A Novel Pseudo-Random Number Generator for Cryptographic Applications

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.

Many fields need random and pseudorandom numbers, especially in cryptographic applications. d-bit segment binary pseudorandom numbers can be more easily used for block encryption. This paper studies on the statistical test for binary d string pseudorandom number generator (PRNG). Three postulates on the randomness for ideal pseudorandom d-bit segment sequences have been proposed. Based on the FIPS140-2 tests, a statistical test suite for d-bit segment sequences generated by PRNG has been proposed. Using the test suite tests the 100 key streams generated by RC4 PRNG and Matlab PRNG, respectively. The test results show that in the two 100 key streams generated via the two PRNGs with different seeds, about 97% 8-bit strings have passed the test suite, respectively. Using the key streams generated via the two PRNGs encrypts an RGB image. The results have shown that the encrypted RGB images have significant stream encryption avalanche effect.KeywordsInformation TheoryPseudorandom Number StringRandomness PostulateFIPS 140-2 TestNew Test Standard

The generation of pseudo-random numbers (bits) plays a critical role in a large number of applications such as statistical mechanics, numerical simulations, gaming industry, communication or cryptography. The choice of secret keys for cryptographic primitives largely depends on the quality of random numbers used. These random numbers are fundamental tools in the generation of secret keys and initialization variables of encryption for cryptographic application, masking protocols, or for internet gambling. Chaotic Pseudorandom numbers were found to be very efficient in this aspect. The relevance of chaotic pseudorandom sequences in ensuring security in cryptosystems is considered, at the same time reviewing statistical tests required to make such sequences cryptographically secure. This paper intends to review the development of chaotic pseudorandom number generators through the years and the statistical tests they are required to pass as a measure of their randomness.KeywordsChaosDeterministic algorithmNon-linear mapPseudorandomStatistical test

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

A fractional-order Lorenz system is optimized to maximize its maximum Lyapunov exponent and Kaplan-York dimension using the Non-dominated Sorting Genetic Algorithm II (NSGA-II) algorithm. The fractional-order Lorenz system is integrated with a recent process called the “modified two-stage Runge-Kutta” (M2sFRK) method, which is very fast and efficient. A Pseudo-Random Number Generator (PRNG) was built using one of the optimized systems that was obtained. The M2sFRK method allows for obtaining a very fast optimization time and also designing a very efficient PRNG with linear complexity, O(n). The designed PRNG generates 24 random bits at each iteration step, and the random sequences pass all the National Institute of Standards and Technology (NIST) and TestU01 statistical tests, making the PRNG suitable for cryptographic applications. The presented methodology could be extended to any other chaotic system.

A new Pseudo random number generator based on generalized Newton complex map with dynamic key

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 stream cipher systems, random key sequence generation is the primary task. The concept of chaotic systems can be considered in generating a random key sequence due to its inherent randomness property. Though the chaotic real sequences are random, the randomness will be lost after converting them to binary sequences. In this context, the authors propose a technique which uses a non‐linear feedback system to enhance the randomness of the binary sequences. In this work, three binary chaotic sequences using a logistic map are generated with three different initial conditions and each real value of the chaotic sequence is converted to ‘k’ bit binary value using a thresholding function. Some of the resulting sequences are not random. Hence, in this article a non‐linear structure is used to make the resulting sequence random. Here, a non‐linear function similar to the structure of the Simplified Data Encryption Standard is used to generate a sequence using two non‐random chaotic binary sequences. The resulting sequence is XORed with another non‐random chaotic binary sequence to get a random sequence. Sequences obtained from this nonlinear system are subjected to randomness tests and the results indicate that the sequences pass all the randomness tests. Hence, the sequences qualify as random key sequences, which can be used in a stream cipher based system to encrypt the data samples like audio, image, video, and so forth.

Random number generators represent basic cryptographic primitives. They are widely used in modern security schemes including security protocols, computer security and password sources. In some algorithms (e.g. DSA) or protocols (e.g. zero-knowledge), random numbers are intrinsic to the computation [3]. In all these applications, strength of security depends greatly on the quality of randomness of the source. Pseudo random number generators (PRNGs) play an important role in cryptographic applications, as the security of these systems depends on the assumption that future values in the random sequence can be unpredictable. A linear feedback shift register (LFSR), in effect, implements a binary polynomial generator. These generators find common use for PRNGs. However, the random sequence generated by LFSR can not guarantee the unpredictability in secure system. We have used genetic algorithm to improve LFSR and proposed a novel random number generator with complex architecture and longer period.

Sequences of pseudorandom numbers are needed for applications of stochastic simulation. Usually they are generated in the computer by a deterministic algorithm which produces a sequence of standard pseudorandom numbers, i.e. a sequence of numbers which “behave” as a realization of a sequence of independent identically distributed random variables having a uniform distribution on the unit interval. In a second step these standard pseudorandom numbers are often transformed in order to fit a given (non-uniform) distribution. For example, Devroy’s book [4] is devoted to this problem. This paper deals only with algorithms producing sequences of standard pseudorandom numbers. Such algorithms are called pseudorandom number generators. Many users of simulation techniques do not think about the pseudorandom number generators implemented in their computers and use the standard software at hand. This habitude is dangerous since the “stochastic quality” of the pseudorandom number sequences is fundamental for the results of stochastic simulation and many pseudorandom number generators in use have serious defects (see e.g. [2], [6], p. 10, and [26], p. 18). The present paper gives a survey on methods for generating deterministic sequences of real numbers which can be used as standard pseudorandom number sequences. Special emphasis is given to generation methods which have been studied by the author’s research group at Darmstadt Technical University.

This article explores randomness and how general purpose computers generate it. It also discusses the security requirements that a pseudo-random number generator must satisfy for use in cryptographic applications. And also special attention is paid to the known and new methods of testing random bit sequences. Analyzing the effectiveness of pseudo-random sequence generators is a pressing problem for smart cards when using more advanced methods of encryption and information protection. The available methods show low flexibility and versatility in the means of finding hidden patterns in data. To solve this problem, it is proposed to use algorithms based on multivariate statistics. These algorithms combine all the advantages of statistical methods and are the only alternative for analyzing short and medium-length sequences. The paper considers the scheme of operation of pseudo-random number generators in limited devices. The main requirements for modern smart cards are highlighted. A criterion for checking the randomness of bit sequences of small length (up to 100 bits) is proposed. This approach is appropriate for testing a lightweight pseudo-random number generator in devices with certain resource constraints. The paper presents the compatible distributions of the number of 2-strings and the number of 3-strings of a fixed form of a random bit sequence, which make it possible to carry out a statistical analysis of local sections of this sequence. A possible application of the obtained formulas can be to test the hypothesis of the randomness of the arrangement of zeros and ones in a (0, 1) -sequence of finite length. Research has shown that even with limited resources and a limited entropy environment like a smart card, good quality pseudo-random sequences can be created that can satisfy all the requirements for pseudo-random number generators, even those used for general purpose computers. In the work, the set of statistical tests was expanded to include other tests that are not included in the statistical set of NIST tests, and to analyze the work of the proposed algorithms. The paper presents algorithms for testing a pseudo-random sequence using multivariate statistics to illustrate their possible application in a smart card environment.

Most commonly-used pseudo-random number generators (PNGs) in computer systems are based on linear recurrence. These deterministic PNGs have fast and compact implementations, andean ensure very long periods. However, the points generated by linear PNGs in fact have a regular lattice structure and are thus not suit able for applications that rely on the assumption of uniformly distributed pseudo-random numbers (PNs). In this paper we propose and evaluate several fast and compact linear, non-linear, and hybrid PNGs for a field- programmable gate array (FPGA). The PNGs have excellent equidistribution properties and very small autocorrelations, and have very long repetition periods. The distribution and long-range correlation properties of the new generators are efficiently, and much more rapidly, estimated at hardware speeds using designed modules within the FPGA. The results of these statistical tests confirm that the combination of several linear PNGs or the combination of even one small non-linear PNG with a linear PNG significantly improves the statistical properties of the generated PNs.

This paper proposes a well-optimized FPGA implementation of a chaos-based cryptosystem for real-time image encryption and decryption. A highly sensitive Pseudo-Random Number Generator (PRNG) based on the Lorenz chaotic system is designed to generate pseudo-random numbers. A high-quality encryption key is acquired by encrypting the numbers of a 128-bit counter using the PRNG. For image encryption, the image is first decomposed into 128-bit blocks. Then, the blocks are encrypted by XORing pixels with the key stream. [Formula: see text] cycles of encryption can be achieved to increase complexity. Finally, the blocks are concatenated to form an encrypted image. The algorithm is designed, implemented, and validated on the Xilinx Zynq FPGA platform using the Vivado/System Generator tool. The hardware design is well optimized for pipeline processing and low resource utilization. The experimental synthesis indicates that the provided architecture achieves high performance in terms of frequency and throughput. The encryption scheme is evaluated and analyzed by several tools and tests using different images. The experimental simulation results demonstrate that the hardware implementation is faster than a software implementation while maintaining the technique’s effectiveness. The proposed hardware implementation is extremely adopted for secret image encryption and decryption that can be used in real-time applications.

We have designed an ultra-low power sensor networking platform called the i-bean network. The i-bean network requires a reliable RNG (random number generator) for various purposes such as random backoffs, random transmission delays and random packet sequence numbers. We could not use the existing RNGs because they require special purpose hardware and/or involve complex computations. We have designed a simple PRNG based on a free-running timer. Although this PRNG was specifically designed for the i-bean network, it could be used in other low-power embedded networks.

Transmission of the information in any form requires security. Security protocols used for communication rely on the use of random numbers. Pseudo-random numbers are required with good statistical properties and efficiency. The use of a single chaotic map may not produce enough randomness. The turbulence is padded into the existing map to improve its chaotic behaviour and increase the periodicity. A Pseudo-random number generator (PRNG) with this architecture is devised to generate random bit sequences from secret keys. The statistical properties of newly constructed PRNG are tested with NIST SP 800–22 statistical test suite and were shown to have good randomness. To ensure its usability in cryptographic applications, we analysed the size of its key space, key sensitivity, and performance speed. The test results show that the newly designed PRNG has a 3.6% increase in key space and a 5% increase in its performance speed compared to existing chaotic PRNGs. The novel PRNG with faster performance is found suitable for lightweight cryptographic applications.