A Study of the Relationship between Foreign Aid and Human Development in Africa

Why are some countries more prosperous than others? Why are some countries still poor? What can be done by the West to help the rest to overcome the poverty trap? Finding better answers to these questions still represents the research agenda for development economists and political agenda for government and international institutions. Of course, the first two questions are age‐old ones and have been asked since the beginning of our history. The economic literature has identified important factors that influence the wealth of nations and they include: openness to trade, natural resources, capital accumulation, and innovation. Recent studies have found that cultural aspects and institutional framework tend to play a major role in a nation\u27s development process. The researchers’ work also helps policy makers to find a better answer to the last question. The purpose of this chapter is to evaluate the effectiveness of aid in eradicating poverty and improving life conditions in African countries since 1980. Since we are at the beginning of a new UN development agenda, it is important for all stakeholders (recipient, donors, international agencies, etc.) to identify the conditions that enable aid to work

Improvements on the Discrete Logarithm Problem in GF(p)

International audienceThis paper speeds up descrete logarithm algorithms in two ways. First we show how the Factorization Factory can be adapted to the discrete logarithm to drop the complexity from Lp(1/3,1.902) to Lp(1/3,1.639). Next we prove that an early abort strategy can decrease the complexity of the individual logarithm from Lp(1/3,1.447) to Lp(1/3,1.232)

An appendix for a recent paper of Kim

This appendix proposes an improvement of Kim\u27s exTNFS. It has been merged the original paper of Taechan Kim 2015/1027 (version 1)

The Multiple Number Field Sieve for Medium and High Characteristic Finite Fields

International audienceIn this paper, we study the discrete logarithm problem in medium and high characteristic finite fields. We propose a variant of the Number Field Sieve~(NFS) based on numerous number fields. Our improved algorithm computes discrete logarithms in $\mathbb{F}_{p^n}$ for the whole range of applicability of NFS and lowers the asymptotic complexity from $L_{p^n}(1/3,(128/9)^{1/3})$ to $L_{p^n}(1/3,(2^{13}/3^6)^{1/3})$ in the medium characteristic case, and from $L_{p^n}(1/3,(64/9)^{1/3})$ to $L_{p^n}(1/3,((92 + 26 \sqrt{13})/27))^{1/3})$ in the high characteristic case.Version 2 contains an erratum.Dans cet article, nous étudions le problème du logarithme discret dans les corps finis de moyenne et grande caractéristique. Nous proposons une variante du crible algébrique basée sur plusieurs corps de nombres. Nous obtenons une accélération de $L_{p^n}(1/3,(128/9)^{1/3})$ à $L_{p^n}(1/3,(2^{13}/3^6)^{1/3})$ pour la moyenne caractéristique et de $L_{p^n}(1/3,(64/9)^{1/3})$ à $L_{p^n}(1/3,((92 + 26 \sqrt{13})/27))^{1/3})$ pour la grande. La version 2 contient un erratum

Finding ECM-friendly curves through a study of Galois properties

In this paper we prove some divisibility properties of the cardinality of elliptic curves modulo primes. These proofs explain the good behavior of certain parameters when using Montgomery or Edwards curves in the setting of the elliptic curve method (ECM) for integer factorization. The ideas of the proofs help us to find new families of elliptic curves with good division properties which increase the success probability of ECM

The special case of cyclotomic fields in quantum algorithms for unit groups

Unit group computations are a cryptographic primitive for which one has a fast quantum algorithm, but the required number of qubits is $\tilde{O}(m^5)$. In this work we propose a modification of the algorithm for which the number of qubits is $\tilde{O}(m^2)$ in the case of cyclotomic fields. Moreover, under a recent conjecture on the size of the class group of $\mathbb{Q}(\zeta_m+\zeta_m^{-1})$, the quantum algorithms is much simpler because it is a hidden subgroup problem (HSP) algorithm rather than its error estimation counterpart: continuous hidden subgroup problem (CHSP). We also discuss the (minor) speed-up obtained when exploiting Galois automorphisms thnaks to the Buchmann-Pohst algorithm over $\mathcal{O}_K$-lattices

A classification of ECM-friendly families using modular curves: intégré à la thèse de doctorat de Sudarshan Shinde, Sorbonne Université, 10 juillet 2020.

Validé par le jury de thèse de Sudarshan Shinde, Sorbonne Université, 10 juillet 2020.jury :Loïc Mérel (président)Jean-Marc Couveignes (rapporteur)David Zureick Brown (rapporteur)Annick ValibouzeBen SmithPierre-Voncent Koseleff (co-directeur)Razvan Barbulescu (co-drecteur)In this work, we establish a link between the classification of ECM-friendly curves and Mazur's program B, which consists in parameterizing all the families of elliptic curves with exceptional Galois image. Building upon two recent works which treated the case of congruence subgroups of prime-power level which occur for infinitely many $j$-invariants, we prove that there are exactly 1525 families of rational elliptic curves with distinct Galois images which are cartesian products of subgroups of prime-power level. This makes a complete list of rational families of ECM-friendly elliptic curves, out of which less than 25 were known in the literature. We furthermore refine a heuristic of Montgomery to compare these families and conclude that the best 4 families which can be put in $a=-1$ twisted Edwards' form are new

Improvements to the number field sieve for non-prime finite fields

This unpublished version contains some inexact statements. Please refer to the version published at Eurocrypt 2015 also available at https://hal.inria.fr/hal-01112879v2We propose various strategies for improving the computation of discrete logarithms in non-prime fields of medium to large characteristic using the Number Field Sieve. This includes new methods for selecting the polynomials; the use of explicit automorphisms; explicit computations in the number fields; and prediction that some units have a zero virtual logarithm. On the theoretical side, we obtain a new complexity bound of $L_{p^n}(1/3,\sqrt[3]{96/9})$ in the medium characteristic case. On the practical side, we computed discrete logarithms in $F_{p^2}$ for a prime number $p$ with $80$ decimal digits.Warning: This unpublished version contains some inexact statements.Nous décrivons plusieurs stratégies pour accélérer le calcul de logarithmes discrets dans un corps fini non premier de caractéristique moyenne ou grande à l'aide du crible algébrique. Parmi elles, de nouvelles méthodes de sélection polynomiale; l'utilisation explicite d'automorphismes; des calculs explicites dans les corps de nombres; et la prédiction de l'annulation des logarithmes virtuels d'unités bien choisies. D'un point de vue théorique, nous obtenons une complexité nouvelle en $L_{p^n}(1/3,\sqrt[3]{96/9})$ dans le cas de la caractéristique moyenne. Du côté pratique, nous avons mené à bien le calcul de logarithmes discrets dans $F_{p^2}$ avec $p$ premier de $80$ chiffres décimaux.Attention : cette version non-publiée contient des énoncés inexacts

Recherche automatique de formules pour calculer des formes bilinéaires

National audienceThis talk will focus on the bilinear rank problem: given a bilinear map (e.g., the product of polynomials, of finite-field elements, or of matrices), what is the smallest number of multiplications over the coefficient ring required to evaluate this function?For instance, Karatsuba's method allows one to compute the product of two linear polynomials using only three multiplications instead of four. In this talk, we give a formalization of the bilinear rank problem, which is known to be NP-hard, and propose a generic algorithm to efficiently compute exact solutions, thus proving the optimality of (or even improving) known complexity bounds from the literature.Dans cet exposé, nous nous intéressons au problème du rang bilinéaire : étant donnée une application bilinéaire (par exemple, le calcul d’un produit de polynômes, d’éléments d’un corps fini, ou encore de matrices), quel est le nombre minimal de multiplications sur le corps de base nécessaires pour évaluer cette application ?Ainsi, par exemple, la méthode de Karatsuba permet de calculer le produit de deux polynômes linéaires en seulement trois multiplications au lieu de quatre. Nous donnons dans cet exposé une formalisation du problème du rang bilinéaire, connu pour être NP-dur, et proposons un algorithme général permettant de calculer efficacement des solutions exactes, qui nous permettent ainsi de prouver l’optimalité de, voire même d’améliorer certaines bornes de la littérature

THE VALORIZING OF DIFFERENT WOODY WASTES AS NATURAL SUBSTRATES FOR INTENSIVE CULTIVATION OF MUSHROOMS

This paper presents the results of laboratory experiments regarding the valorizing of different types of lignocellulosic wastes coming from woody species through controlled cultivation of two mushroom species, namely Ganoderma lucidum and Pleurotus ostreatus. Both mushroom species were cultivated in controlled conditions of temperature, humidity, and aeration in order to get their carpophores. The main aim of this work was focused on finding out the best way to convert the woody wastes into useful food products, such as mushroom fruit bodies, by using them as growing sources for the mentioned edible and medicinal mushrooms. The final produced carpophores were weighted and the results were compared to find out the optimal variant to be applied for intensive cultivation of mushrooms