Pseudo-random Sequence Generator Research Articles

Improving the Statistical Qualities of Pseudo Random Number Generators

Pseudo random and true random sequence generators are important components in many scientific and technical fields, playing a fundamental role in the application of the Monte Carlo methods and stochastic simulation. Unfortunately, the quality of the sequences produced by these generators are not always ideal in terms of randomness for many applications. We present a new nonlinear filter design that improves the output sequences of common pseudo random generators in terms of statistical randomness. Taking inspiration from techniques employed in symmetric ciphers, it is based on four seed-dependent substitution boxes, an evolving internal state register, and the combination of different types of operations with the aim of diffusing nonrandom patterns in the input sequence. For statistical analysis we employ a custom initial battery of tests and well-regarded comprehensive packages such as TestU01 and PractRand. Analysis results show that our proposal achieves excellent randomness characteristics and can even transform nonrandom sources (such as a simple counter generator) into perfectly usable pseudo random sequences. Furthermore, performance is excellent while storage consumption is moderate, enabling its implementation in embedded or low power computational platforms.

A Double-Layer Image Encryption Scheme Based on Chaotic Maps and DNA Strand Displacement

The image encryption schemes combining chaotic maps, DNA coding, and DNA sequence operation can effectively protect the image. In this paper, a double-layer image encryption scheme is proposed by combining chaotic maps with DNA strand displacement (DSD). Chaotic maps are used to generate pseudorandom sequences and perform routine scrambling and diffusion operations on the plaintext image. We propose three DSD-based encryption rules according to the diversity of DNA strand displacement, and these three encryption rules are used to encrypt the image at the DNA sequence level. The plaintext image can be transformed into the cipher image, which is difficult to be recognized without the correct keys through the double-layer encryption at the level of chaotic maps and DNA. Simulation results and security analysis show that the proposed encryption scheme can effectively protect image information and resist conventional information attacks.

A full duplex FSO transmission system using RZ-4PAM downlink signals with 67% duty cycle and AMI uplink signals

To improve the transceiver quality of Free Space Optical (FSO) system and ensure that user access is feasible the network, a high-speed full-duplex 100 meters FSO transmission scheme using 67% duty cycle RZ-4PAM downlink and alternative mark inversion (AMI) uplink signals is designed system. In the downlink, one PAM sequence generator and one Mary pulse generator (MPG) module are used to generate 67% RZ-4PAM optical signals at 10Gbit/s through a Mach-Zehnder intensity modulator (MZM). The upstream AMI signals generator by the pseudo-random binary sequence (PRBS) generator and the precoding process. We have measured optical spectrums, time-domain waveforms and eye diagrams before and after signals transmission by system simulation. The transceiver performance of the downstream RZ-4PAM with 67% duty cycle and upstream AMI optical signals the in the 100m FSO transmission system is analyzed.

A Modified PRBS: Vertical Stacked LFSR Primitive Polynomial for Secure Data Communication

Linear Feedback Shift Register (LFSR) generates the fault coverage test patterns to compute the target fault of data compression methods. Future Generation wireless communication covers irrespective of complex situation and dense environments marginable throughput to everyone. LFSR widely applied to generate Pseudo Random Noise Sequence, Digital Random Number Generator commonly employed in Cryptography, encoding techniques, Built in Self-Test (BIST) etc. Sequence generated by the LFSR are easily predictable as periodic nature of the sequence. A Modified Pseudo Random Sequence Generator (PRBS) with vertical stacked LFSR (VS-LFSR) is proposed to improve security against predictability nature of PRBS. The primitive polynomial of the nbit LFSR is vertically stacked with top most polynomial and ends with the least polynomial with this flexible of the primitive polynomial are processed and Random sequences are generated. The proposed method generates the random numbers of flexible ranges by appropriately selecting necessity primitive polynomial code in the vertical stack. Compare to conventional LFSR, all zero (0) states also generated in the VS-LFSR, enables the test pattern to have all 2npossible states of n-bit LFSR. With little hardware complexity, periodic pattern of LFSR is further improved with the maximum number of states and result attained maximum number of random outputs as Πn-202n-m - 1.

Fast Chaotic Image Encryption Algorithm Using a Novel Divide and Conquer Diffusion Strategy

To protect image privacy in real-time transmission, a fast chaotic image encryption algorithm using a novel divide and conquer diffusion strategy is proposed in this paper. Firstly, a fast pseudo-random sequence generator is constructed using 2D hyperchaotic systems. And by performing bitwise XOR operation between two integer sequences obtained from different systems, the final key stream used for diffusion will have better randomness and unpredictability. Secondly, to achieve divide and conquer diffusion, the plain image is divided into three parts, then a parallel CBC-based diffusion method can simultaneously act on upper and bottom parts (or left and right parts), which achieves a time complexity of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\boldsymbol {O}$ </tex-math></inline-formula> ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$W+H$ </tex-math></inline-formula> ). Moreover, within the diffusion process, the mechanism of information interaction on the central row or column further enhances avalanche effect to resist differential attack. Thirdly, the session key of the proposed algorithm is a mixture of the plain image’s hash value and a true random sequence, which not only improve plaintext sensitivity but also realize one-time pad. Finally, experimental results indicate the superiority of our algorithm to resist statistical, chosen-plaintext, entropy, and other common attacks. Furthermore, by comparison with previous works, our algorithm preforms much faster execution speed with only average of 0.08s to encrypt images of size <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$512\times 512$ </tex-math></inline-formula> , while it provide the same or even higher level of security. Therefore, the proposed algorithm can meet security and efficiency requirements of real-time communications of image data.

Cryptographic strength investigation of the algorithm for generating pseudorandom sequences based on a blender

Aim. The purpose of the article is to study the cryptographic strength characteristics of Boolean functions used in the blender algorithm. This algorithm is designed for information security tasks as part of a pseudorandom sequence generator. Methods. The methods of cryptographic Boolean functions theory, the methods of analysis and comparison were used in the work. Results. The general features of the blender Boolean functions are formulated. To assess their cryptographic strength, a computational study of compliance with criteria such as balancedness, algebraic degree, the presence of fictitious variables, the absence of linear structures, correlation immunity, high nonlinearity, avalanche criterion, etc. was performed. A comparison is made with similar results for Boolean functions that are part of nonlinear s-blocks of known cryptographic algorithms. Conclusions. The ability to adjust the blender dimension to obtain blocks of the desired size, forming the output sequence, allows increasing the values of some characteristics of Boolean functions cryptographic strength. It is detected that some cryptographic strength indicators of the Boolean blender functions (balancedness, nonlinearity and global avalanche characteristic) have asymptotic regularities of behavior. The results of the study makes it possible to consider the level of cryptographic strength of the blender Boolean functions acceptable for use in cryptographic protection systems.

КЛЕТОЧНЫЕ АВТОМАТЫ И ИХ ОБОБЩЕНИЯ В ЗАДАЧАХ КРИПТОГРАФИИ. ЧАСТЬ 2

The purpose of the article is an analytical review of the application of cellular automata and their generalizations in cryptography. Research method: an analysis of scientific publications on the topic of the article. Results: The review article analyzes the literature devoted to the use of cellular automata and their generalizations for the construction of cryptographic algorithms. The article consists of two parts. The first part was devoted to classical cellular automata and symmetric cryptographic algorithms based on them. It briefly discussed the history of the theory of cellular automata and its application in various scientific fields. A review of the works of a number of authors who proposed symmetric cryptographic algorithms and pseudorandom sequence generators based on one-dimensional cellular automata was presented. The security of such cryptographic algorithms turned out to be insufficient. The following was a review of articles devoted to the use of two-dimensional cellular automata for constructing ciphers (this approach gave the best results). Multidimensional cellular automata were also mentioned. This second part of the article is devoted to a review of works devoted to the use of generalized cellular automata in cryptography – on the basis of such automata, it is possible to create symmetric encryption algorithms and cryptographic hash functions that provide a high level of security and high performance in hardware implementation (for example, on FPGA), as well as having fairly low requirements for hardware resources. In addition, an attention is paid to interesting connections of generalized cellular automata, in the context of their use in cryptography, with the theory of expander graphs. Attention is also paid to the security of cryptographic algorithms based on generalized cellular automata. The works devoted to the implementation of various cryptographic algorithms based on generalized cellular automata on FPGA and GPU are mentioned. In addition, an overview of asymmetric cryptoalgorithms based on cellular automata is given. The questions about the belonging of some problems on cellular automata and their generalizations to the class of NP-complete problems, as well as to some other complexity classes, are also considered.

A Novel Measurement Scheme for Crossly-Polarized Channel Based on the Pseudorandom Codes of Analyzing the Fuzzy Function

With the rapid development of 5G communication, crossly-polarized transmitting and receiving scalable channels have received wide attention. We conduct an in-depth analysis of the 5.8 GHz horizontal and vertical crossly-polarized electromagnetic (EM) wave propagation and propose a novel test scheme for the feature of the particular EM wave propagation. The scheme acquires the channel characteristics and the interchannel coupling interference strength by transmitting and receiving pseudorandom codes and analyzing the fuzzy function of the corresponding noise-like signals. We then optimize the pseudorandom codes with parallel pseudorandom sequence generation method based on Hash function, greatly reducing calculation time. The transceiver’s mode adopts time division duplexing and chooses the pseudorandom codes as the system transceiver’s pseudorandom codes. The fuzzy function analysis and processing are performed by a MATLAB code and we can clearly obtain pin-shaped fuzzy images and coupling interference between crossly-polarized channels.

Memristor-based time-delay chaotic system with hidden extreme multi-stability and pseudo-random sequence generator

Memristor-based time-delay chaotic system with hidden extreme multi-stability and pseudo-random sequence generator

Authenticated encryption mode with blocks skipping

Block symmetric ciphers are one of the most important components of modern information security systems. At the same time, in addition to the structure of the applied block symmetric cipher, the cryptographic strength and performance of the information protection system is largely determined by the applied encryption mode. In addition to high performance and high-quality destruction of block statistics, modern encryption modes should also protect encrypted information from occurred or intentionally introduced errors. In this paper, we have developed an encryption mode with blocks skipping and using a pseudo-random key sequence generator, which allows checking the integrity of encrypted information with accurate detection of the place where an error was introduced. In this case, the error detection accuracy is determined by the adjustable parameter of the macroblock size and can be set depending on the level of importance of the protected information. The developed encryption mode is characterized by the following key advantages: reducing the number of required encryption operations by half, while providing a high level of cryptographic quality; more effective destruction of macroblock statistics due to the use of an additional generator of pseudo-random key sequences, the impossibility of propagation of the occurred (intentionally introduced) error outside the macroblock, as well as higher values of the number of protection levels due to the possibility of classifying the initial states of the applied generators of pseudo-random key sequences. As proposed in this paper, the mode of authenticated encryption with blocks skipping can be recommended for use on mobile platforms that are demanding both in terms of the quality and reliability of the protected information and are limited in terms of computing and power resources.

Chaotic Features of a Class of Discrete Maps without Fixed Points

Chaotic dynamical systems without fixed points are promising in the generation of pseudo-random sequences because orbits will not converge to a fixed point. In this class of systems there are no final fixed points, so the basin of attraction of a fixed point does not exist. The absence of fixed points makes it difficult to analyze the dynamics of the systems because a fixed point gives us a lot of information about the dynamics of the system. In addition, if there is an amplitude control parameter for the generated chaotic signals, the tolerance and adaptability are higher and better in the application process. In view of the aforementioned, in this paper, a novel class of discrete maps is presented and described by a kind of piecewise linear (PWL) maps. Necessary and sufficient conditions are given to guarantee that this class of discrete maps does not have any fixed point. Furthermore, we introduce families of these PWL discrete maps without fixed points that present positive Lyapunov exponents and have chaotic dynamics with amplitude control. From these families, we select one particular map, which is analyzed theoretically and proved to be chaotic in the sense of Devaney.

Memory-Efficient LFSR Encoding and Weightage Driven Bit Transition for Improved Fault Coverage

Linear Feedback Shift Registers (LFSRs) have been employed as test pattern generators in BIST for decades; however, an emerging problem with design constraints leads to a lot of improvements in this field. This paper presents a memory-efficient encoding-based method to generate test patterns for a given primitive polynomial LFSR TPG. Here, test patterns generated from LFSR are divided into groups and follow encoding to transform into multiple test patterns. These newly generated encoded test patterns are further divided into transitional and non-transitional blocks which control the bit transitions over encoded values. This weighted driven bit transition also prevents certain bit transitions that reduce the dynamic power as well during the testing process. This TPG technique can be used for generating both pseudo-random test sequence and deterministic pattern generation by allowing fine control over bit transition and appropriate encoder design with the least hardware complexity overhead. The proposed technique has experimented over ISCAS ‘85 and some sequential part of ISCAS ‘89 benchmark circuits to validate the superiority in terms of memory efficiency compared to some well-known LFSR reseeding techniques and the hardware complexity reduction during BIST implementation. The proposed encoded test pattern also achieves a minimum of 14% test data volume and toggle control scheme in power reduction.

The Dynamic Analysis of a Novel Reconfigurable Cubic Chaotic Map and Its Application in Finite Field

Dynamic degradation occurs when chaotic systems are implemented on digital devices, which seriously threatens the security of chaos-based pseudorandom sequence generators. The chaotic degradation shows complex periodic behavior, which is often ignored by designers and seldom analyzed in theory. Not knowing the exact period of the output sequence is the key problem that affects the application of chaos-based pseudorandom sequence generators. In this paper, two cubic chaotic maps are combined, which have symmetry and reconfigurable form in the digital circuit. The dynamic behavior of the cubic chaotic map and the corresponding digital cubic chaotic map are analyzed respectively, and the reasons for the complex period and weak randomness of output sequences are studied. On this basis, the digital cubic chaotic map is optimized, and the complex periodic behavior is improved. In addition, a reconfigurable pseudorandom sequence generator based on the digital cubic chaotic map is constructed from the point of saving consumption of logical resources. Through theoretical and numerical analysis, the pseudorandom sequence generator solves the complex period and weak randomness of the cubic chaotic map after digitization and makes the output sequence have better performance and less resource consumption, which lays the foundation for applying it to the field of secure communication.

METHOD FOR DEVELOPING PSEUDO-RANDOM NUMBER GENERATORS FOR CRYPTOGRAPHIC APPLICATIONS IN 5G NETWORKS

Today, pseudo-random number generators are used in various systems and applications, including as key generators in stream ciphers. The implementation of the latest information and communication technologies (in particular, 5G networks) strengthens the requirements for ensuring the confidentiality of critical data and forces the development of new methods and means for cryptographic protection. Existing generators, like other cryptographic algorithms, do not meet the requirements for processing speed and security against known types of attacks. From this position, in the paper a method for constructing pseudo-random sequence generators was developed. It allows to build efficient generators for cryptographic applications. Based on this method, software generators of pseudo-random numbers have been developed and implemented. These will be useful for cryptographic applications in modern 5G networks. The developed pseudo-random number generators have passed complex statistical testing by the NIST STS technique (showed results not worse than the results of known pseudo-random sequence generators used in practice to solve similar problems). Besides, they are faster in comparison with analogues used today in 5G networks (for example, with algorithms SNOW and Trivium). In further works it is planned to investigate the security of the developed pseudo-random generators against different types of cryptanalytic attacks, as well as to simulate the work of the developed pseudo-random sequence generators using the base station equipment of modern 5G networks.

A novel color image encryption method based on an evolved dynamic parameter-control chaotic system

The majority of existing image encryption algorithms use single chaotic systems, such as Logistic map or Lorentz system, to be the pseudo-random sequence generator. Actually, neither low nor high dimensional chaotic system can get rid of pseudo-randomness deterioration of chaotic sequence calculated by limited precision computer. Additionally, most of them use only one chaotic pseudo-random sequence throughout the encryption process. These are the more obvious deficiencies. In the current paper, a novel compound chaotic system is applied to color images domain to solve the mentioned problems. Dynamic parameter-control chaotic system can enhance the sequence’s randomness after digitalizing. Corresponding the different sequences generated by the novel chaotic system to each color channel of image is a helpful method to reduce the image’s statistical characteristics in the scrambling process. Finally, the effectiveness and security of the proposed encryption has been illustrated by the experimental, and at the meantime, excellent performance is also demonstrated.

Nanocircuits for Protection of the Cipher Information

While using side-channel attacks, cipher devices was defenseless to power and electromagnetic analysis attacks. These attacks are due to the use of low cost equipment. Currently, most of the cipher circuits are implemented on complementary metal-oxide-semiconductor. The disadvantage is the relationship between the data processing the curcuit to energy consumption. When processing the CMOS transistor logic "1" and the logic "0", through the transistor passes a different volume of current. If don't implement significant counteractions, it will allow another person to decrypt the key of the cipher module. A new logical approach to quantum-dot cellular automata and single-electron transistors is explored. The proposed approach has low power consumption and complicated clocking circuits. In theory and practice of cipher protection one of the key problems is the formation of binary pseudorandom sequences of maximum length of acceptable statistical characteristics. Generators of pseudorandom sequences usually based on linear shift registers with linear feedback. Here expanded the concept of linear shift register, believing that his every category (memory cell) can be in one of the states. Call registers are "generalized linear shift registers".

A Pseudo Random Binary Sequence Generator Based on Chaotic Logistic Maps

One of the major applications of Pseudo-Random Numbers is cryptography. Cryptography is a technique of securing information and communications through the use of codes so that only those people for whom the information is intended can understand it and process it thus preventing unauthorized access to information. Attackers can bypass cryptography, hack into computers that are responsible for data encryption and decryption, and exploit weak implementations, such as the use of default keys. To tackle this problem, logistic chaotic maps are used to generate a Pseudo-Random Binary Sequence (PRBS). The output of the designed PRBS Generator has successfully passed all the performance assessments of the NIST test suite. Hence a highly efficient Cryptographic Pseudo Random Bit Sequence Key is developed which not only has good performance in terms of statistical properties but can also achieve high product throughput if realized by FPGA hardware.

Dynamical analysis, circuit realization, and application in pseudorandom number generators of a fractional-order laser chaotic system* *Project supported by the National Natural Science Foundation of China (Grant No. 62061014) and the Natural Science Foundation of Liaoning Province, China (Grant No. 2020-MS-274).

A new five-dimensional fractional-order laser chaotic system (FOLCS) is constructed by incorporating complex variables and fractional calculus into a Lorentz–Haken-type laser system. Dynamical behavior of the system, circuit realization and application in pseudorandom number generators are studied. Many types of multi-stable states are discovered in the system. Interestingly, there are two types of state transition phenomena in the system, one is the chaotic state degenerates to a periodical state, and the other is the intermittent chaotic oscillation. In addition, the complexity of the system when two parameters change simultaneously is measured by the spectral entropy algorithm. Moreover, a digital circuit is design and the chaotic oscillation behaviors of the system are verified on this circuit. Finally, a pseudo-random sequence generator is designed using the FOLCS, and the statistical characteristics of the generated pseudo-random sequence are tested with the NIST-800-22. This study enriches the research on the dynamics and applications of FOLCS.

Simple method of selecting totalistic rules for pseudorandom number generator based on nonuniform cellular automaton

This paper is devoted to selecting rules for one-dimensional (1D) totalistic cellular automaton (TCA). These rules are used for the generation of pseudorandom sequences, which could be useful in cryptography. The power of pseudorandom number generator (PRNG) based on nonuniform TCA can be improved using not only one rule but a large set of rules. For this purpose, each subset of rules should be analyzed with its assignation to cellular automaton (CA) cells should be analyzed. We examine each of the subsets of totalistic rules, consisting of rules with neighborhood radius equal to 1 and 2. The entropy of bitstreams generated by the nonuniform TCA points out the best set of rules appropriate for the TCA-based generator. The paper also presents the method of simple selection of CA rules based on a cryptographic criterion known as a balance. The proposed method selects a maximal size of the set of available CA rules for a given neighborhood radius and suitable for PRNG. The method guarantees to avoid conflicting assignments of rules resulting in the creation of unwanted stable bit sequences, and provides high-quality pseudorandom sequences. This technique is used to verify the subsets of rules selected experimentally. Verified rules are proposed for 1D TCA-based PRNG as a new subset of best nonuniform TCA rules. New picked, examined, and verified subset of rules could be used in TCA-based PRNG and provide cryptographically strong bit sequences and huge keyspace.

Nonsingularity of Feedback Shift Registers of Degree at Most Three over a Finite Field

As a kind of generators of pseudorandom sequences, the Feedback shift register (FSR) is widely used in channel coding, cryptography and digital communication. A necessary and sufficient condition for the nonsingularity of a feedback shift register of degree at most three over a finite field is established. Using the above result, we can easily determine the nonsingularity of a feedback shift register from the algebraic normal form of the corresponding feedback function.