Speeding up Exponentiation using an Untrusted Computational Resource

We present protocols for speeding up fixed-base variable-exponent exponentiation and variable-base fixed-exponent exponentiation using an untrusted computational resource. In the fixed-base protocols, the exponent may be blinded. In the variable-base protocols, the base may be blinded. The protocols are described for exponentiation in a cyclic group. We describe how to extend them to exponentiation modulo an integer where the modulus is the product of primes with single multiplicity. The protocols provide a speedup of over the square-and-multiply algorithm, where k is the bitlength of the exponent. One application of the protocols is to speed up exponentiation-based verification in discrete log-based signature and credential schemes. The protocols also allow signature verifiers to dynamically choose, for each message, the amount of work it would like to perform to verify the signature. This results in a work-security tradeoff. We introduce a fifth protocol to perform variable-base variable- exponent exponentiation, which also has this feature. Our model allows the trusted resource to perform computations in its idle time. The protocols facilitate the offloading of work to the offline stage, such that the work the trusted resource performs when it has to do an exponentiation is smaller. Our protocols are unconditionally secure.     

High oxygen pressures and the stabilization of six-coordinated Ir(VI) in an oxygen lattice

Abstract

During these last twenty five years a great efforts have been made in the Laboratoire de Chimie du Solide du CNRS in order to develop high oxygen pressure for the stabilization of unusual oxidation state of transition elements.

The aims of such research works was to correlate the increase of the Mⁿ⁺-O bond covalency versus the increase of the oxidation state n+ to the physicochemical properties of resulting oxides [1].

Iridium was an interesting element due to its position (5d) in the Periodic Table. In 1980 Ir(V) (d⁴) was stabilized in La₂LiIrO₆ in the perovskite structure [2]. Such a study had underlined the strong value of the spin-orbit coupling associated to Ir(V) [3].

The stabilization of Ir(VI) is interesting from two points of view : (i) its isotropic electronic configuration (d³), (ii) such a high oxidation state could lead to the strongest M-O bond in an oxygen lattice.

Selecting, through a specific methodology, the most appropriate local structural and chemical factors and with the help of high oxygen pressure, Ir(V1) was stabilized in the perovskite Ba₂CaIrO₆. Structural, magnetic and Mössbauer studies have been carried out in order to characterize the physicochemical properties induced by this unusual oxidation state.     

Wave packet dynamics of nonlinear Gazeau–Klauder coherent states of a position-dependent mass system in a Coulomb-like potential

AD = 1 position-dependent mass approach to constructing nonlinear quantum states for a modified Coulomb potential is used to generate Gazeau–Klauder coherent states. It appears that their energy eigenvalues are scaled down by the quantum number and the nonlinearity coefficient. We study the basic properties of these states, which are found to be undefined on the whole complex plane, and some details of their revival structure are discussed.     

Correction to: Multistage thermal decomposition in films of cadmium chloride-doped PVA–PVP polymeric blend

Core/shell composites of CuC₂O₄·2H₂O@AP and ZnC₂O₄·2H₂O@AP were prepared from metal oxalates on suspended AP particles in ethanol. CuO and ZnO nano-metal oxides as the nano-catalysts were made from CuC₂O₄·2H₂O and ZnC₂O₄·2H₂O simultaneously by thermal decomposition of AP. The particle size of CuO nano-particles was very finer, and the ZnO particles showed a considerable growth during formation. The kinetic triplet of activation energy, frequency factor, and model of thermal decomposition of pure AP, CuC₂O₄·2H₂O@AP, and ZnC₂O₄·2H₂O@AP composites were estimated by applying three model-free (FWO, KAS, and Starink) and model-fitting (Starink) methods. Based on the thermal analysis, the CuC₂O₄@AP composite has better catalytic performance and the thermal decomposition temperature of AP decreased to about 126.44 °C.     

Amphiphilic and mesomorphic fullerene-based dendrimers

Growing attention is currently devoted to large dendritic structures for applications in nanotechnology and materials science. In this respect, the incorporation of such compounds into thin ordered films appears to be an important issue. One of the most widely pursued approaches to structurally ordered dendrimer assemblies has been the preparation of Langmuir films at the air-water interface. We report on the case of a diblock globular fullerene-based dendrimer and show that peripheral substitution of the dendrimer with hydrophobic chains on one hemisphere and hydrophilic groups on the other provides the required hydrophobic/hydrophilic balance allowing the formation of stable Langmuir films. A second approach has been to consider the case of fullerene containing dendrimers terminated by mesogenic groups such as cyanobiphenyl subunits. Whatever the generation is, up to the fourth one, all these compounds exhibit a well-defined liquid crystalline smectic A phase. The molecular organisation within the smectic layers is found to be monolayered or bilayered depending on the generation. For the smallest dendrimers, the organisation is mainly governed by the size of the fullerene moiety, whereas for the higher ones, it is governed by the interactions between the terminal mesogenic groups. These two approaches appear particularly interesting for functional groups such as fullerenes, which are not well adapted to be organised in nanoscale architectures. The present study shows that fullerenes can indeed be introduced into different types of ordered structure when they have been chemically adequately modified.     

New and highly efficient synthesis of 3-substituted 1-hydroxybenz[g]isoquinoline-5,10-diones

A new and efficient strategy for the synthesis of 3-substituted 1-hydroxybenz[g]isoquinoline-5,10-diones by reaction of 2-methoxycarbonyl-1,4-naphthoquinone with different pyridinium salts under Kröhnke conditions is disclosed. This one-step reaction was found to be dependent on the substitution pattern of the aromatic nucleus in the pyridinium salts.     

Multistage thermal decomposition in films of cadmium chloride-doped PVA–PVP polymeric blend

Several reports exist on the use of natural-oil-based materials as rejuvenators to restore the properties of aged binders—more specifically, regarding their ability to enhance the binders’ low-temperature properties and to reduce their stiffness. Rejuvenators are typically made of low molecular weight constituents which could easily volatilize and thus render the rejuvenated binder thermally unstable. Hence, the study of the thermal stability of rejuvenated binders is of paramount importance. In this research, a binder with a performance grade (PG) of PG58-28 modified with a soybean-derived rejuvenator at 12% by mass is added to an extracted reclaimed asphalt pavement (RAP) binder at a ratio of 1:5 resulting in a rejuvenator dosage rate of 2% by total mass of binder. The PG of the rejuvenated RAP binder is determined using both dynamic shear rheometer and bending beam rheometer. The thermal stability of the rejuvenator and the binders is verified using thermogravimetric analysis (TG). The rejuvenator shows good thermal stability up to a temperature of 302 °C. The RAP binder containing the rejuvenator shows similar thermal stability to the unrejuvenated RAP binder. The evolved gases from the TG analysis are analyzed using Fourier transform infrared (FTIR) to chemically characterize the rejuvenator and the binders. The FTIR spectrum of the rejuvenator reveals characteristic peaks. The intensity of these peaks serves as an indication of the rate of mass loss of the rejuvenator within the rejuvenated RAP binder.     

Nouveaux modeles polysilicies a partir d'indoles,du benzothiophene et du benzofuranne

Direct polysilylation of bicyclic heterosubstrates was performed without (in the case of indole or its N-methyl or N-trimethylsilyl derivatives) or with (benzothiophene, benzofuranne) ring-opening. Hexasilylation from benzothiophene occurred with desulfurization.     

Investigation of redox properties of different PtSn/Al2O3 catalysts.

Alumina-supported Sn and PtSn particles are studied by 119Sn M?ssbauer spectroscopy after oxidation and reduction under various conditions. The observed species of Sn(IV), Sn(II) and Sn(0) are grouped in several categories, each being characterised by distinct structural properties. Tin phases in contact with the support or with platinum are identified. The results are used to establish a model describing the phase transformations occurring in PtSn particles under oxidising or reducing conditions. Particular attention is paid to the reduction/reoxidation mechanisms governing H2/O2 double titrations. An increased reactivity of tin towards oxygen, induced by the contact with platinum, is demonstrated. It is shown that tin contributes to the oxygen uptake VO1 of a first titration cycle by platinum-catalysed transformation of Sn(II) into an oxometallic phase Pt(x)Sn(O). The oxygen titre VO2 of a second cycle is due to O2 chemisorption on platinum only.     

An AM1 and DFT-AM1 computational study of methyl phenylpropiolate addition to 1-phenyl-3,4-dimethylphosphole

The transition state structures for the addition of maleic acid anhydride and methyl phenylpropiolate to 1-phenyl-3,4-dimethylphosphole were generated with the AM1 semiempirical method. The competitive transition state structures for 1,5-phenyl rearrangement in 1-phenyl-3,4-dimethylphosphole was also optimized with AM1. The energies were evaluated with the SVWN and Becke3LYP DFT methods using a 6-31G(d) basis set. The reaction outcome based on the evaluated energies were discussed and compared with experimental observations.