New results and applications for multi-secret sharing schemes

In a multi-secret sharing scheme (MSSS), \(\ell \) different secrets are distributed among the players in some set \(\mathcal{P }=\{P_1,\ldots ,P_n\}\) , each one according to an access structure. The trivial solution to this problem is to run \(\ell \) independent instances of a standard secret sharing scheme, one for each secret. In this solution, the length of the secret share to be stored by each player grows linearly with \(\ell \) (when keeping all other parameters fixed). Multi-secret sharing schemes have been studied by the cryptographic community mostly from a theoretical perspective: different models and definitions have been proposed, for both unconditional (information-theoretic) and computational security. In the case of unconditional security, there are two different definitions. It has been proved that, for some particular cases of access structures that include the threshold case, a MSSS with the strongest level of unconditional security must have shares with length linear in \(\ell \) . Therefore, the optimal solution in this case is equivalent to the trivial one. In this work we prove that, even for a more relaxed notion of unconditional security, and for some kinds of access structures (in particular, threshold ones), we have the same efficiency problem: the length of each secret share must grow linearly with \(\ell \) . Since we want more efficient solutions, we move to the scenario of MSSSs with computational security. We propose a new MSSS, where each secret share has constant length (just one element), and we formally prove its computational security in the random oracle model. To the best of our knowledge, this is the first formal analysis on the computational security of a MSSS. We show the utility of the new MSSS by using it as a key ingredient in the design of two schemes for two new functionalities: multi-policy signatures and multi-policy decryption. We prove the security of these two new multi-policy cryptosystems in a formal security model. The two new primitives provide similar functionalities as attribute-based cryptosystems, with some advantages and some drawbacks that we discuss at the end of this work.     

Rinneite,K3Na[FeCl6], at 293, 84 and 9.5 K

The crystal structure of tripotassium sodium hexa­chloro­ferrate(II) has been determined by X‐ray diffraction at 293, 84 and 9.5 K. The accurate and extensive data sets collected should be suitable for charge–density analysis studies.     

Microwave-assisted synthesis of α-ethoxycarbamates

An efficient and reproducible synthesis of various α-ethoxycarbamates is described via a microwave heating mode. Compared to the thermal process, the microwave dielectric heating induces a dramatic reduction of the reaction time and the improvement of the yields. The reaction is general since applicable to aromatic and aliphatic aldehydes with various primary amines. Several examples involving chiral aldehydes have also been considered.     

Minimizing the number of machines for minimum length schedules

In this paper, we present a new objective function for scheduling on parallel machines: minimizing the number of machines for schedules of minimum length. We study its complexity and we prove the NP-completeness of this problem, even if there is no precedences or for unitary execution times. We propose several polynomial algorithms for various particular cases.     

Concentration-Dependent Interactions of Amphiphilic PiB Derivative Metal Complexes with Amyloid Peptides Aβ and Amylin**

Metal chelates targeted to amyloid peptides are widely explored as diagnostic tools or therapeutic agents. The attachment of a metal complex to amyloid recognition units typically leads to a decrease in peptide affinity. We show here that by separating a macrocyclic GdL chelate and a PiB targeting unit with a long hydrophobic C10 linker, it is possible to attain nanomolar affinities for both Aβ_1-40 (K_d=4.4 nm ) and amylin (K_d=4.5 nm ), implicated, respectively in Alzheimer's disease and diabetes. The Scatchard analysis of surface plasmon resonance data obtained for a series of amphiphilic, PiB derivative GdL complexes indicate that their Aβ_1-40 or amylin binding affinity varies with their concentration, thus micellar aggregation state. The GdL chelates also affect peptide aggregation kinetics, as probed by thioflavin-T fluorescence assays. A 2D NMR study allowed identifying that the hydrophilic region of Aβ_1-40 is involved in the interaction between the monomer peptide and the Gd³⁺ complex. Finally, ex vivo biodistribution experiments were conducted in healthy mice by using ¹¹¹In labeled analogues. Their pancreatic uptake, ∼3 %ID g⁻¹, is promising to envisage amylin imaging in diabetic animals.     

Experimental and Computational Study on the Anti-Markovnikov Hydrofunctionalization of Olefins Using Glycine-Extended AQ-Auxiliaries

Two similar tridentate directing groups derived from glycine and 8-aminoquinoline were shown to enable the palladium-catalyzed anti-Markovnikov hydrofunctionalization of 4-pentenylamine with drastically different efficiencies. A computational investigation into the origin of the reactivity difference between these isomeric, carbonyl-transposed auxiliaries suggests that protonation state, thus charge of the substrate-metal complex prior to nucleopalladation is key. These investigations have culminated in a directing group design that can undergo Pd-catalyzed hydrofunctionalization under relatively mild conditions, as low as room temperature.     

Fine-tunable monodentate phosphoroamidite and aminophosphine ligands for Rh-catalyzed asymmetric hydroformylation

A biaryl-based monophosphoroamidite L1–L4a–f and aminophosphine L5–L7a–f ligand library was screened in the Rh-catalyzed asymmetric hydroformylation of several vinylarenes and heterocyclic olefins. Our results indicate that the selectivity is strongly dependent on the ligand parameters and on the substrate type. Enantioselectivities (up to 46%) were moderate in the hydroformylation of several vinylarenes S1–S5 and promising (up to 58%) for the more challenging heterocyclic olefins S6–S9.     

Non-Algebraic Quadrature Domains

It is well known that, in the plane, the boundary of any quadrature domain (in the classical sense) coincides with the zero set of a polynomial. We show, by explicitly constructing some four-dimensional examples, that this is not always the case. This confirms, in dimension 4, a conjecture of the second author. Our method is based on the Schwarz potential and involves elliptic integrals of the third kind.