On Index Calculus Algorithms for Subfield Curves

In this paper we further the study of index calculus methods for solving the elliptic curve discrete logarithm problem (ECDLP). We focus on the index calculus for subfield curves, also called Koblitz curves, defined over Fq with ECDLP in Fqn. Instead of accelerating the solution of polynomial systems during index calculus as was predominantly done in previous work, we define factor bases that are invariant under the q-power Frobenius automorphism of the field Fqn, reducing the number of polynomial systems that need to be solved. A reduction by a factor of 1/n is the best one could hope for. We show how to choose factor bases to achieve this, while simultaneously accelerating the linear algebra step of the index calculus method for Koblitz curves by a factor n2. Furthermore, we show how to use the Frobenius endomorphism to improve symmetry breaking for Koblitz curves. We provide constructions of factor bases with the desired properties, and we study their impact on the polynomial system solving costs experimentally.SCOPUS: cp.kinfo:eu-repo/semantics/publishe

On Index Calculus Algorithms for Subfield Curves

In this paper we further the study of index calculus methods for solving the elliptic curve discrete logarithm problem (ECDLP). We focus on the index calculus for subfield curves, also called Koblitz curves, defined over $\mathbb{F}_q$ with ECDLP in $\mathbb{F}_{q^n}$. Instead of accelerating the solution of polynomial systems during index calculus as was predominantly done in previous work, we define factor bases that are invariant under the $q$-power Frobenius automorphism of the field $\mathbb{F}_{q^n}$, reducing the number of polynomial systems that need to be solved. A reduction by a factor of $1/n$ is the best one could hope for. We show how to choose factor bases to achieve this, while simultaneously accelerating the linear algebra step of the index calculus method for Koblitz curves by a factor $n^2$. Furthermore, we show how to use the Frobenius endomorphism to improve symmetry breaking for Koblitz curves. We provide constructions of factor bases with the desired properties, and we study their impact on the polynomial system solving costs experimentally. This work gives an answer to the problem raised in the literature on how the Frobenius endomorphism can be used to speed-up index calculus on subfield curves

Beyond element-wise interactions: identifying complex interactions in biological processes

Background: Biological processes typically involve the interactions of a number of elements (genes, cells) acting on each others. Such processes are often modelled as networks whose nodes are the elements in question and edges pairwise relations between them (transcription, inhibition). But more often than not, elements actually work cooperatively or competitively to achieve a task. Or an element can act on the interaction between two others, as in the case of an enzyme controlling a reaction rate. We call “complex” these types of interaction and propose ways to identify them from time-series observations. Methodology: We use Granger Causality, a measure of the interaction between two signals, to characterize the influence of an enzyme on a reaction rate. We extend its traditional formulation to the case of multi-dimensional signals in order to capture group interactions, and not only element interactions. Our method is extensively tested on simulated data and applied to three biological datasets: microarray data of the Saccharomyces cerevisiae yeast, local field potential recordings of two brain areas and a metabolic reaction. Conclusions: Our results demonstrate that complex Granger causality can reveal new types of relation between signals and is particularly suited to biological data. Our approach raises some fundamental issues of the systems biology approach since finding all complex causalities (interactions) is an NP hard problem

Cellular and Behavioral Effects of Cranial Irradiation of the Subventricular Zone in Adult Mice

Background: In mammals, new neurons are added to the olfactory bulb (OB) throughout life. Most of these new neurons, granule and periglomerular cells originate from the subventricular zone (SVZ) lining the lateral ventricles and migrate via the rostral migratory stream toward the OB. Thousands of new neurons appear each day, but the function of this ongoing neurogenesis remains unclear. Methodology/Principal Findings: In this study, we irradiated adult mice to impair constitutive OB neurogenesis, and explored the functional impacts of this irradiation on the sense of smell. We found that focal irradiation of the SVZ greatly decreased the rate of production of new OB neurons, leaving other brain areas intact. This effect persisted for up to seven months after exposure to 15 Gray. Despite this robust impairment, the thresholds for detecting pure odorant molecules and short-term olfactory memory were not affected by irradiation. Similarly, the ability to distinguish between odorant molecules and the odorant-guided social behavior of irradiated mice were not affected by the decrease in the number of new neurons. Only long-term olfactory memory was found to be sensitive to SVZ irradiation. Conclusion/Significance: These findings suggest that the continuous production of adult-generated neurons is involved i

Director Characteristics and Firm Performance

The traditional methodology examining optimal boards relates a simple board variable (e.g. independence or board demography) to firm performance, however, ig- noring other board characteristics. This paper investigates how the education and business experience of directors affect firm performance. The sample consists of 1,574 directorships from 224 listed firms in Switzerland. Using OLS and including control variables, the results show that graduates of minor Swiss universities are negatively related to Tobin’s Q, and industrial knowledge and Tobin’s Q are nega- tively correlated if the firm has more divisions. In addition, director fixed effects (or unobserved characteristics) are significant, but improve the explanatory power of the models only by 5 percent

Association of the PHACTR1/EDN1 genetic locus with spontaneous coronary artery dissection

Background: Spontaneous coronary artery dissection (SCAD) is an increasingly recognized cause of acute coronary syndromes (ACS) afflicting predominantly younger to middle-aged women. Observational studies have reported a high prevalence of extracoronary vascular anomalies, especially fibromuscular dysplasia (FMD) and a low prevalence of coincidental cases of atherosclerosis. PHACTR1/EDN1 is a genetic risk locus for several vascular diseases, including FMD and coronary artery disease, with the putative causal noncoding variant at the rs9349379 locus acting as a potential enhancer for the endothelin-1 (EDN1) gene. Objectives: This study sought to test the association between the rs9349379 genotype and SCAD. Methods: Results from case control studies from France, United Kingdom, United States, and Australia were analyzed to test the association with SCAD risk, including age at first event, pregnancy-associated SCAD (P-SCAD), and recurrent SCAD. Results: The previously reported risk allele for FMD (rs9349379-A) was associated with a higher risk of SCAD in all studies. In a meta-analysis of 1,055 SCAD patients and 7,190 controls, the odds ratio (OR) was 1.67 (95% confidence interval [CI]: 1.50 to 1.86) per copy of rs9349379-A. In a subset of 491 SCAD patients, the OR estimate was found to be higher for the association with SCAD in patients without FMD (OR: 1.89; 95% CI: 1.53 to 2.33) than in SCAD cases with FMD (OR: 1.60; 95% CI: 1.28 to 1.99). There was no effect of genotype on age at first event, P-SCAD, or recurrence. Conclusions: The first genetic risk factor for SCAD was identified in the largest study conducted to date for this condition. This genetic link may contribute to the clinical overlap between SCAD and FMD

"Deux siècles d’ennui"

International audienc

"Les prospérités du fouet : la flagellation ou la logique de l’excès"

International audienc

Histoire des sensibilités au 20e siècle. N° 123. Vingtième siècle. Revue d'histoire

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