Ring-LWE Cryptography for the Number Theorist

In this paper, we survey the status of attacks on the ring and polynomial learning with errors problems (RLWE and PLWE). Recent work on the security of these problems [Eisentr\"ager-Hallgren-Lauter, Elias-Lauter-Ozman-Stange] gives rise to interesting questions about number fields. We extend these attacks and survey related open problems in number theory, including spectral distortion of an algebraic number and its relationship to Mahler measure, the monogenic property for the ring of integers of a number field, and the size of elements of small order modulo q.Comment: 20 Page

Représentation d'un polynôme par un circuit arithmétique et chaînes additives

Un circuit arithmétique dont les entrées sont des entiers ou une variable x et dont les portes calculent la somme ou le produit représente un polynôme univarié. On assimile la complexité de représentation d'un polynôme par un circuit arithmétique au nombre de portes multiplicatives minimal requis pour cette modélisation. Et l'on cherche à obtenir une borne inférieure à cette complexité, et cela en fonction du degré d du polynôme. A une chaîne additive pour d, correspond un circuit arithmétique pour le monôme de degré d. La conjecture de Strassen prétend que le nombre minimal de portes multiplicatives requis pour représenter un polynôme de degré d est au moins la longueur minimale d'une chaîne additive pour d. La conjecture de Strassen généralisée correspondrait à la même proposition lorsque les portes du circuit arithmétique ont degré entrant g au lieu de 2. Le mémoire consiste d'une part en une généralisation du concept de chaînes additives, et une étude approfondie de leur construction. On s'y intéresse d'autre part aux polynômes qui peuvent être représentés avec très peu de portes multiplicatives (les d-gems). On combine enfin les deux études en lien avec la conjecture de Strassen. On obtient en particulier de nouveaux cas de circuits vérifiant la conjecture.An arithmetic circuit with inputs among x and the integers which has product gates and addition gates represents a univariate polynomial. We define the complexity of the representation of a polynomial by an arithmetic circuit as the minimal number of product gates required for this modelization. And we seek a lower bound to this complexity, with respect to the degree d of the polynomial. An addition chain for d corresponds to an arithmetic circuit computing the monomial of degree d. Strassen's conjecture states that the minimal number of product gates required to represent a polynomial of degree d is at least the minimal length of an addition chain for d. The generalized Strassen conjecture corresponds to the same statement where the indegree of the gates of the arithmetic circuit is g instead of 2. The thesis consists, on the one hand, of the generalization of the concept of addition chains, and a study of the subject. On the other hand, it is concerned with polynomials which can be represented with very few product gates (d-gems). Both studies related to Strassen's conjecture are combined. In particular, we get new classes of circuits verifying the conjecture

Educação Ambiental na promoção e humanização da saúde: estudo de caso do presídio regional de Montes Claros – MG

A Educação Ambiental (EA) tem autonomia suficiente, pelos seus pressupostos, de redefinir o tipo de cidadão que se queira formar e os novos espaços territoriais a serem construídos para a humanidade. Nota-se a necessidade de articular as propostas e os objetivos da EA, no que tange as práticas de ensino aprendizagem em seus diversos níveis e modalidades, formais e informais. É importante também conhecer as particularidades de cada espaço, respeitando sua identidade cultural, ética, socioeconômica de sua população. Diante desse exposto, o objetivo deste trabalho é conhecer as políticas de integração que são desenvolvidas dentro do Presídio Regional de Montes Claros - PRMC4***, tomando como principal vertente a EA e compreender, como esses processos se articulam na humanização e promoção à saúde dos presos. A metodologia empregada foi pautada em uma discussão ampla em diversas referências teóricas de autores e pesquisadores imbuídos na Educação Ambiental, Território, Espaço Geográfico, na Promoção da Saúde e nos Sistemas Prisionais. Em seguida, foi elaborado um estudo de caso no PRMC, com visitas, onde os objetivos foram diagnosticados com maior afinco. A contribuição deste trabalho consiste em fortalecer as práticas da EA - ferramenta fundamental na elaboração de novos paradigmas entre sociedade e ambiente

Optimal Randomized Group Testing Algorithm to Determine the Number of Defectives

We study the problem of determining the exact number of defective items in an adaptive group testing by using a minimum number of tests. We improve the existing algorithm and prove a lower bound that shows that the number of tests in our algorithm is optimal up to small additive terms

Relação genética entre cepas de Neisseria meningitidis sorogrupo B sorotipo 4

We compared the results obtained by serotyping of PorB epitopes using an expanded panel of monoclonal antibodies (mAb) including mAb 7 and mAb 10, with results obtained by RFLP of rRNA genes (ribotyping). The purpose of this study was to assess the correlation between phenotypic- and genotypic- methods for typing N. meningitidis. The ribotypes obtained using ClaI or EcoRV endonucleases grouped the strains in seven and two different patterns, respectively. This additional characterization of PorB epitopes improved the correlation between these two methods of typing N. meningitidis.Nós comparamos os resultados obtidos pela sorotipagem usando um painel de anticorpos monoclonais (mAb) ao qual se incluíam os mAbs 7 e 10, com os resultados obtidos pelo RFLP do gene rRNA (ribotipagem). O propósito deste estudo foi avaliar a correlação entre os métodos fenotípico e genotípico de tipagem de N. meningitidis. Os ribotipos obtidos usando as endonucleases de restrição ClaI e EcoRV foram hábeis em dividir as cepas em sete e dois diferentes perfis de restrição, respectivamente. A caracterização adicional de epítopos na proteína PorB melhorou a correlação entre os dois métodos de tipagem de N. meningitidis

Copy Number Alteration and Mutational Profile of High-Grade B-Cell Lymphoma with MYC and BCL2 and/or BCL6 Rearrangements, Diffuse Large B-Cell Lymphoma with MYC-Rearrangement, and Diffuse Large B-Cell Lymphoma with MYC-Cluster Amplification.

The authors thank the technicians and scientists of the Genomics Core Facility of the IDIBAPS for their assistance in performing the NGS analysis.Diffuse large B-cell lymphoma (DLBCL) with MYC alteration is classified as high-grade B-cell lymphoma with MYC and BCL2 and/or BCL6 rearrangements (double/triple-hit lymphoma; DHL/THL), DLBCL with MYC rearrangement (single-hit lymphoma; SHL) and DLBCL with MYC-cluster amplification (MCAD). To elucidate the genetic features of DHL/THL, SHL, and MCAD, 23 lymphoma cases from Tokai University Hospital were analyzed. The series included 10 cases of DHL/THL, 10 cases of SHL and 3 cases of MCAD. The analysis used whole-genome copy number microarray analysis (OncoScan) and a custom-made next-generation sequencing (NGS) panel of 115 genes associated with aggressive B-cell lymphomas. The copy number alteration (CNA) profiles were similar between DHL/THL and SHL. MCAD had fewer CNAs than those of DHL/THL and SHL, except for +8q24. The NGS profile characterized DHL/THL with a higher "mutation burden" than SHL (17 vs. 10, p = 0.010), and the most relevant genes for DHL/THL were BCL2 and SOCS1, and for SHL was DTX1. MCAD was characterized by mutations of DDX3X, TCF3, HLA-A, and TP53, whereas MYC was unmutated. In conclusion, DHL/THL, SHL, and MCAD have different profiles.S