Index Of Coincidence Research Articles

Informationally overcomplete measurements from generalized equiangular tight frames

Informationally overcomplete measurements find important applications in quantum tomography and quantum state estimation. The most popular are maximal sets of mutually unbiased bases, for which trace relations between measurement operators are well known. In this paper, we introduce a more general class of informationally overcomplete positive, operator-valued measure (POVMs) that are generated by equiangular tight frames of arbitrary rank. This class provides a generalization of equiangular measurements to non-projective POVMs, which include rescaled mutually unbiased measurements and bases. We provide a method of their construction, analyze their symmetry properties, and provide examples for highly symmetric cases. In particular, we find a wide class of generalized equiangular measurements that are conical two-designs, which allows us to derive the index of coincidence. Our results show benefits of considering a single informationally overcomplete measurement over informationally complete collections of POVMs.

Entropic uncertainty relations for measurements assigned to a projective two-design

The current study aims to examine uncertainty relations for quantum measurements assigned to a projective two-design. Complete sets of mutually unbiased bases and symmetric informationally complete measurements are important cases of such measurements. To characterize the amount of uncertainty, we use the Tsallis and Rényi entropies as well as the probabilities of separate outcomes. The obtained results are based on an estimation of the index of coincidence. They improve some uncertainty relations given in the literature.

An artificial neural network approach to finding the key length of the Vigenère cipher

In this article, we create an artificial neural network (ANN) that combines both classical and modern techniques for determining the key length of a Vigenère cipher. We provide experimental evidence supporting the accuracy of our model for a wide range of parameters. We also discuss the creation and features of this ANN along with a comparative analysis between our ANN, the index of coincidence, and the twist-based algorithms.

Avaliação precoce da interação genótipo x safras na cultura da mandioca sob déficit hídrico

ABSTRACT The aim of this study was to evaluate the effect of genotype x harvest interactions on different agronomic traits, the genetic correlation between traits in early selection under water stress, and early selection in cassava. 25 cassava genotypes were evaluated in a randomized block experimental design with four replications. The variables root weight (RW), root number per plant (RN), root diameter (RD), root length (RL), root dry matter content (DMC), stem number per plant (SN), plant height (PH), stem diameter (SD), mite severity (MS), and harvest index (HI) were evaluated under water stress conditions in two harvests. Broad-sense heritability (h²), realized heritability ( ( h R 2 )), and the index of coincidence (IC) were estimated. Accuracy estimates ranged from 0.62 for RL to 0.86 for DMC. A significant genotype effect was identified on all traits, except for RW, RL and SD. Significant genotype x harvest interactions occurred for the variables SN, PH, SD, and HI. (h²) estimates ranged from 0.27 for RL to 0.79 for SN. The estimates of the index of coincidence ranged from 100% to 25%. A positive correlation was observed between all variables under study, except for MS, RN and SN, and the other traits. The genotypes showed similar performance in the two harvests for most variables, except for SN, PH, SD, and HI.

Evaluation of the Aging of Oil‐Paper Insulation Using an Improved Fractional Poynting‐Thomson Model

Assessment of the aging of oil‐paper insulation is analyzed in this article, based on an improved fractional Poynting‐Thomson model, which includes dc and hopping conductivity (P‐T model2). Based on samples of oil paper produced in laboratories with different thermal aging times, it has been found that the proposed improved model provides a better fit and a higher index of coincidence concerning the measured values than the traditional P‐T model and the model that only incorporates the effect of dc conductivity (P‐T model1). Nevertheless, comparing the proposed improved P‐T model with the traditional Cole–Cole (C‐C), Davidson–Cole (D‐C), and Havriliak–Negami (H‐N) models, the improved P‐T model2 also demonstrated a superior fit for the measured value and a higher coincidence index than another model. In addition, there was an excellent exponential relationship between the quantities εa, εb and τ of the improved model and the furfural content of the samples. Consequently, these characteristic quantities could be utilized to estimate the furfural content in the oil‐paper insulation and evaluate the insulation's condition. © 2023 Institute of Electrical Engineer of Japan and Wiley Periodicals LLC.

Entropic uncertainty relations from equiangular tight frames and their applications

Finite tight frames are interesting in various topics including questions of quantum information. Each complex tight frame leads to a resolution of the identity in the Hilbert space. Symmetric informationally complete measurements are a special class of equiangular tight frames. Applications of such frames in quantum physics deserve more attention than they have obtained. We derive uncertainty relations for a quantum measurement assigned to an equiangular tight frame. Main results follow from estimation of the corresponding index of coincidence. State-dependent and state-independent formulations are both addressed. Also, we discuss applications of considered measurements to detect entanglement and other correlations.

Modified Vigenère cipher algorithm based on new key generation method

Nowadays, as communication and network technologies evolve in modern life, ensuring the confidentiality of a cryptography system has become a critical requirement. The Vigenère cipher is attracting the attention of cryptography specialists, although the Vigenère cipher algorithm has a problem. The problem is due to a repeating encryption key. As a result of the multiple cryptographic approaches described in the literature, this paper proposes a novel encryption strategy for safe and secure data exchange by utilizing a new key generation process. The proposed encryption approach avoids the issue of repeating keys. Additionally, the classic Vigenère cipher encrypts the plaintext using a 26x26 Vigenère table, the researcher modified the original Vigenère table to 95x95, which adds more potential letters, mathematical symbols, numerals, and punctuation to a standard QWERTY keyboard layout. Additionally, the researcher added case sensitivity. To observe the performance of the proposed method, the index of coincidence and entropy have been calculated. The obtained results confirm the high performance of the proposed algorithm in comparison to the other algorithms used in this paper. The primary goal of this paper is to make cryptanalysis extremely complex and to promote data security.

University of Library Studies and Information Technologies

This paper provides implementations of three well-known ciphers – Caesar Cipher, Vigenere Cipher and Hill Cipher in Microsoft Excel. It is shown how the ciphers can be broken by using Brute-force Attack, Frequency Analysis Attack and Known-plaintext Attack. For the purpose of the cryptanalysis the relative occurrence frequencies of the letters and the index of coincidence (κ ) in Bulgarian language are determined. The classical Frequency Analysis Attack is modified using the cross-correlation between frequencies of letters in the natural language and the cipher text. Modular matrix operations in MS Excel are shown.

Selection of the Optimal Number of Topics for LDA Topic Model-Taking Patent Policy Analysis as an Example.

This study constructs a comprehensive index to effectively judge the optimal number of topics in the LDA topic model. Based on the requirements for selecting the number of topics, a comprehensive judgment index of perplexity, isolation, stability, and coincidence is constructed to select the number of topics. This method provides four advantages to selecting the optimal number of topics: (1) good predictive ability, (2) high isolation between topics, (3) no duplicate topics, and (4) repeatability. First, we use three general datasets to compare our proposed method with existing methods, and the results show that the optimal topic number selection method has better selection results. Then, we collected the patent policies of various provinces and cities in China (excluding Hong Kong, Macao, and Taiwan) as datasets. By using the optimal topic number selection method proposed in this study, we can classify patent policies well.

Strategies for the analysis of single-tree plot experiments in Eucalyptus plantations

To verify if the response by Eucalyptus clones in a single-tree plot is influenced by neighboring plants and to determine the effect of missing and/or dominated plants, seven eucalyptus trials in four Brazilian states were analyzed in a randomized complete block design with one plant/plot and 30 replications. Mean annual increment (MAI, m3 ha−1 per year) was determined for three-year-old clones. The influence of neighboring clones was estimated by a linear regression coefficient between the MAI of each clone/plot and the average of a clonal MAI and its eight neighbors. To determine the effect of missing and/or dominated trees, a correction between the MAI and the area available/plant was applied. Subsequent analysis considered unadjusted and adjusted data for missing and dominated trees. Estimate of accuracy and index of coincidence were used to compare the adjustments. In single-tree plots, clone performances were not influenced by neighboring plants. Experimental accuracy was not increased by any of the adjustments employed and the clone ranking was not altered, and therefore did not justify their use.

A sequence of Appell polynomials and the associated Jakimovski–Leviatan operators

We are concerned with a special sequence of Appell polynomials, related to the Renyi and Tsallis entropies for the binomial distribution. The generating function is investigated: it is logarithmically convex and has remarkable connections with the modified Bessel function $$I_0(t)$$ and with the index of coincidence for Poisson distribution. The specific form of the Appell polynomials leads to specific properties of the associated Jakimovski–Leviatan operators.

Diagnostic and Prognostic Markers of Chronic Heart Failure in Patients with Occupational Chronic Obstructive Pulmonary Disease

Aim Heart failure (HF) and chronic obstructive pulmonary disease (COPD) are a common comorbidity. Professional chronic obstructive pulmonary disease (PCOPD) is a specific phenotype, which suggests peculiarities in the development of HF. Difficulties of HF diagnosis in such patients determine the relevance of searching for additional markers. The aim of the study was identifying HF markers in patients with PCOPD.Material and methods This single-site, cohort, prospective, observational study included 345 patients. The main group consisted of PCOPD patients; the comparison group consisted of patients with COPD induced by tobacco smoking; and the control group included conventionally healthy individuals. The groups were matched by the index of coincidence; pairs were matched at 1:1 by the "nearest neighbor index"; covariates for matching included COPD duration, sex, and age. Each group included 115 patients. The major professional adverse factors were silica-containing dust and organic solvents. COPD was diagnosed according to GOLD criteria; HF was diagnosed in accordance with Russian clinical guidelines. The markers were determined by multifactorial logistic regression. Likelihood of events with allowance for the time to the event was analyzed by the Kaplan-Meier method.Results HF in PCOPD patients was characterized by biventricular damage, preserved left ventricular ejection fraction, and frequent hospitalizations for decompensation (17.5 % vs. 9.5 % for COPD in smokers). HF markers in patients with PCOPD included the length of work of more than 20 years, pulmonary artery systolic pressure (PASP) higher than 35 mm Hg according to data of Doppler echocardiography, diffusing capacity of lungs for carbon monoxide (DLCO) less than 50 %, increased serum concentrations of CC-chemokine ligand 18 (CCL18), S-100‑beta protein, and N-terminal pro-brain natriuretic peptide (NT-pro-BNP). Diagnostic sensitivity of the multifactorial model was 84 % and specificity was 81 %. Two models were proposed for purposes of screening, which included the following parameters: length of work, exposure to aromatic hydrocarbons, decreased distance in 6-min walk test by more than 60 m per year and length of work, exposure to inorganic dust, and decreased forced expiratory volume during the first second by more than 55 ml per year.Conclusion The markers for development of HF in PCOPD patients are length of work >20 years, PASP >35 mm Hg, DLCO <50 %, and increased serum concentrations of CCL18, S-100‑beta protein, and NT-pro-BNP.

The Comparison of Sensitivity and Specificity of ELISA-based Microneutralization Test with Hemagglutination Inhibition Test to Evaluate Neutralizing Antibody against Influenza Virus (H1N1)

The most common serological assay to measure anti-influenza antibodies is hemagglutination inhibition (HI) assay. Recently, neutralizing antibodies against influenza virus infection or vaccination can also be detected using microneutralization assays and occasionally, have greater sensitivity than the standard HI assays. The study aimed to compare the sensitivity and specificity of ELISA-based microneutralization (microNT-ELISA) and conventional HI assays in order to detect influenza H1N1 virus antibodies.MicroNT-ELISA was set up according to the WHO Manual on Influenza Diagnosis and Surveillance in Virology Department of Tehran University of Medical Sciences for the detection of neutralizing antibodies against H1N1 influenza virus in 2013. Fifty serum samples were analyzed with both HI and microNT-ELISA assays. Correlation between methods was calculated by linear regression analysis.The linear correlation coefficient squares, R2, of microNT-ELISA and HI test was 0.61 (P<0.0001) and we observed a high index of coincidence between the two tests. According to McNemar's test, there was no statistically significant difference between these two assays (P>0.05).The sensitivity and specificity of microNT-ELISA assay were high (87% and 73%, respectively) and closely related to gold standard test results. Therefore, microNT-ELISA is recommended as an alternative or complementary test to conventional HI assay for serological and epidemiological purposes.

Genetic algorithm attack on Enigma’s plugboard

The history, operating principles, strengths, and weaknesses, of the German cipher machine Enigma, have been widely studied for almost 50 years. Even though Bletchley Park regularly broke Enigma encrypted traffic during World War II, new pieces of information and fresh analysis are still aggregated to the remarkable “puzzle” called Enigma. This paper shows that Enigma’s plugboard is vulnerable to Genetic Algorithm (GA) attacks, which solves Enigma’s plugboard faster than earlier published ciphertext-only techniques. The Genetic Algorithm does this using the counting measure Index of Coincidence (IC). Independently of the GA, but related to the analysis, we introduce a new measure Progress Index of Coincidence (PIC). PIC is a measure of the relative progress in decryption between the ciphertext and plaintext measured by IC.

Graphemic-phonetic diachronic linguistic invariance of the frequency and of the Index of Coincidence as cryptanalytic tools.

Languages have inherent characteristics that make them their own and differentiated entities within their phyla and families. Even messages written in any language and later encrypted by cryptographic systems do not lose all of their characteristics, there remain aspects that help the cryptanalyst to recover them without knowing the decryption keys. For the characterization of the languages we will consider the frequencies of their graphemic and phonetic units and the Index of Coincidence, tools of fundamental utility in the field of Cryptography. Their diachronic invariance or survival over time in one language and their ability to discriminate against other languages will be analized. In order to do so, we will examine a total of 101 languages of which 261 texts have been taken. All of them are very diverse in style and time, taking us through a wide linguistic and temporal spectrum that will cover the period from the 6th century BC to the present day.

Bounds for some entropies and special functions

We consider a family of probability distributions depending on a real parameter and including the binomial, Poisson and negative binomial distributions. The corresponding index of coincidence satisfies a Heun differential equation and is a logarithmically convex function. Combining these facts we get bounds for the index of coincidence, and consequently for Renyi and Tsallis entropies of order 2.

Vigenère scores for malware detection

Previous research has applied classic cryptanalytic techniques to the malware detection problem. Specifically, scores that are based on simple substitution cipher cryptanalysis have been considered. In this research, we analyze two malware scoring techniques based on the classic Vigenere cipher. Our first approach relies only on the index of coincidence (IC), which is used for example, to determine the length of the keyword in a Vigenere ciphertext. To compute the IC, we consider both the Kasisky Test and Friedman’s Test. We also consider a score based on a more complete cryptanalysis of a Vigenere cipher, where the IC calculation is the first step. We find that both of these scores outperform comparable malware scores in selected cases.

Cryptanalysis of Chaocipher and solution of Exhibit 6

ABSTRACTChaocipher is a manual encryption method designed by John F. Byrne in 1918. Until he passed away in 1960, Byrne fervently believed that his cipher system was unbreakable, regardless of the amount of material available to a cryptanalyst. For several decades, he tried (unsuccessfully), to propose the Chaocipher to government agencies. In 1953, he exposed his Chaocipher in his autobiography, Silent Years, providing several examples of texts encrypted with Chaocipher as challenges, but without divulging the inner workings of the cipher. Those were made public only in 2010, when Byrne’s family donated the entire corpus of Chaocipher papers to the National Cryptologic Museum (NCM) in Fort Meade.A known-plaintext method for recovering the key settings, given sufficient matching plaintext and ciphertext, was published in 2010. However, to date, no method for the cryptanalysis of a single ciphertext-only Chaocipher message has been proposed, nor for the cryptanalysis of short messages “in-depth,” i.e., multiple messages generated with the same initial key settings.In this article, the authors present a new hillclimbing algorithm for a ciphertext-only cryptanalysis of Chaocipher in-depth messages. This algorithm is based on a “divide-and-conquer” approach and the use of the Index of Coincidence. It takes advantage of a major weakness in the design of the cipher. This previously unknown weakness may have been the reason why William F. Friedman, the inventor of the Index of Coincidence, rejected Byrne’s offer for the use of Chaocipher by the U.S. government. Additionally, the authors present a known-plaintext attack for short in-depth messages, as well as the solution for Lou Kruh’s and Cipher Deavours’s alternate Exhibit 5, also known as “Exhibit 6.” Finally, the authors reevaluate the security of the Chaocipher in view of those findings, with the conclusion that in its classic form, as designed by Byrne, the Chaocipher was a relatively weak cipher, despite Byrne’s rather strong assertions to the contrary.

GENETIC DIVERSITY IN A STRUCTURED FAMILY OF SIX GENERATIONS OF ORNAMENTAL CHILI PEPPERS (CAPSICUM ANNUUM)

The genus Capsicum has been used as an ornamental plant, but there are only a few commercial cultivars for this purpose available in Brazil. The aim of this study was to analyze the genetic diversity in a structured family of six generations of ornamental pepper based on quantitative and qualitative data, separately and integrated in the same analysis. These studies are part of the Capsicum breeding program developed at Universidade Federal da ParaA­ba and Universidade Federal de ViA§osa. Six generations (P1, P2, F1, F2, BC1, and BC2) of ornamental pepper, belonging to the germplasm bank of Universidade Federal da ParaA­ba, were evaluated. Two accessions of ornamental pepper plants belonging to the germplasm bank of UFPB (01 and 132) were chosen based on an earlier diallel study. Ten plants of each parent and F1, 72 plants of backcross 1 (BC1), 75 plants of backcross 2 (BC2), and 147 plants of the segregating F2 generation were studied. Analysis of genetic diversity was performed for all generations. Quantitative data were subjected to cluster analysis by Tocher’s method. Multi-traits were analyzed based on the arithmetic complement of the index of coincidence. The matrices of quantitative and multi-categorical traits were summed, and data were subjected to cluster analysis by Tocher’s optimized method. The relative importance of the traits was evaluated by Singh (1981)’s method. High genetic variability was determined in F2 and backcrosses by three cluster analyses, showing that parents 01 and 132 differ for the evaluated traits. According to the relative importance of traits, those that most contributed to genetic divergence were number of seeds per fruit, number of fruits per plant, days to flowering and days to fruiting.

Uncertainty relations based on mutually unbiased measurements

We derive uncertainty relation inequalities according to the mutually unbiased measurements. Based on the calculation of the index of coincidence of probability distribution given by \(d+1\) MUMs on any density operator \(\rho \) in \({\mathbb {C}}^{d}\), both state-dependent and state-independent forms of lower entropic bounds are given. Furthermore, we formulate uncertainty relations for MUMs in terms of Rényi and Tsallis entropies.