with controlled deviation from the multivariate normal distribution is noted in order to trace the changes in distributions of the studied statistics of the correlation analysis. The results extend the scope of correct use of the methods of classical correlation analysis in applications.

Discrepancy bounds for hybrid sequences involving matrix-method pseudorandom vectors

Discrepancy bounds for hybrid sequences involving matrix-method pseudorandom vectors

Pseudorandom vector sequences of maximal period generated by triangular polynomial dynamical systems

In this paper we study the period of vector sequences generated by triangular polynomial systems and we characterize the case when their orbits are of maximal period. Moreover, we estimate multiplicative character sums with these sequences and we obtain better results using a different approach.