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La importancia de la formación del docente a nivel educativo digital obliga a una revisión continua de los contenidos docentes. Para ello, se pretende revisar el programa de Matemáticas Empresariales en FBS y proponer recursos educativos digitales

Security in different applications is closely related to the goodness of the sequences generated for such purposes. Not only in Cryptography but also in other areas, it is necessary to obtain long sequences of random numbers or that, at least, behave as such. To decide whether the generator used produces sequences that are random, unpredictable and independent, statistical checks are needed. Different batteries of hypothesis tests have been proposed for this purpose. In this work, a survey of the main test batteries is presented, indicating their pros and cons, giving some guidelines for their use and presenting some practical examples., Depto. de Estadística e Investigación Operativa, Fac. de Ciencias Matemáticas, TRUE, pub

Communication, among others. Throughout history, different algorithms have been developed for the generation of such values and advances in computing have made them increasingly faster and more efficient from a computational point of view. These advances also allow the generation of higher-quality inputs (from the point of view of randomness and uniformity) for these algorithms that are easily tested by different statistical batteries such as NIST, Dieharder, or TestU01 among others. This article describes the existing algorithms for the generation of (independent and identically distributed—i.i.d.) Gamma distribution values as well as the theoretical and mathematical foundations that support their validity., Depto. de Estadística e Investigación Operativa, Fac. de Ciencias Matemáticas, TRUE, pub

2023 Acuerdos transformativos CRUE, In multiple applications, from Statistics to Particle Physics and notably in Cryptography and Computer Security, it is necessary to obtain long sequences of random numbers. In order to verify the properties of these sequences, different statistical tests are commonly applied, which are usually included in the so-called test batteries or test suites. The batteries need to be both effective and efficient. Their effectiveness relates to how well they can spot non-randomness behaviour, the efficiency is related to the computational time they require. It is therefore essential for tests included in batteries to measure their independence features: Test independence is important for good effectiveness, as high correlations between tests could lead to a decreased efficiency (testing for the same features multiple times) and effectiveness (missing an opportunity to test for an orthogonal randomness property when we essentially measure the same twice). Moreover, the related study of test coverage is often based on the assumption that tests are independent. This paper describes a series of experiments aimed at scrutinizing dependencies among the statistical tests in the NIST SP 800-22 suite. In order to do so, sequences of varying lengths from sources of varying entropy have been generated and tested. Afterwards, an inferential study was carried out to find whether significant correlations exist and to present our findings in a statistically sound way., Depto. de Ingeniería de Software e Inteligencia Artificial (ISIA), Fac. de Informática, TRUE, pub, APC financiada por la UCM

One of the fundamental aspects when working with batteries of statistic tests is that they should be as efficient as possible, i.e. that they should check the properties and do so in a reasonable computational time. This assumes that there are no tests that are checking the same properties, i.e. that they are not correlated. One of the most commonly used measures to verify the interrelation between variables is the Pearson’s correlation. In this case, linear dependencies are checked, but it may be interesting to verify other types of non-linear relationships between variables. For this purpose, mutual information has recently been proposed, which measures how much information, on average, one random variable provides to another. In this work we analyze some well-known batteries by using correlation analysis and mutual information approaches., Universidad Complutense de Madrid, Depto. de Ingeniería de Software e Inteligencia Artificial (ISIA), Depto. de Estadística e Investigación Operativa, Fac. de Informática, Fac. de Ciencias Matemáticas, TRUE, pub

Depto. de Estadística e Investigación Operativa, Fac. de Ciencias Matemáticas, TRUE, pub

Randomness testing is a key tool to analyse the quality of true (physical) random and pseudo-random number generators. There is a wide variety of tests that are designed for this purpose, i.e., to analyse the goodness of the sequences used. These tests are grouped in different sets called suites or batteries. The batteries must be designed in such a way that the tests that form them are independent, that they have a wide coverage, and that they are computationally efficient. One such battery is the well-known ENT battery, which provides four measures and the value of a statistic (corresponding to the chi-square goodness-of-fit test). In this paper, we will show that this battery presents some vulnerabilities and, therefore, must be redefined to solve the detected problems., Universidad Complutense de Madrid, Engineering and Physical Sciences Research Council (Reino Unido) - Proyecto Quantum Communications Hub, Innovate UK Industrial Strategy Challenge Fund, Depto. de Estadística e Investigación Operativa, Depto. de Ingeniería de Software e Inteligencia Artificial (ISIA), Fac. de Ciencias Matemáticas, Fac. de Informática, TRUE, pub

This work presents an analysis of the existing dependencies between the tests of the FIPS 140-2 battery. Two main analytical approaches are utilized, the first being a study of correlations through the Pearson’s correlation coefficient that detects linear dependencies, and the second one being a novel application of the mutual information measure that allows detecting possible non-linear relationships. In order to carry out this study, the FIPS 140-2 battery is reimplemented to allow the user to obtain p-values and statistics that are essential for more rigorous end-user analysis of random number generators (RNG)., Universidad Complutense de Madrid - Proyecto THEIA, Engineering & Physical Sciences Research Council (Reino Unido) - Proyecto Quantum Communications Hub, InnovateUK, Depto. de Estadística e Investigación Operativa, Depto. de Ingeniería de Software e Inteligencia Artificial, Fac. de Ciencias Matemáticas, Fac. de Informática, TRUE, pub

The generation of random sequences is the basis of simulation and can be used in many different areas such as Statistics, Computer Science, Systems Management and Control, Biology, Particle Physics, Cryptography or Cyber-Security, among others. It is crucial that the numbers generated were random or at least, behave as such. The fundamental statistical properties required for such sequences are randomness and independence and, from a cryptographic perspective, unpredictability. There is a variety of methods to generate these sequences. The main ones are physical and arithmetic methods. In this work, a detailed study of the main arithmetic methods is carried out. On the other hand, the necessity of secure sequence generation will be analyzed and new lines of ongoing research focusing applications in Internet of Things and new generator designs will be described., Depto. de Estadística e Investigación Operativa, Fac. de Ciencias Matemáticas, TRUE, pub

En este trabajo se trata la importancia de la computación cuántica en la informática, y más en concreto en la ciberseguridad. Para ello, en primer lugar, se realiza una introducción detallada de qué es la criptografía así como los principales algoritmos criptográficos. En segundo lugar, se expone la computación cuántica, comentando sus orígenes, explicando su funcionamiento y enfocándose en aspectos de ciberseguridad así como los principales algoritmos que usa o los ataques más conocidos. Una vez detallados estos conceptos, se centra en las VPNs, más en concreto en WireGuard, del cual se analizan detalladamente sus distintos algoritmos y se proponen cambios para adecuarlo al futuro post-cuántico. Por último también se explica y prueba la aplicación web de laboratorio de análisis de firma digitales, con la que se realizan pruebas entre distintos algoritmos de hash para ver sus distintas características y rendimientos., In this work we will deal with the importance of quantum computing in computing, and more specifically in cybersecurity. To do this, first, a detailed introduction of what cryptography is as well as the main cryptographic algorithms is made. Secondly, quantum computing is exposed, commenting on its origins, explaining its operation and focusing on cybersecurity aspects as well as the main algorithms it uses or the most well-known attacks. Once these concepts are detailed, it focuses on VPNs, more specifically on WireGuard, of which its different algorithms are analyzed in detail and changes are proposed to adapt it to the post-quantum future. Finally, the digital signature analysis laboratory web application is also explained and tested, with which tests are carried out between different hash algorithms to see their different characteristics and performance.

La información mutua es una cantidad que mide la dependencia entre dos variables aleatorias. En particular, mide cuánta información, en promedio, proporciona una variable aleatoria a otra. En el artículo “Measuring Independence between Statistical Randomness Tests by Mutual Information” [KALPMC+20] de Jorge Augusto Karell-Albo, Carlos Miguel Legón-Pérez, Evaristo José Madarro-Capó, Omar Rojas y Guillermo Sosa-Gómez, se propuso la información mutua para medir la dependencia entre pruebas de aleatoriedad. Esta nueva herramienta puede ser útil para futuros avances en criptografía: no solo tendríamos otra forma de ver las posibles dependencias entre pruebas, además de la conocida correlación de Pearson, sino que también puede ayudarnos a ver otras dependencias que esta última no era capaz de detectar, ya que la correlación de Pearson solo detecta dependencias lineales (una restricción que no afecta la información mutua). Para empezar, replicaremos los resultados del artículo, que utiliza información mutua para buscar dependencias en la batería NIST, para verificar que nuestras implementaciones del cálculo de información mutua y la posterior prueba de permutación son correctas. Luego, ampliaremos los análisis a otras baterías de tests conocidas, como ENT, FIPS 140-2 o DieHarder, para detectar sus dependencias y comprobar si la información mutua es una buena medida de independencia., Mutual information is a quantity that measures the dependence between two random variables. Particularly, it measures how much information, on average, one random variable provides to another. In the article “Measuring Independence between Statistical Randomness Tests by Mutual Information”[KALPMC+20] by Jorge Augusto Karell-Albo, Carlos Miguel Leg´on-P´erez, Evaristo Jos´e Madarro-Cap´o, Omar Rojas, and Guillermo Sosa-G´omez, this quantity is proposed to measure the dependence between randomness tests. This new tool can be helpful for future advances in cryptography: not only would we have another way of seeing possible dependencies between tests, apart from the well-known Pearson correlation, but it can also help us to see other dependencies that the latter was not able to detect, since the correlation Pearson’s only detects linear dependencies (a constraint that does not affect mutual information). To begin with, we will replicate the results of the article, which uses mutual information to look for dependencies in the National Institute of Standards and Technology (NIST) battery, to verify that our implementations of the mutual information calculation and the permutation test are correct. Then, we will extend the analyses to other known test batteries, such as ENT, Federal Information Processing Standards (FIPS) 140-2, or DieHarder, to detect their dependencies and to test the mutual information as an independence measure.

The mobile device ecosystem has dramatically evolved over the last few years, since users have openly embraced a massive use of mobile phones for different purposes: professional use, personal use, etc. Digital videos can be used to define legal responsibilities or as part of the evidence in trials. The forensic analysis of digital videos becomes very relevant to determine the origin and authenticity of a video in order to link an individual with a device, place or event. The field of forensic analysis of digital videos is constantly facing new and direct challenges. Even though the basic principles of this discipline remain unchanged, numerous issues appear every year that require new procedures and tools. Therefore, it is necessary to provide forensic analysts with techniques to identify the origin of multimedia content. In this paper, the topic of source identification in open scenarios will be discussed, since analysts do not know in advance the set of cameras to which a video belongs so they find it difficult to identify its source. This approach is similar to real-life situations since in most cases, analysts are unaware of the set of video cameras. This paper aims to create a technique that identifies the source of digital videos generated by digital devices through the use of unsupervised algorithms based on the analysis of the structure of multimedia video devices., Depto. de Estadística e Investigación Operativa, Fac. de Ciencias Matemáticas, TRUE, pub

Uno de los aspectos críticos de la comunicación encriptada consiste en la buena generación de números aleatorios, tanto para usarlos directamente como cifrado como para poder inicializar otros métodos de encriptación. No obstante, medir un concepto como la aleatoriedad no es una tarea sencilla. Para tratar de solucionar este problema, se usa la inferencia estadística. Mediante test de hipótesis, se trata de buscar debilidades en una secuencia, que permitan rechazar la hipótesis de que esa secuencia es aleatoria. Para que estos test nos aporten información real sobre la secuencia, deben ser independientes entre sí. Hemos realizado un experimento con una gran cantidad de datos para determinar si la batería de test de aleatoriedad más ampliamente utilizada, la NIST SP 800-22, realmente cumple, tal como dice cumplir, con la independencia de sus test. Hemos analizado los datos para ver qué test aportan más información, y cuáles pueden ser redundantes. Además,hemos puesto a prueba otros tipos de debilidades en la batería., One of the most critical aspects of encrypted communications consists on properly generating random numbers, either for straight use as a cipher or else to initialise other encryption algorithms. Nonetheless, assessing randomness is no easy task. In order to tackle this problem, statistical inference is used. Vulnerabilities of randomness are sought in sequences by means of hypothesis tests, through which the hypothesis that the sequence is random can be rejected. For these tests to yield real information on the sequence, the tests cannot be redundant, and should be independent. We have carried out an experiment with a big amount of data in order to assess whether the most widely used randomness tests battery, National Institute of Standards and Technology (NIST) Special Publication (SP) 800-22, really has independent tests, as the organisation claims to have. We have analysed the data to determine which tests offer more information, and which are redundant. Besides, we have tested for other flaws in the battery.

We study a stochastic model for the spread of two pathogen strains –termed type-1 and type-2 – amongst a homogeneously mixing community consisting of a finite number of individuals. In the model we assume partial cross-immunity,exogenous streams of infection, and that the degree of severity of a newly infective individual depends on who this infective individual was infected by. The aim is to characterize the joint probability distribution of the numbers M1 and M2 of type-1 and type-2 infections suffered by a focal individual during an outbreak of the disease. We present iterative procedures for computing the probability mass function of (M1, M2) under the assumption that the initial state of the focal individual is known, and a numerical study of the model is performed to investigate the influence of certain key parameters on the spread of resistant bacteria in hospitals., Ministerio de Economía y Competitividad (MINECO), Depto. de Estadística e Investigación Operativa, Fac. de Ciencias Matemáticas, FALSE, pub

A Markov-modulated framework is presented to incorporate correlated inter-event times into the stochastic susceptible-infectious-recovered (SIR) epidemic model for a closed finite community. The resulting process allows us to deal with non-exponential distributional assumptions on the contact process between the compartment of infectives and the compartment of susceptible individuals, and the recovery process of infected individuals, but keeping the dimensionality of the underlying Markov chain model tractable. The variability between SIR-models with distinct level of correlation is discussed in terms of extinction times, the final size of the epidemic, and the basic reproduction number, which is defined here as a random variable rather than an expected value., Universidad Complutense de Madrid, Depto. de Estadística e Investigación Operativa, Fac. de Ciencias Matemáticas, TRUE, pub

It is proved that for any quasi-filiform of non-zero rank the solvable Lie algebra obtained by adjoining a maximal torus of outer derivations is complete. Further, for any positive integer m, it is shown that there exist solvable complete Lie algebras with the second ChevalleyEilenberg cohomology group of arbitrary dimension., Depto. de Álgebra, Geometría y Topología, Fac. de Ciencias Matemáticas, Instituto de Matemática Interdisciplinar (IMI), TRUE, pub

The aim of this work is to show that on certain ocasions classic decision rules used in the context of options (Stochastic Dominance criteria and Mean-Variance rules) do not provide a selection of one specific option over the other, therefore, the need of working with other criteria that can help us in our choice. We place special interest in economic and financial applications., Depto. de Estadística e Investigación Operativa, Fac. de Ciencias Matemáticas, TRUE, pub

We consider the classical ruin problem due to Cramér and Lundberg and we generalize it. Ruin times of the considered models are studied and sufficient conditions to usual stochastic dominance between ruin times are established. In addition an algorithm to simulate processes verifying the conditions under consideration is proposed., Depto. de Estadística e Investigación Operativa, Fac. de Ciencias Matemáticas, TRUE, pub

Depto. de Estadística e Investigación Operativa, Fac. de Ciencias Matemáticas, TRUE, pub

Las aproximaciones mas usuales para comparar inversiones en riesgo estan basadas en la media y en la varianza de las variables aleatorias. Esto tiene sus inconvenientes ya que la presencia de la varianza provoca inconsistencia con la regla FSD. Debido a esto, se ha intentado generalizar este concepto atendiendo a otras medidas de riesgo. Es de interes el preguntarse si dichas funciones de utilidad propuestas son consistentes o no con las reglas de dominancia estocasticas. El objetivo de este trabajo es establecer relaciones entre las funciones de utilidad de nidas por Ogryczak, de variables aleatorias ponderadas dadas las relaciones entre las variables originales y estudiar bajo que condiciones la relacion existente entre las utilidades de las variables aleatorias originales se conserva para el caso de la ponderacion de las mismas, ademas de abordar la aplicacion a las nanzas y analisis de riesgos.

El objetivo es analizar con evidencias empíricas, obtenidas mediante herramientas estadísticas e informáticas, las posibles diferencias de género en el rendimiento académico en las asignaturas de Matemáticas, en grados no STEM, como son ADE y FBS