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Journal articles on the topic 'Random binary sequences'

Author: Grafiati

Published: 5 June 2025

Last updated: 24 June 2025

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1

Hertling, Peter. "Nonrandom Sequences between Random Sequences." JUCS - Journal of Universal Computer Science 11, no. (12) (2005): 1970–85. https://doi.org/10.3217/jucs-011-12-1970.

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Let us say that an infinite binary sequence q lies above an infinite binary sequence p if q can be obtained from p by replacing selected 0's in p by 1's. We show that above any infinite binary Martin-Löf random sequence p there exists an infinite binary nonrandom sequence q above which there exists an infinite binary random sequence r. This result is of interest especially in connection with the new randomness notion for sets of natural numbers introduced in [Hertling and Weihrauch 1998, Hertling and Weihrauch 2003] and in connection with its relation to the Martin-Löf randomness notion for infinite binary sequences.

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2

Šajić, Slavko, Nebojša Maletić, Branislav M. Todorović, and Milan Šunjevarić. "Random Binary Sequences in Telecommunications." Journal of Electrical Engineering 64, no. 4 (2013): 230–37. http://dx.doi.org/10.2478/jee-2013-0033.

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Realization of modern telecommunication systems is inconceivable without use of different binary sequences. In this paper, an overview of random binary sequences used in different telecommunication systems is given. Basic principles of pseudorandom, chaotic, and true random sequence generation are presented, as well as their application in telecommunications in respect to advantages and drawbacks of the same. Moreover, particular scheme for true random binary sequence generation is given, as well as results of randomness assessment obtained by NIST statistical test suite. Finally, short insight into importance of random binary sequence in secure communications is given.

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3

De Felice, Antonello. "Binary Pseudo-Random Sequences Theory." Journal of Information and Optimization Sciences 12, no. 2 (1991): 325–33. http://dx.doi.org/10.1080/02522667.1991.10699074.

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4

MERCER, IDRIS DAVID. "Autocorrelations of Random Binary Sequences." Combinatorics, Probability and Computing 15, no. 05 (2006): 663. http://dx.doi.org/10.1017/s0963548306007589.

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5

NICKERSON, RAYMOND S., and SUSAN F. BUTLER. "On producing random binary sequences." American Journal of Psychology 122, no. 2 (2009): 141–51. http://dx.doi.org/10.2307/27784387.

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Abstract This experiment addressed the opinion prevailing among researchers that people are poor at producing random binary sequences. Participants tried to produce sets of sequences of outcomes of imaginary coin tosses that could not be distinguished statistically from sets expected from actual coin tossing. The results generally support the conclusion that people are not very good at this task, although the distributional properties of the sets of sequences produced are qualitatively similar to those expected of sets produced by a random process. The results do not support the common finding that people consistently produce substantially more alternations and fewer repetitions than would be produced by chance, nor do they provide evidence of the pervasive operation of a gambler’s fallacy manifesting itself in a tendency for an alternation to increase with the length of a preceding run.

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M., Vishwas C. G., and R. Sanjeev Kunte. "Chaotic Map based Random Binary Key Sequence Generation." International Journal of Computer Network and Information Security 16, no. 4 (2024): 102–17. http://dx.doi.org/10.5815/ijcnis.2024.04.07.

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Image encryption is an efficient mechanism by which digital images can be secured during transmission over communication in which key sequence generation plays a vital role. The proposed system consists of stages such as the generation of four chaotic maps, conversion of generated maps to binary vectors, rotation of Linear Feedback Shift Register (LFSR), and selection of generated binary chaotic key sequences from the generated key pool. The novelty of this implementation is to generate binary sequences by selecting from all four chaotic maps viz., Tent, Logistic, Henon, and Arnold Cat map (ACM). LFSR selects chaotic maps to produce random key sequences. Five primitive polynomials of degrees 5, 6, 7, and 8 are considered for the generation of key sequences. Each primitive polynomial generates 61 binary key sequences stored in a binary key pool. All 61 binary key sequences generated are submitted for the NIST and FIPS tests. Performance analysis is carried out of the generated binary key sequences. From the obtained results, it can be concluded that the binary key sequences are random and unpredictable and have a large key space based on the individual and combination of key sequences. Also, the generated binary key sequences can be efficiently utilized for the encryption of digital images.

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Liu, Lingfeng, Suoxia Miao, Mengfan Cheng, and Xiaojing Gao. "Permutation Entropy for Random Binary Sequences." Entropy 17, no. 12 (2015): 8207–16. http://dx.doi.org/10.3390/e17127872.

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8

Borbély, József, and András Sárközy. "Quasi-Random Graphs, Pseudo-Random Graphs and Pseudorandom Binary Sequences, I. (Quasi-Random Graphs)." Uniform distribution theory 14, no. 2 (2019): 103–26. http://dx.doi.org/10.2478/udt-2019-0017.

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AbstractIn the last decades many results have been proved on pseudo-randomness of binary sequences. In this series our goal is to show that using many of these results one can also construct large families of quasi-random, pseudo-random and strongly pseudo-random graphs. Indeed, it will be proved that if the first row of the adjacency matrix of a circulant graph forms a binary sequence which possesses certain pseudorandom properties (and there are many large families of binary sequences known with these properties), then the graph is quasi-random, pseudo-random or strongly pseudo-random, respectively. In particular, here in Part I we will construct large families of quasi-random graphs along these lines. (In Parts II and III we will present and study constructions for pseudo-random and strongly pseudo-random graphs, respectively.)

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9

Sanderson, Yasmine B. "Effective generation of subjectively random binary sequences." Advances in Applied Mathematics 43, no. 1 (2009): 1–11. http://dx.doi.org/10.1016/j.aam.2008.11.003.

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10

Tsuneda, Akio. "Various Auto-Correlation Functions of m-Bit Random Numbers Generated from Chaotic Binary Sequences." Entropy 23, no. 10 (2021): 1295. http://dx.doi.org/10.3390/e23101295.

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This paper discusses the auto-correlation functions of m-bit random numbers obtained from m chaotic binary sequences generated by one-dimensional nonlinear maps. First, we provide the theoretical auto-correlation function of an m-bit sequence obtained by m binary sequences that are assumed to be uncorrelated to each other. The auto-correlation function is expressed by a simple form using the auto-correlation functions of the binary sequences. This implies that the auto-correlation properties of the m-bit sequences can be easily controlled by the auto-correlation functions of the original binary sequences. In numerical experiments using a computer, we generated m-bit random sequences using some chaotic binary sequences with prescribed auto-correlations generated by one-dimensional chaotic maps. The numerical experiments show that the numerical auto-correlation values are almost equal to the corresponding theoretical ones, and we can generate m-bit sequences with a variety of auto-correlation properties. Furthermore, we also show that the distributions of the generated m-bit sequences are uniform if all of the original binary sequences are balanced (i.e., the probability of 1 (or 0) is equal to 1/2) and independent of one another.

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11

Голембиовская, Оксана, Oksana Golembiovskaya, Александр Козачок, et al. "COMPUTATION COMPLEXITY DECREASE IN MACHINE EXPERIMENTS AT VERIFICATION OF CRYPTOGRAPHIC ALGORITHMS." Bulletin of Bryansk state technical university 2017, no. 1 (2017): 144–52. http://dx.doi.org/10.12737/24905.

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The problem of obtaining a set of samples for the assessment of cryptographic algorithms quality on the basis of statistical tests use is considered. New properties of Markov binary chains taking into account dependences of probabilities of binary vectors with different length are described. The analytical expressions allowing the computation of dependences of range limits in values of probabilities of multidimen-sional binary random values upon probabilities of bi-nary random values with smaller dimension are of-fered. The reasons for the necessity of an additional procedure of rejection at the simulation of the realiza-tion of Markov binary processes are defined. A method for the directed search of probability values of sets in the distribution of Markov binary sequences allowing the generation of ergodic binary random sequences that allows refusing completely the procedure of rejection is considered. An algorithm realizing a mentioned method possessing a lowered computational complexity in comparison with the wellknown algorithms for the organization of a computational experiment on the investigation of statistical properties of binary random sequences is presented.

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12

Schmidt, Kai-Uwe. "The peak sidelobe level of random binary sequences." Bulletin of the London Mathematical Society 46, no. 3 (2014): 643–52. http://dx.doi.org/10.1112/blms/bdu021.

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13

Compagner, Aaldert. "The hierarchy of correlations in random binary sequences." Journal of Statistical Physics 63, no. 5-6 (1991): 883–96. http://dx.doi.org/10.1007/bf01029989.

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14

Khan, Mushfeq. "Shift-complex sequences." Bulletin of Symbolic Logic 19, no. 2 (2013): 199–215. http://dx.doi.org/10.2178/bsl.1902020.

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AbstractA Martin-Löf random sequence is an infinite binary sequence with the property that every initial segment σ has prefix-free Kolmogorov complexity K(σ) at least ∣σ∣ − c, for some constant c ϵ ω. Informally, initial segments of Martin-Löf randoms are highly complex in the sense that they are not compressible by more than a constant number of bits. However, all Martin-Löf randoms necessarily have contiguous substrings of arbitrarily low complexity. If we demand that all substrings of a sequence be uniformly complex, then we arrive at the notion of shift-complex sequences. In this paper, we collect some of the existing results on these sequences and contribute two new ones. Rumyantsev showed that the measure of oracles that compute shift-complex sequences is zero. We strengthen this result by proving that the Martin-Löf random sequences that do not compute shift-complex sequences are exactly the incomplete ones, in other words, the ones that do not compute the halting problem. In order to do so, we make use of the characterization by Franklin and Ng of the class of incomplete Martin-Löf randoms via a notion of randomness called difference randomness. Turning to the power of shift-complex sequences as oracles, we show that there are shift-complex sequences that do not compute Martin-Löf random (or even Kurtz random) sequences.

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15

Kramosil, Ivan. "On Pseudo-Random Sequences over Finite Automata." Fundamenta Informaticae 8, no. 1 (1985): 55–62. http://dx.doi.org/10.3233/fi-1985-8104.

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It is a well-known fact that binary sequences (strings) of high algorithmic complexity can be taken as good approximations of statistically independent random sequences with two equiprobable outputs. Here “sequence of high algorithmic complexity” is such one, that the length of the shortest program generating this sequence by a universal Turing machine differs only by an a priori given constant from the length of the generated sequence. The present paper generalizes this result to the case of a finite (not necessarily binary) alphabet. Considering an infinite sequence of finite sequences of high algorithmic complexity over a finite alphabet, the relative frequency of occurences of each letter or finite string of letters is proved to tend to the inverted value of the total number of letters, or strings of letters of the given length, in question. This result may be seen as an analogy to the strong law of large numbers in the case of equiprobable probability distribution.

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16

G. M., Vishwas C., R. Sanjeev Kunte, and Varun Yarehalli Chandrappa. "Encryption Using Binary Key Sequences in Chaotic Cryptosystem." International Journal of Computer Network and Information Security 15, no. 4 (2023): 48–60. http://dx.doi.org/10.5815/ijcnis.2023.04.05.

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Transmission of images on the network is considered insecure which has security-related issues. In this paper, to provide security to digital images, an encryption system that uses four chaotic maps for binary key sequence generation is proposed. The system consists of stages namely, confusion, generation of random binary chaotic key sequence, pseudo-random number generation (RN), and diffusion. Keys for encryption are chosen randomly based on a pseudo random generator from the selected chaotic maps by the linear feedback shift register (LFSR). The algorithm achieves good results in terms of NPCR, UACI, and entropy values. The developed cryptosystem resists differential attacks, is sensitive to minor alterations in the keys, and has a large key space.

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17

Pushpalatha, Gopalakrishna Saraswathy, and Siddaiah Ramesh. "Randomness properties of sequence generated using logistic map with novel permutation and substitution techniques." International Journal of Electrical and Computer Engineering (IJECE) 13, no. 4 (2023): 4369–78. https://doi.org/10.11591/ijece.v13i4.pp4369-4378.

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In this paper, a design of a chaos-based keystream generator (KSG) using a novel permutation technique with various two-dimensional patterns and a substitution technique with Z4 mapping is proposed. Initially, a chaotic function such as a logistic map is used to generate a pseudo-random number. Then these numbers are converted into binary sequences using binary mapping. In order to achieve statistical properties of the resultant binary sequences, a novel method of KSG is developed by considering parameters such as initial value “x0”, system parameter “r”, novel permutation techniques defined by 2-dimensional patterns, and substitution technique defined over Z4 transformation. The binary sequences so obtained are subjected to randomness tests by applying the National Institute of Standards and Technology (NIST) SP-800-22 (Revision 1a) test suite for investigation of its randomness properties to obtain suitable sequences which can be used as a key for cryptographic applications. From the results obtained, it is found that the binary sequences exhibit better randomness properties as per the cryptographic requirements.

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18

Budescu, David V. "A Markov model for generation of random binary sequences." Journal of Experimental Psychology: Human Perception and Performance 13, no. 1 (1987): 25–39. http://dx.doi.org/10.1037/0096-1523.13.1.25.

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19

G S, Pushpalatha, and Ramesh S. "Pseudo Random Binary Sequences Obtained Using Novel Chaos Based Key Stream Generator and their Auto-correlation Properties." International Journal on Recent and Innovation Trends in Computing and Communication 11, no. 5 (2023): 141–47. http://dx.doi.org/10.17762/ijritcc.v11i5.6588.

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In this paper, psuedo random binary sequences are generated from the “Chaos Based Key Stream Generator- using novel Permutation technique with two dimensional patterns and substitution technique with Z4 mapping” and investigation of auto correlation property for the generated seuwnces is presented. Initially a chaotic function, considering Logistic map is used to generate a Pseudo Random Numbers (PRNs). Then these numbers are converted into binary sequences using binary mapping. These sequences are further modified by novel permutation techniques defined using 2-Dimensional patterns, and substitution technique defined over Z4 transformation in order to improve their statistical properties. The resulting sequences are investigated for auto correlation properties using Normalized Hamming Auto Correlation function. The purpose of this work is to assessing the quality of sequences of uniformly distributed pseudorandom numbers from the proposed generator. It is found that, generated sequences exhibit good auto-correlation property which is suitable for key sequence or secret key for cryptographic applications.

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20

Mamun, Md Selim Al, and Fatema Akhter. "Pseudo Random Binary Sequence Based on Cyclic Difference Set." Symmetry 12, no. 8 (2020): 1202. http://dx.doi.org/10.3390/sym12081202.

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With the increasing reliance on technology, it has become crucial to secure every aspect of online information where pseudo random binary sequences (PRBS) can play an important role in today’s world of Internet. PRBS work in the fundamental mathematics behind the security of different protocols and cryptographic applications. This paper proposes a new PRBS namely MK (Mamun, Kumu) sequence for security applications. Proposed sequence is generated by primitive polynomial, cyclic difference set in elements of the field and binarized by quadratic residue (QR) and quadratic nonresidue (QNR). Introduction of cyclic difference set makes a special contribution to randomness of proposed sequence while QR/QNR-based binarization ensures uniformity of zeros and ones in sequence. Besides, proposed sequence has maximum cycle length and high linear complexity which are required properties for sequences to be used in security applications. Several experiments are conducted to verify randomness and results are presented in support of robustness of the proposed MK sequence. The randomness of proposed sequence is evaluated by popular statistical test suite, i.e., NIST STS 800-22 package. The test results confirmed that the proposed sequence is not affected by approximations of any kind and successfully passed all statistical tests defined in NIST STS 800-22 suite. Finally, the efficiency of proposed MK sequence is verified by comparing with some popular sequences in terms of uniformity in bit pattern distribution and linear complexity for sequences of different length. The experimental results validate that the proposed sequence has superior cryptographic properties than existing ones.

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21

Feng, Yalan, Huabin Wang, Dailei Zhang, Jiahao Li, and Liang Tao. "One-Factor Cancellable Fingerprint Template Protection Based on Index Self-Encoding." Journal of Database Management 34, no. 3 (2023): 1–18. http://dx.doi.org/10.4018/jdm.321546.

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The existing one-factor cancellable biometrics algorithms generally require random sequences to reorder the biometrics, which reduces the discrimination of the transformed biometrics. Some algorithms hide and transmit the random sequence by XORing the random sequence with original biometrics, which may cause the leakage of the original biometrics. Therefore, this paper proposes a one-factor cancellable fingerprint template protection based on index self-encoding. First, the integer sequence generated by the hash function is used as the index. The random sequence is automatically encoded directly by the index value, and the generated binary sequence retains the original biological characteristics to the greatest extent. Second, self-encoding binary sequence and random binary sequence are XORed to obtain the encoded key without directly storing binary factor sequences. Experiments are implemented on the fingerprint database of FVC2002 and FVC2004, the results show that the recognition rate is enhanced; meanwhile, it fits the design criteria of cancellable biometrics.

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22

Lehnert, J., and M. Pursley. "Error Probabilities for Binary Direct-Sequence Spread-Spectrum Communications with Random Signature Sequences." IEEE Transactions on Communications 35, no. 1 (1987): 87–98. http://dx.doi.org/10.1109/tcom.1987.1096667.

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23

Jugé, Vincent, and Irène Marcovici. "Finding automatic sequences with few correlations." Pure Mathematics and Applications 30, no. 1 (2022): 75–81. http://dx.doi.org/10.2478/puma-2022-0012.

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Abstract Although automatic sequences are very simple algorithmically, some of them have pseudo-random properties. In particular, some automatic sequences such as the Golay–Shapiro sequence are known to be 2-uncorrelated, meaning that they have the same correlations of order 2 as a uniform random sequence. However, the existence of ℓ-uncorrelated automatic sequences (for ℓ ⩾ 3) was left as an open question in a recent paper of Marcovici, Stoll and Tahay. We exhibit binary block-additive sequences that are 3-uncorrelated and, with the help of analytical results supplemented by an exhaustive search, we present a complete picture of the correlation properties of binary block-additive sequences of rank r ⩽ 5, and ternary sequences of rank r ⩽ 3.

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Haliuk, Serhii, Oleh Krulikovskyi, Dmytro Vovchuk, and Fernando Corinto. "Memristive Structure-Based Chaotic System for PRNG." Symmetry 14, no. 1 (2022): 68. http://dx.doi.org/10.3390/sym14010068.

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This paper suggests an approach to generate pseudo-random sequences based on the discrete-time model of the simple memristive chaotic system. We show that implementing Euler’s and Runge–Kutta’s methods for the simulation solutions gives the possibility of obtaining chaotic sequences that maintain general properties of the original chaotic system. A preliminary criterion based on the binary sequence balance estimation is proposed and applied to separate any binary representation of the chaotic time sequences into random and non-random parts. This gives us the possibility to delete obviously non-random sequences prior to the post-processing. The investigations were performed for arithmetic with both fixed and floating points. In both cases, the obtained sequences successfully passed the NIST SP 800-22 statistical tests. The utilization of the unidirectional asymmetric coupling of chaotic systems without full synchronization between them was suggested to increase the performance of the chaotic pseudo-random number generator (CPRNG) and avoid identical sequences on different outputs of the coupled systems. The proposed CPRNG was also implemented and tested on FPGA using Euler’s method and fixed-point arithmetic for possible usage in different applications. The FPGA implementation of CPRNG supports a generation speed up to 1.2 Gbits/s for a clock frequency of 50 MHz. In addition, we presented an example of the application of CPRNG to symmetric image encryption, but nevertheless, one is suitable for the encryption of any binary source.

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Gan, Hongping, Song Xiao, and Feng Liu. "Chaotic Binary Sensing Matrices." International Journal of Bifurcation and Chaos 29, no. 09 (2019): 1950121. http://dx.doi.org/10.1142/s0218127419501219.

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As an emerging field for sampling paradigms, compressive sensing (CS) can sample and represent signals at a sub-Shannon–Nyquist rate. To realize CS from theory to practice, the random sensing matrices must be substituted by faster measurement operators that correspond to feasible hardware architectures. In recent years, binary matrices have attracted much research interest because of their multiplier-less and faster data acquisition. In this work, we aim to pinpoint the potential of chaotic binary sequences for constructing high-efficiency sensing implementations. In particular, the proposed chaotic binary sensing matrices are verified to meet near-optimal theoretical guarantees in terms of both the restricted isometry condition and coherence analysis. Simulation results illustrate that the proposed chaotic constructions have considerable sampling efficiency comparable to that of the random counterparts. Our framework encompasses many families of binary sensing architectures, including those formed from Logistic, Chebyshev, and Bernoulli binary chaotic sequences. With many chaotic binary sensing architectures, we can then more easily apply CS paradigm to various fields.

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Sathyanarayana, S. V., M. Aswatha Kumar, and K. N. Hari Bhat. "Random Binary and Non-Binary Sequences Derived from Random Sequence of Points on Cyclic Elliptic Curve Over Finite FieldGF(2m) and Their Properties." Information Security Journal: A Global Perspective 19, no. 2 (2010): 84–94. http://dx.doi.org/10.1080/19393550903482759.

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27

Kozachok, A. V., A. A. Spirin, and O. M. Golembiovskaya. "Random forest based pseudorandom sequences classification algorithm." Proceedings of Tomsk State University of Control Systems and Radioelectronics 23, no. 3 (2020): 55–60. http://dx.doi.org/10.21293/1818-0442-2020-23-3-55-60.

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Recently, the number of confidential data leaks caused by internal violators has increased. Since modern DLP-systems cannot detect and prevent information leakage channels in encrypted or compressed form, an algorithm was proposed to classify pseudo-random sequences formed by data encryption and compression algorithms. Algorithm for constructing a random forest was used. An array of the frequency of occurrence of binary subsequences of 9-bit length and statistical characteristics of the byte distribution of sequences was chosen as the feature space. The presented algorithm showed the accuracy of 0,99 for classification of pseudorandom sequences. The proposed algorithm will improve the existing DLP-systems by increasing the accuracy of classification of encrypted and compressed data.

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Kawamoto, Kazuhiko, and Kaoru Hirota. "Random Scanning Algorithm for Tracking Curves in Binary Image Sequences." International Journal of Intelligent Computing in Medical Sciences & Image Processing 2, no. 2 (2008): 101–10. http://dx.doi.org/10.1080/1931308x.2008.10644158.

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29

Sanna, Carlo. "On the l.c.m. of random terms of binary recurrence sequences." Journal of Number Theory 213 (August 2020): 221–31. http://dx.doi.org/10.1016/j.jnt.2019.12.004.

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Merhav, Neri, and Tsachy Weissman. "Universal prediction of random binary sequences in a noisy environment." Annals of Applied Probability 14, no. 1 (2004): 54–89. http://dx.doi.org/10.1214/aoap/1075828047.

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Yarmolik, V. N., V. V. Petrovskaya, D. V. Demenkovets, and V. A. Levantsevich. "Controlled random tests with limited Hamming distance." Informatics 22, no. 1 (2024): 7–26. https://doi.org/10.37661/1816-0301-2025-22-1-7-26.

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Objectives. The problem of constructing controlled random tests with a fixed minimum Hamming distance is solved. The limitations of classical approaches to generating test patterns based on enumeration of test pattern candidates are shown. With an increase in the threshold values of the difference measures of binary test patterns, the computational complexity of constructing such tests increases. The main goal of this article is to develop methods for constructing tests based on initial templates and rules for expanding them to the required bit size.Methods. Based on the Hamming distance used in the theory and practice of forming controlled random tests, new measures of difference are considered for comparing two binary test patterns. The basis of the proposed measures of difference is the formation of a set of Hamming distances for the original patterns, represented as sequences of symbols of different alphabets.Results. The paper demonstrates the indistinguishability of pairs of binary test patterns using a difference measure based on the Hamming distance. In this case, different pairs of patterns may have coinciding Hamming distance values. New measures of difference for binary test sequences based on their representation as sequences consisting of symbols of different alphabets are considered. As an alternative to known solutions, an approach is proposed based on increasing the number of test patterns in a test while maintaining the minimum Hamming distance between patterns at an acceptable level. The main feature of the proposed approach is the use of the difference measure proposed by the authors based on determining the Hamming distance for test patterns consisting of symbols of different alphabets. It is shown that achieving the maximum Hamming distance value for patterns represented by a large number of binary symbols ensures the same distance value for the case when the symbols are specified by a smaller number of bits. This allows one to construct controlled random tests without the procedure of listing candidates for test patterns.Conclusion. The considered measures of difference expand the possibilities of generating test patterns when forming controlled random tests. It is shown that the use of various templates and rules applied to them allows constructing tests with a fixed minimum Hamming distance and the required bit size of test patterns.

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Sabir, Firas Ali, and Sadiq Habeeb Abdulhussain. "IMAGE BASED MULTI-LENGTH RANDOM KEY GENERATOR." Journal of Engineering 17, no. 03 (2011): 486–98. http://dx.doi.org/10.31026/j.eng.2011.03.11.

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Random Number Generators (RNGs) are an important building block for algorithms and protocols incryptography. They are dominant in the construction of encryption keys and other cryptographic algorithm parameters. In practice, statistical testing is employed to gather evidence that a generator indeed produces numbers that appear to be random. In this paper a new algorithm is proposed to generate variable length random binary sequence. The random sequence is generated by selecting different point from hashed digital images; the selecting process is organized in such a way to ensure randomness and to avoid regeneration of same sequence within a year. The generated sequences are tested to meet the National Institute of Standard and Technology (NIST) criteria. In proposed algorithm the traditional key exchange is not needed which gives advantage to the system from the security point of view. This proposed algorithm is capable of generating random binary sequences that can meet security requirements of cryptographic algorithms.

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Liu, Huaning, and Yinyin Yang. "Weighted Measures of Pseudorandom Binary Lattices." Studia Scientiarum Mathematicarum Hungarica 58, no. 3 (2021): 319–34. http://dx.doi.org/10.1556/012.2021.58.3.1502.

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In cryptography one needs pseudorandom sequences whose short subsequences are also pseudorandom. To handle this problem, Dartyge, Gyarmati and Sárközy introduced weighted measures of pseudorandomness of binary sequences. In this paper we continue the research in this direction. We introduce weighted pseudorandom measure for multidimensional binary lattices and estimate weighted pseudorandom measure for truly random binary lattices. We also give lower bounds for weighted measures of even order and present an example by using the quadratic character of finite fields.

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Ahmad, A., and A. Al Maashri. "On Sequence Lengths of Some Special External Exclusive OR Type LFSR Structures – Study and Analysis." Journal of Engineering Research [TJER] 11, no. 2 (2014): 1. http://dx.doi.org/10.24200/tjer.vol11iss2pp1-14.

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The study of the length of pseudo-random binary sequences generated by Linear- Feedback Shift Registers (LFSRs) plays an important role in the design approaches of built-in selftest, cryptosystems, and other applications. However, certain LFSR structures might not be appropriate in some situations. Given that determining the length of generated pseudo-random binary sequence is a complex task, therefore, before using an LFSR structure, it is essential to investigate the length and the properties of the sequence. This paper investigates some conditions and LFSR’s structures, which restrict the pseudo-random binary sequences’ generation to a certain fixed length. The outcomes of this paper are presented in the form of theorems, simulations, and analyses. We believe that these outcomes are of great importance to the designers of built-in self-test equipment, cryptosystems, and other applications such as radar, CDMA, error correction, and Monte Carlo simulation.

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Kumari, Priti, and Pramod Kumar Kewat. "2-Adic and Linear Complexities of a Class of Whiteman’s Generalized Cyclotomic Sequences of Order Four." International Journal of Foundations of Computer Science 30, no. 05 (2019): 759–79. http://dx.doi.org/10.1142/s0129054119500205.

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Although for more than 20 years, Whiteman’s generalized cyclotomic sequences have been thought of as the most important pseudo-random sequences, but, there are only a few papers in which their 2-adic complexities have been discussed. In this paper, we construct a class of binary sequences of order four with odd length (product of two distinct odd primes) from Whiteman’s generalized cyclotomic classes. After that, we determine both 2-adic complexity and linear complexity of these sequences. Our results show that these complexities are greater than half of the period of the sequences, therefore, it may be good pseudo-random sequences.

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Ding, Cunsheng. "Linear Complexity of Some Generalized Cyclotomic Sequences." International Journal of Algebra and Computation 08, no. 04 (1998): 431–42. http://dx.doi.org/10.1142/s021819679800020x.

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There are several kinds of cyclotomic sequences. They have a number of good random properties. In this paper we compute the linear complexity (linear span) of generalized cyclotomic binary sequences of order 2 with respect to p2.

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Li , Chunlei. "A Survey on Complexity Measures for Pseudo-Random Sequences." Cryptography 8, no. 2 (2024): 25. http://dx.doi.org/10.3390/cryptography8020025.

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Since the introduction of the Kolmogorov complexity of binary sequences in the 1960s, there have been significant advancements on the topic of complexity measures for randomness assessment, which are of fundamental importance in theoretical computer science and of practical interest in cryptography. This survey reviews notable research from the past four decades on the linear, quadratic and maximum-order complexities of pseudo-random sequences, and their relations with Lempel–Ziv complexity, expansion complexity, 2-adic complexity and correlation measures.

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Chmielowiec, Andrzej, and Paweł Litwin. "Efficient Inverted Index Compression Algorithm Characterized by Faster Decompression Compared with the Golomb-Rice Algorithm." Entropy 23, no. 3 (2021): 296. http://dx.doi.org/10.3390/e23030296.

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This article deals with compression of binary sequences with a given number of ones, which can also be considered as a list of indexes of a given length. The first part of the article shows that the entropy H of random n-element binary sequences with exactly k elements equal one satisfies the inequalities klog2(0.48·n/k)<H<klog2(2.72·n/k). Based on this result, we propose a simple coding using fixed length words. Its main application is the compression of random binary sequences with a large disproportion between the number of zeros and the number of ones. Importantly, the proposed solution allows for a much faster decompression compared with the Golomb-Rice coding with a relatively small decrease in the efficiency of compression. The proposed algorithm can be particularly useful for database applications for which the speed of decompression is much more important than the degree of index list compression.

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39

Jugé, Vincent, and Irène Marcovici. "Finding automatic sequences with few correlations." RAIRO - Theoretical Informatics and Applications 58 (2024): 10. http://dx.doi.org/10.1051/ita/2024008.

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Although automatic sequences are algorithmically very simple, some of them have pseudorandom properties. In particular, some automatic sequences such as the Golay–Shapiro sequence are known to be 2-uncorrelated, meaning that they have the same correlations of order 2 as a uniform random sequence. However, the existence of ℓ-uncorrelated automatic sequences (for ℓ ⩾ 3) was left as an open question in a recent paper of Marcovici, Stoll and Tahay. We exhibit binary block-additive sequences that are 3-uncorrelated and, with the help of analytical results supplemented by an exhaustive search, we present a complete picture of the correlation properties of binary block-additive sequences of rank r ⩽ 5, and ternary sequences of rank r ⩽ 3.

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Mohamed, Krim, Ali-Pacha Adda, and Hadj Said Naima. "The Quality of the New Generator Sequence Improvent to Spread the Color System's Image Transmission." TELKOMNIKA Telecommunication, Computing, Electronics and Control 16, no. 1 (2018): 402–14. https://doi.org/10.12928/TELKOMNIKA.v16i1.6583.

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This paper shows a new technic applicable for the digital devices that are the result of the finite’s effect precision in the chaotic dynamics used in the coupled technic and the chaotic map’s perturbation technics used for the generation of a Pseudo-Random Number Generator (PRNGs).The use of the pseudo- chaotic sequences coupled to the orbit perturbation method in the chaotic logistic map and the NewPiece-Wise Linear Chaotic Map (NPWLCM). The pseudo random number generator’s originality proposed from the perturbation of the chaotic recurrence. Furthermore the outputs of the binary sequences with NPWLCM are reconstructed conventionally with the Bernoulli’s sequences shifts map to change the shapes with the bitwise permetation then the results in simulation are shown in progress.After being perturbed, the chaotic system can generate the chaotic binary sequences in uniform distribution and the statistical properties invulnerable analysis. This generator also has many advantages in the possible useful applications of spread spectrum digitalimages, such as sensitive secret keys, random uniform distribution of pixels in Crypto system in secure and synchronize communication.

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Block, Henry, Mainak Mazumdar, and Sheldon M. Ross. "A NOTE ON GENERATING SYSTEMS COMPOSED OF BINARY AND TERNARY RANDOM VARIABLES." Probability in the Engineering and Informational Sciences 19, no. 2 (2005): 213–17. http://dx.doi.org/10.1017/s0269964805050114.

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Wan, Jie, and Jeffrey Z. J. Zheng. "Permutation and Complementary Algorithm to Generate Random Sequences for Binary Logic." International Journal of Communications, Network and System Sciences 04, no. 05 (2011): 345–50. http://dx.doi.org/10.4236/ijcns.2011.45039.

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Fairweather, A. J., M. P. Foster, and D. A. Stone. "MLS TESTING OF VRLA BATTERIES USING PSEUDO RANDOM BINARY SEQUENCES (PRBS)." World Electric Vehicle Journal 4, no. 2 (2010): 405–13. http://dx.doi.org/10.3390/wevj4020405.

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Cohan, Megan C., Min Kyung Shinn, Jared M. Lalmansingh, and Rohit V. Pappu. "Uncovering Non-random Binary Patterns Within Sequences of Intrinsically Disordered Proteins." Journal of Molecular Biology 434, no. 2 (2022): 167373. http://dx.doi.org/10.1016/j.jmb.2021.167373.

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Sinha, Aditya Kumar, Judhistir Mahapatro, and Bidisha Bhabani. "Random binary sequences generation using heartbeats for cryptographic keys in WBSNs." International Journal of Sensor Networks 38, no. 3 (2022): 191. http://dx.doi.org/10.1504/ijsnet.2022.121708.

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Golomb, S. W. "Distributions of periods and frequencies of runs in random binary sequences." Advances in Applied Mathematics 10, no. 3 (1989): 278–84. http://dx.doi.org/10.1016/0196-8858(89)90015-8.

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47

Savova, Zhaneta N., Antoniya T. Tasheva, and Rosen A. Bogdanov. "Method for the Simultaneous Generation of Two Nonlinear Pseudo Random Sequences: 5-ary and Binary." WSEAS TRANSACTIONS ON ELECTRONICS 14 (December 31, 2023): 71–78. http://dx.doi.org/10.37394/232017.2023.14.9.

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Multi-level signals and sequences have become a significant aspect of modern high-speed communication systems. Hence, to ensure the confidentiality and integrity of the transmitted information, advanced methods and devices are necessary to produce strong cryptographic properties for not only binary but also for nonbinary keystreams, which can be used in resource-constrained microcontrollers. The proposed method and apparatus generate both a balanced nonlinear 5-ary pseudo-random sequence and a binary keystream sequence. The nonlinearity is determined by applying shrinking and multiplexing techniques to the generated linear 5-ary pseudo-random sequence and the running zero in its conversion to a binary balanced sequence.

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48

Pikuza, M. O., S. Yu Mikhnevich, and A. Yu Siankevich. "Stability of Characteristics of Physical Random Number Generators." Doklady BGUIR 21, no. 3 (2023): 34–40. http://dx.doi.org/10.35596/1729-7648-2023-21-3-34-40.

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The development of technologies leads to the need of revising the methods used to obtain cryptographic keys. The randomness parameters of sequences generated by physical random sequence generators are affected by the physical parameters of the recording equipment and the environment. The requirements for the randomness of the sequence, when passing the binary test, are obtained. It is shown that as the sequence length increases, the requirements for possible deviations from the equiprobable distribution of 0 and 1 increase. The randomness stability of the sequences generated by the generator based on the study of photons is estimated. The oscillator under study consists of an LED and a compact silicon photomultiplier designed to detect low-power light radiation. Possible physical processes leading to the deterioration of the randomness of sequences are shown. The possibility of using a generator of random numerical sequences based on a small-sized silicon photomultiplier for cryptographic purposes is estimated.

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Ma, Jiang, Wei Zhao, Yanguo Jia, Xiumin Shen, and Haiyang Jiang. "Linear Complexity and Trace Representation of New Ding Generalized Cyclotomic Sequences with Period pq and Order Two." Mathematics 9, no. 18 (2021): 2285. http://dx.doi.org/10.3390/math9182285.

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Linear complexity is an important property to measure the unpredictability of pseudo-random sequences. Trace representation is helpful for analyzing cryptography properties of pseudo-random sequences. In this paper, a class of new Ding generalized cyclotomic binary sequences of order two with period pq is constructed based on the new segmentation of Ding Helleseth generalized cyclotomy. Firstly, the linear complexity and minimal polynomial of the sequences are investigated. Then, their trace representation is given. It is proved that the sequences have larger linear complexity and can resist the attack of the Berlekamp–Massey algorithm. This paper also confirms that generalized cyclotomic sequences with good randomness may be obtained by modifying the characteristic set of generalized cyclotomy.

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Korchynskyi, Volodymyr, Vitalii Kildishev, Oleksandr Riabukha, and Oleksandr Berdnikov. "THE GENERATING RANDOM SEQUENCES WITH THE INCREASED CRYPTOGRAPHIC STRENGTH." Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska 10, no. 1 (2020): 20–23. http://dx.doi.org/10.35784/iapgos.916.

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Random sequences are used in various applications in construction of cryptographic systems or formations of noise-type signals. For these tasks there is used the program generator of random sequences which is the determined device. Such a generator, as a rule, has special requirements concerning the quality of the numbers formation sequence. In cryptographic systems, the most often used are linearly – congruent generators, the main disadvantage of which is the short period of formation of pseudo-random number sequences. For this reason, in the article there is proposed the use of chaos generators as the period of the formed selection in this case depends on the size of digit net of the used computing system. It is obvious that the quality of the chaos generator has to be estimated through a system of the NIST tests. Therefore, detailed assessment of their statistical characteristics is necessary for practical application of chaos generators in cryptographic systems. In the article there are considered various generators and there is also given the qualitative assessment of the formation based on the binary random sequence. Considered are also the features of testing random number generators using the system. It is determined that not all chaos generators meet the requirements of the NIST tests. The article proposed the methods for improving statistical properties of chaos generators. The method of comparative analysis of random number generators based on NIST statistical tests is proposed, which allows to select generators with the best statistical properties. Proposed are also methods for improving the statistical characteristics of binary sequences, which are formed on the basis of various chaos generators.

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