Publication: Análisis de la Independencia Estadística de las Pruebas de Aleatoriedad NIST SP 800-22
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2020-06
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Almaraz Luengo, Elena Salomé
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Abstract
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.
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.
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Trabajo de Fin de Grado en Ingeniería Informática, Facultad de Informática UCM, Departamento de Ingeniería del Software e Inteligencia Artificial, Curso 2020/2021.