Números primos especiales y sus aplicaciones criptográficas

El objeto de esta memoria es el estudio de ciertas clases de primos que, por estar dotados de propiedades especiales, resultan de interés para su uso en los criptosistemas de clave pública. Las clases de primos consideradas son las siguientes: a.- Los primos 1 - seguros, determinados por la siguiente propiedad: un primo p se denomina 1 - seguro si y sólo si p = 2q + 1 donde q es otro primo. b.- Los primos 2-seguros, determinados por la siguiente propiedad : un primo p se dice 2- seguro si p = 2q + 1 y además q es 1-seguro. c.- Los primos robustos. Sin entrar en definiciones muy rigurosas, podemos decir que esta clase de primos presenta varias variantes, que comparten entre sí la propiedad de que si p es un primo robusto entonces p + 1 y p 1 contienen factores primos "grandes"; y además algunos de estos factores presentan a su vez esta misma propiedad. En este trabajo se generalizan las definiciones de los puntos 1 y 2 introduciendo la noción de primo k- seguro de signatura arbitraria. Por ejemplo, de acuerdo con tal definición existen dos clases de primos 1- seguros: los de signatura + 1, que coinciden con los definidos en el punto 1 anterior; y los de signatura 1, que se escriben como 2q 1, donde q es otro primo. Obsérvese que la condición "p + 1 contiene un factor primo grande" se verifica de modo óptimo cuando p es un primo 1 - seguro de signatura 1. Análogamente, la condición "p 1 contiene un factor primo grande" se verifica de modo óptimo cuando p es un primo 1-seguro de signatura + 1. Se introduce una clase novedosa de primos robustos designados como "primos robustos óptimos". La idea consiste en definir una cierta función de variable discreta que permita caracterizar el grado de "robustez" de un primo robusto. Para cada clase de primos propuesta se estudian su distribución, su función recuento, la probabilidad de seleccionar uno de ellos aleatoriamente dentro del conjunto de los enteros positivos y el tiempo de computación asociado a la extracción aleatoria de uno de ellos. Con estos datos, es sencillo predecir un parámetro de importancia vital para los criptosistemas de clave pública; a saber, el tiempo necesario para el cambio de las claves, estimado con suficiente precisión: un buen sistema criptográfico para el que fuera muy costosa la modificación de claves resultaría inútil en la práctica. Muchos de los resultados obtenidos no han sido demostrados rigurosamente, si bien todos ellos se apoyan en conjeturas que, establecidas por autores clásicos, están confirmadas por múltiples experimentos numéricos dentro de los rangos que se utilizan en las aplicaciones actuales: conviene no perder de vista que las demostraciones de las conjeturas clásicas en teoría de números avanzan muy lentamente. El interés de esta memoria radica en que proporciona estimaciones heurísticas fiables acerca de los tiempos de computación necesarios para obtener primos de cada una de las clases antes referidas. Se presentan, por último, las aplicaciones prácticas junto con experimentos numéricos que constituyen la confirmación práctica de la exactitud de las predicciones teóricas

A group signature scheme based on the integer factorization and the subgroup discrete logarithm problems

8 pagesGroup signature schemes allow a user, belonging to a speci c group of users, to sign a message in an anonymous way on behalf of the group. In general, these schemes need the collaboration of a Trusted Third Party which, in case of a dispute, can reveal the identity of the real signer. A new group signature scheme is presented whose security is based on the Integer Factorization Problem (IFP) and on the Subgroup Discrete Logarithm Problem (SDLP).This work has been partially supported by the \Fundaci on Memoria D. Samuel Sol orzano Barruso" under the Project FS/7-2010.Peer reviewe

A multisignature scheme based on the SDLP and on the IFP

8 páginasMultisignature schemes are digital signature schemes that permit one to determine a unique signature for a given message, depending on the signatures of all the members of a speci c group. In this work, we present a new semi-short multisignature scheme based on the Subgroup Discrete Logarithm Problem (SDLP) and on the Integer Factorization Problem (IFP). The scheme can be carried out in an on- and o -line basis, is efficient, and the bitlength of the multisignature does not depend on the number of signers.This work has been partially supported by the \Fundación Memoria D. Samuel Solórzano Barruso" under the Project FS/7-2010.Peer reviewe

A group signature scheme based on the integer factorization and the subgroup discrete logarithm problems

8 pagesGroup signature schemes allow a user, belonging to a speci c group of users, to sign a message in an anonymous way on behalf of the group. In general, these schemes need the collaboration of a Trusted Third Party which, in case of a dispute, can reveal the identity of the real signer. A new group signature scheme is presented whose security is based on the Integer Factorization Problem (IFP) and on the Subgroup Discrete Logarithm Problem (SDLP).This work has been partially supported by the \Fundaci on Memoria D. Samuel Sol orzano Barruso" under the Project FS/7-2010.Peer reviewe

Trace-based cryptoanalysis of cyclotomic Rq,0×RqR_{q,0}\times R_q-PLWE for the non-split case

We describe a decisional attack against a version of the PLWE problem in which the samples are taken from a certain proper subring of large dimension of the cyclotomic ring $\mathbb{F}_q[x]/(\Phi_{p^k}(x))$ with $k>1$ in the case where $q\equiv 1\pmod{p}$ but $\Phi_{p^k}(x)$ is not totally split over $\mathbb{F}_q$. Our attack uses the fact that the roots of $\Phi_{p^k}(x)$ over suitable extensions of $\mathbb{F}_q$ have zero-trace and has overwhelming success probability as a function of the number of input samples. An implementation in Maple and some examples of our attack are also provided.Comment: 19 pages; 1 figure; Major update to previous version due to some weaknesses detecte

A Method for Unsupervised Semi-Quantification of Inmunohistochemical Staining with Beta Divergences

In many research laboratories, it is essential to determine the relative expression levels of some proteins of interest in tissue samples. The semi-quantitative scoring of a set of images consists of establishing a scale of scores ranging from zero or one to a maximum number set by the researcher and assigning a score to each image that should represent some predefined characteristic of the IHC staining, such as its intensity. However, manual scoring depends on the judgment of an observer and therefore exposes the assessment to a certain level of bias. In this work, we present a fully automatic and unsupervised method for comparative biomarker quantification in histopathological brightfield images. The method relies on a color separation method that discriminates between two chromogens expressed as brown and blue colors robustly, independent of color variation or biomarker expression level. For this purpose, we have adopted a two-stage stain separation approach in the optical density space. First, a preliminary separation is performed using a deconvolution method in which the color vectors of the stains are determined after an eigendecomposition of the data. Then, we adjust the separation using the non-negative matrix factorization method with beta divergences, initializing the algorithm with the matrices resulting from the previous step. After that, a feature vector of each image based on the intensity of the two chromogens is determined. Finally, the images are annotated using a systematically initialized k-means clustering algorithm with beta divergences. The method clearly defines the initial boundaries of the categories, although some flexibility is added. Experiments for the semi-quantitative scoring of images in five categories have been carried out by comparing the results with the scores of four expert researchers yielding accuracies that range between 76.60% and 94.58%. These results show that the proposed automatic scoring system, which is definable and reproducible, produces consistent results.FEDER / Junta de Andalucía-Consejería de Economía y Conocimiento US-1264994Fondo de Desarrollo (FEDER). Unión Europea PGC2018-096244-B-I00, SAF2016-75442-RMinisterio de Economía, Industria y Competitividad (MINECO). España TEC2017- 82807-

Dimension of the intersection of a pair of orthogonal groups

Let $g,h\colon V\times V\rightarrow mathbb{C}$ be two non-degenerate symmetric bilinear forms on a finite-dimensional complex vector space $V$. Let $G$ (resp.\ $H$) be the Lie group of isometries of $g$ (resp.\ $h$). If the endomorphism $L\colon \rightarrow V$ associated to $g,h$ is diagonalizable, then the dimension of the intersection group $G\cap H$ is computed in terms of the dimensions of the eigenspaces of $L$.Peer reviewe

Trace-based cryptanalysis of cyclotomic R_{q,0}xR_q-PLWE for the non-split case

We describe a decisional attack against a version of the PLWE problem in which the samples are taken from a certain proper subring of large dimension of the cyclotomic ring Fq[x]/(Φp k (x)) with k > 1 in the case where q ≡ 1 (mod p) but Φp k (x) is not totally split over Fq. Our attack uses the fact that the roots of Φp k (x) over suitable extensions of Fq have zero-trace and has overwhelming success probability as a function of the number of input samples. An implementation in Maple and some examples of our attack are also provided.Agencia Estatal de InvestigaciónUniversidad de Alcal

Two parallel pathways connect glutamine metabolism and mTORC1 activity to regulate glutamoptosis

Glutamoptosis is the induction of apoptotic cell death as a consequence of the aberrant activation of glutaminolysis and mTORC1 signaling during nutritional imbalance in proliferating cells. The role of the bioenergetic sensor AMPK during glutamoptosis is not defined yet. Here, we show that AMPK reactivation blocks both the glutamine-dependent activation of mTORC1 and glutamoptosis in vitro and in vivo. We also show that glutamine is used for asparagine synthesis and the GABA shunt to produce ATP and to inhibit AMPK, independently of glutaminolysis. Overall, our results indicate that glutamine metabolism is connected with mTORC1 activation through two parallel pathways: an acute alpha-ketoglutarate-dependent pathway; and a secondary ATP/AMPK-dependent pathway. This dual metabolic connection between glutamine and mTORC1 must be considered for the future design of therapeutic strategies to prevent cell growth in diseases such as cancer.Unión Europea(PGC2018-096244- B-I00, SAF2016-75442-R

Proyecto IRESUD: interconexión de sistemas fotovoltaicos a la red eléctrica en ambientes urbanos : Estado de avance a julio de 2014 y primeras mediciones en sistemas piloto

En el marco de una convocatoria del Ministerio de Ciencia, Tecnología e Innovación Productiva, se conformó, en el año 2011, el consorcio público-privado IRESUD entre la Comisión Nacional de Energía Atómica (CNEA), la Universidad Nacional de San Martín (UNSAM) y 5 empresas privadas, para la ejecución del proyecto “Interconexión de Sistemas Foto voltaicos a la Red Eléctrica en Ambientes Urbanos”. El principal objetivo del mismo es introducir en el país tecnologías asociadas con la interconexión a la red eléctrica, en áreas urbanas, de sistemas fotovoltaicos (FV), contemplando para ello cuestiones técnicas, económicas y regulatorias. En este trabajo, se presenta el grado de avance del proyecto en lo referente a las cuestiones regulatorias y a las instalaciones piloto realizadas o en ejecución en diferentes partes del país. Asimismo, se muestran las primeras mediciones de algunas de las instalaciones actualmente en operación y se analiza el comportamiento de un inversor FV de conexión a red.In the framework of a call from the Ministry of Science, Technology and Innovation, the public-private partnership IRESUD, formed by the National Atomic Energy Commission (CNEA), the National University of San Martín (UNSAM) and 5 private companies, was created to implement the project "Interconnection of Photovoltaic Systems to the Electrical Grid in Urban Areas". The main objective is to introduce technologies in the country associated with the interconnection to the grid of photovoltaic (PV) systems in urban areas, taking into account technical, economic and regulatory issues. In this paper, the degree of progress of the project regarding regulatory issues and pilot installations in different parts of the country is presented. Also, the first measurements of some of the facilities are also given and the behavior of a PV grid connected inverter is analyzed.Asociación Argentina de Energías Renovables y Medio Ambiente (ASADES