How to Choose Secret Parameters for RSA-Type Cryptosystems over Elliptic Curves

Recently, and contrary to the common belief, Rivest and Silverman argued that the use of strong primes is unnecessary in the RSA cryptosystem. This paper analyzes how valid this assertion is for RSA-type cryptosystems over elliptic curves. The analysis is more difficult because the underlying groups are not always cyclic. Previous papers suggested the use of strong primes in order to prevent factoring attacks and cycling attacks. In this paper, we only focus on cycling attacks because for both RSA and its elliptic curve-based analogues, the length of the RSA-modulus n is typically the same. Therefore, a factoring attack will succeed with equal probability against all RSA-type cryptosystems. We also prove that cycling attacks reduce to find fixed points, and derive a factorization algorithm which (most probably) completely breaks RSA-type systems over elliptic curves if a fixed point is found.     

Materials for optics: The growth of single crystals and the assesment of their quality in view of real and future applications

Abstract

One of the main problems in optical materials in the growth of single crystals and the characterization of their defects in view of performances and applications.     

Anisotropic behaviour law for sheets used in stamping:: A comparative study of steel and aluminium

For a car manufacturer, reducing the weight of vehicles is an obvious aim. Replacing steel by aluminium moves towards that goal. Unfortunately, aluminium's stamping numerical simulation results are not yet as reliable as those of steel. Punch-strength and spring-back phenomena are not correctly described. This study on aluminium validates the behaviour law Hill 48 quadratic yield criterion with both isotropic and kinematic hardening. It is based on the yield surface and on associated experimental tests (uniaxial test, plane tensile test, plane compression and tensile shearing). To cite this article: J.-J. Sinou, B. Macquaire, C. R. Mecanique 331 (2003).     

Vers une théorie énergétique de la rupture fragile

The drawbacks of the classical theory of brittle fracture, based on Griffith's criterion – a notion of critical energy release rate –, and a fracture toughness k, are numerous (think for instance the issue of crack initiation) and penalize its validity as a good model. Are all attempts at building a macroscopic theory of fracture doomed? The variety and complexity of micromechanical phenomena would suggest that this is indeed the case. We believe however that structural effects still preside over fracture and consequently propose to modify slightly Griffith theory without altering its fundamental components so that it becomes amenable to the widest range of situations. The examples presented here will demonstrate that a revisited energetic framework is a sound basis for a theory which can be used at the engineering level and which reconciles seemingly contradictory viewpoints. To cite this article: G. Francfort, J.-J. Marigo, C. R. Mecanique 330 (2002) 225–233.     

The influence of crack-imbalance orientation and orbital evolution for an extended cracked Jeffcott rotor

Vibration peaks occurring at rational fractions of the fundamental rotating critical speed, here named Local Resonances, facilitate cracked shaft detection during machine shut-down. A modified Jeffcott-rotor on journal bearings accounting for gravity effects and oscillating around nontrivial equilibrium points is employed. Modal parameter selection allows this linear model to represent first mode characteristics of real machines. Orbit evolution and vibration patterns are analyzed, yielding useful results. Crack detection results indicate that, instead of 1x and 2x components, analysis of the remaining local resonances should have priority; this is due to crack-residual imbalance interaction and to 2x multiple induced origins. Therefore, local resonances and orbital evolution around 1/2, 1/3 and 1/4 of the critical speed are emphasized for various crack-imbalance orientations. To cite this article: J. Gómez-Mancilla et al., C. R. Mecanique 332 (2004).

Résumé

Les pics de vibration apparaissant au passage des fractions de la vitesse de critique de rotation des systèmes tournants, appelées résonances locales, facilitent la détection de fissures sur les machines. Dans cette étude, un modèle de rotor Jeffcott modifié avec une fissure tournante, comportant des coussinets et prenant en compte les effets de pesanteur et de balourd est présenté. Le choix modal des paramètres permet de représenter les caractéristiques liées au premier mode des machines tournantes usuelles. Les évolutions des vibrations et des orbites du système comportant une fissure sont analysées et permettent d'obtenir des résultats utiles pour la détection des fissures sur les machines tournantes. Ainsi, ces résultats indiquent que, en plus des composants 1x et 2x, l'analyse des autres résonances locales restantes doivent être regardées avec attention du fait de l'interaction possible entre les différentes orientations de la fissure et du balourd, et des origines multiples pouvant engendrer la présence des résonances 2x. Par conséquent les résonances et l'évolution des orbites obtenus autour de 1/2, 1/3 et 1/4 de la vitesse critique sont étudiées pour différentes variations d'angle entre le balourd et l'orientation de la fissure. Pour citer cet article : J. Gómez-Mancilla et al., C. R. Mecanique 332 (2004).     

Using Gas Modifiers to Significantly Improve Sensitivity and Selectivity in a Cylindrical FAIMS Device

Recent reports describing enhanced performance when using gas additives in a DMS device (planar electrodes) have indicated that comparable benefits are not attainable using FAIMS (cylindrical electrodes), owing to the non-homogeneous electric fields within the analyzer region. In this study, a FAIMS system (having cylindrical electrodes) was modified to allow for controlled delivery of gas additives. An experiment was carried out that illustrates the important distinction between gas modifiers present as unregulated contaminants and modifiers added in a controlled manner. The effect of contamination was simulated by adjusting the ESI needle position to promote incomplete desolvation, thereby permitting ESI solvent vapor into the FAIMS analyzer region, causing signal instability and irreproducible CV values. However, by actively controlling the delivery of the gas modifier, reproducible CV spectra were obtained. The effects of adding different gas modifiers were examined using 15 positive ions having mass-to-charge (m/z) values between 90 and 734. Significant improvements in peak capacity and increases in ion transmission were readily attained by adding acetonitrile vapor, even at trace levels (≤0.1%). Increases in signal intensity were greatest for the low m/z ions; for the six lowest molecular weight species, signal intensities increased by ～10- to over 100-fold compared with using nitrogen without gas additives, resulting in equivalent or better signal intensities compared with ESI without FAIMS. These results confirm that analytical benefits derived from the addition of gas modifiers reported with a uniform electric field (DMS) also are observed using a non-homogenous electric field (FAIMS) in the analyser region.

A damage mechanics approach to stress softening and its application to rubber

We analyze stress softening phenomena within the framework of the ‘generalized standard material’ based on the notion of a ‘normal dissipative mechanism’. We prove that the monotonicity properties of the ‘yield function’ governing such mechanism lead to local and global uniqueness of the response. Applications to oscillators with a single degree of freedom, whose anharmonic spring exhibits stress softening, are also presented.     

Backscattering of s-polarized light from a cloud of small particles above a dielectric substrate

The scattering of s-polarized electromagnetic waves by a cloud of small particles above an interface is numerically studied, accounting for multiple scattering. The backscattering effect is first observed without the interface and the influence of the index of the particles is shown. In the case of a dilute system of particles with a low index such that no backscattering peak appears without the interface, it is shown that the introduction of an interface restores the backscattering effect. A physical mechanism responsible for this peak is described. In conclusion, a comparison of this model with scattering by rough surfaces is made.