Generating High Quality Pseudo Random Number Using Evolutionary methods

Pseudo random number generators (PRNG) play a key role in various security and cryptographic applications where the performance of these applications is directly related to the quality of generated random numbers. The design of such random number generators is a challenging task. In this paper, we propose an application of Hopfield Neural Networks (HNN) as pseudo random number generator. This is done based on a unique property of HNN, i.e., its unpredictable behavior under certain conditions. We compare the main features of ideal random number generators with those of PRNG based on Hopfield Neural Networks. We use a battery of statistical tests developed by National Institute of Standards and Technology (NIST) to measure the performance, and to evaluate the quality of the proposed Hopfield random number generator.

Pseudo random number generators (PRNGs) are crucial for numerous applications in HPC ranging from molecular dynamics to quantum chemistry, and hydrodynamics. These applications require high throughput and good statistical quality from the PRNGs - especially for parallel computing where long pseudo-random sequences can be exhausted rapidly. Although a handful PRNGs have been adapted to parallel computing, they do not fully exploit the features of wide-SIMD many-core processors and GPU accelerators in modern supercomputers. Multiple Recursive Generators (MRGs) are a family of random number generators based on higher order recursion, which provide statistically high-quality random number sequences with extremely long-recurrence lengths, and deterministic jump-ahead for effective parallelism. We reformulate the MRG8 (8th-order recursive implementation) for Intel's KNL and NVIDIA's P100 GPU - named MRG8-AVX512 and MRG8-GPU respectively. Our optimized implementation generates the same random number sequence as the original well-characterized MRG8. We evaluated MRG8-AVX512 and MRG8-GPU together with vender tuned random number generators for Intel KNL and GPU. MRG8-AVX512 achieves a substantial 69% improvement compared to Intel's MKL, and MRG8-GPU shows a maximum 3.36x speedup compared to NVIDIA's cuRAND library.

In order to scale down a circuit size for hardware realization of neural network systems, there are many researches on a conventional pulse model neuron, in which, a conventional numerical calculation is replaced by a stochastic calculation. In the conventional stochastic calculation, LFSR (linear feedback shift register) has been used as a random number generator. In general, a good randomness is required for an exact calculation result. However, since the random numbers which are generated by LFSR is lacking in the randomness, there is a problem which affects an accuracy of the conventional stochastic calculation which uses LFSR for generating the random numbers. In our work, in order to improve the accuracy of the conventional stochastic calculation, we propose to use GLFSR (generalized-LFSR) which generates the random numbers which are rich in randomness as the random number generator for the stochastic calculation. The accuracy of the stochastic calculation is also evaluated using a standard deviation value (SD) and a maximum error. As a result, the proposed stochastic calculation which using GLFSR as the random number generator shows a highest accuracy of the calculation result.

The use of random numbers in day-to-day digital life is increasing drastically to make the digital data more secure in various disciplines, particularly in cryptography, cloud data storage, and big data applications. Generally, all the random numbers or sequences are not truly random enough to be used in various applications of randomness, predominantly in cryptographic applications. Therefore, the sequences generated by pseudorandom number generator (PRNGs) are not cryptographically secure. Hence, this study proposes a concept that the diffusion sequences which are used during cryptographic operations need to be validated for randomness, though the random number generator produces the random sequences. This study discusses the NIST, Diehard and ENT test suite results of random diffusion sequences generated by two improved random number generators namely, Enhanced Chaotic Economic Map (ECEM), and Improved Linear Congruential Generator (ILCG).

Monte Carlo (MC) method is widely used in resolving mathematical problems that are too complicated to solve analytically. The method involves with sampling process of the random numbers and probability to estimate the result. As MC method depending on a large number of good quality random numbers to produce a high accuracy result, developing a good random number generator (RNG) is vital. Most of random number generators are developed in software based, with the improvement of Field Programmable Gate Arrays (FPGA) density and speed in recent days, implementing random number generator (RNG) directly into hardware is feasible. Random Walk on the Boundary (WOB) is one of MC methods that applied to calculate the unit cube capacitance. The unique requirement of this method is the random numbers produced by RNG must fall within the Gaussian distribution and the maximum decimal values in the range of [0, 1]. Thus, in this paper we presented a novel hardware RNG for Random WOB method to calculate unit cube capacitance in FPGA. The RNG is implemented in floating-point base, using the combination of Cellular Automata Shift Register (CASR) and Linear Feedback Shift Register (LFSR) then channeled through Box-Muller transformation. There is linear approximation in computing logarithmic function applied in Box-Muller transformation. Based on statistical tests, the random numbers generated is nearly 97.5% resembling the standard normal distribution.

Random number generation is a fundamental aspect of computer science, cryptography, simulations, and statistical sampling. This paper explores the definitions, classifications, and implementations of random and pseudo-random number generators (RNGs and PRNGs). We examine true random number generators (TRNGs), which derive randomness from physical phenomena, and pseudo-random number generators (PRNGs), which use deterministic algorithms to produce sequences that mimic randomness. Case studies, including Random.org, HotBits, laser-based RNGs, and the Linux random number generator, illustrate practical implementations. We also discuss vulnerabilities, security considerations, and the importance of entropy in generating unpredictable sequences.

Random numbers play a key-role in cryptography, since they are used, e.g., to define enciphering keys or passwords [1]. Nowadays, the generation of random numbers is obtained referring to two types of devices, that are often properly combined together: True Random Number Generators (TRNGs), and Pseudo Random Number Generators (PRNGs). The former are devices that exploit truly stochastic physical phenomena [2, 3, 4, 5, 6], such as the electronic noise or the chaotic dynamics of certain nonlinear systems: for these devices the output sequences have an intrinsic degree of unpredictability, that is measured referring to the theoretical tools provided by Information Theory (e.g., in terms of the Shannon entropy) [7,4]. On the other hand, PRNGs are deterministic periodic finite state machines whose aim is to emulate, within the period, the random behavior of a truly random source of numbers. From a theoretical point of view, due to their deterministic nature, PRNGs are potentially predictable by observing their generated sequences [8, 9, 10, 1]. Nevertheless, in literature some families of PRNGs are classified to be ‘secure’, meaning that their algorithmic structure involves calculations that in average, referring to the prediction task, require an amount of computation time that is asymptotically unfeasible with the size of the problem, when referring to both the computational equipment at disposal and the known computing fastest algorithms [1,11]. It is worth noting that a given generator, even if belonging to an asymptotically secure family of PRNGs, can generate short periodic (and unsecure) sequences for several values of the initial seed. Therefore, apart from the cryptographic robustness of their algorithmic structure, a cryptographic PRNG must generate sequences that are acceptable from a statistical point of view, i.e., that pass a certain number of standard statistical tests [1, 12].

Random numbers have a wide usage in the area of cryptography. In practice, pseudo random number generators are used in place of true random number generators, as regeneration of them may be required. Therefore because of generation methods of pseudo random number sequences, statistical randomness tests have a vital importance. In this paper, a randomness test suite is specified for long binary sequences. In literature, there are many randomness tests and test suites. However, in most of them, to apply randomness test, long sequences are partitioned into a certain fixed length and the collection of short sequences obtained is evaluated instead. In this paper, instead of partitioning a long sequence into fixed length subsequences, a concept of dynamic partitioning is introduced in accordance with the random variable in consideration. Then statistical methods are applied. The suggested suite, containing four statistical tests: Collision Tests, Weight Test, Linear Complexity Test and Index Coincidence Test, all of them work with the idea of dynamic partitioning. Besides the adaptation of this approach to randomness tests, the index coincidence test is another contribution of this work. The distribution function and the application of all tests are given in the paper.

We present a new way of testing Random Number Generators (RNGs). Our approach allows to test Pseudo Random Number Generators (PRNGs) including Cryptographically Secure Pseudo Random Number Generators (CSPRNGs). The paper describes how to use machine learning for this. To construct a tester we compare the properties of three most common learning techniques to find the one most suitable one for testing RNGs. By analyzing the system during training and regarding the expected behavior of random numbers, we define an optimizer for learning RNGs. Based on the results and regarding the behavior of the machine learning algorithm, we define a rating for RNGs. On a state-of-the-art GPU cluster, we evaluate the full tester for multiple PRNGs. Additionally, we compare the results with the results from the commonly used test suite dieharder. The results prove that the developed tester is suitable for testing random numbers. In comparison to dieharder, it is even more powerful and able to replace it. Our tester could disclose weaknesses in PRNGs that are wrongly considered as CSPRNG. This could increase the security of many cryptographic protocols based on random numbers.

A secure communication over wireless environments by using a data connection core

This paper presents a method to hide three binary images in a grayscale image with same resolution. Pseudo Random Number Generator(PRNG) produces the random numbers that rearranges the binary values. PRNG algorithm is unique and the strength of random numbers generated are equal to random numbers generated without a seed value. Each binary image pixel values are rearranged through three random number series and it is hidden in a grayscale image through Ultra Unique Numbers (UUN). By comparing both concealed image and original image, modification among the image is identified. To identify concealed secret binary information in a grayscale image at the destination, UUN is reapplied. PRNG is used to rearrange the binary values for transforming the binary images. The main aim of this paper is to increase the embedding capacity of carter image without degrading the quality of the secret information with high Peak Signal Noise Ratio(PSNR).

Background: Pseudo random numbers have indispensable role in designing cryptography systems such as key stream in stream ciphers. Efficiency of most crypto systems are in depend on the quality of secret key generated by a pseudo random number generator. Improvements/Methods: In the present paper, an efficient pseudo random number generator is presented for cryptographic applications. The algorithm is based on controlling distribution of generated random numbers with the chaotic henon congruential generator. Statistical Analyses: Statistical tests and histograms are performed over the proposed generator and the results confirm the improvements over the proposed algorithms. According to the results of statistical tests, proposed algorithms generate pseudo random numbers with acceptable independency and uniformity and random sequences with long enough period. Applications: Key streams in stream cipher system can be considered as the most important applications of pseudo random numbers. With this regard proposed generators are statistically proved as proper key stream generator for designing stream cipher systems.

Pseudo random number generators (PRNGs) are one of the most important components in security and cryptography applications. We propose an application of Hopfield Neural Networks (HNN) as pseudo random number generator. This research is done based on a unique property of HNN, i.e., its unpredictable behavior under certain conditions. Also, we propose an application of Fuzzy Hopfield Neural Networks (FHNN) as pseudo random number generator. We compare the main features of ideal random number generators with our proposed PRNGs. We use a battery of statistical tests developed by National Institute of Standards and Technology (NIST) to measure the performance of proposed HNN and FHNN. We also measure the performance of other standard PRNGs and compare the results with HNN and FHNN PRNG. We have shown that our proposed HNN and FHNN have good performance comparing to other PRNGs accordingly.

RNGAVXLIB: Program library for random number generation, AVX realization

Image steganography conceals secret information in a cover image .It is used for secure data transfer. Various LSB (least significant bits) approaches have been used over the years in steganography. This paper proposes a novel technique to improve the conventional LSB technique for image steganography by using pseudo random number generation using Henon chaotic map. The random numbers are used to encrypt the hide image which is embedded in the cover picture. This encryption using pseudo random generator provides sufficient security to the payload as the same set of random numbers cannot be regenerated without knowing the exact random generator function and thus the secret data cannot be retrieved easily. The proposed technique has been tested successfully on various .jpg files and corresponding PSNR values have been calculated.