Worst case QC-MDPC decoder for McEliece cryptosystem

McEliece encryption scheme which enjoys relatively small key sizes as well as a security reduction to hard problems of coding theory. Furthermore, it remains secure against a quantum adversary and is very well suited to low cost implementations on embedded devices. Decoding MDPC codes is achieved with the (iterative) bit flipping algorithm, as for LDPC codes. Variable time decoders might leak some information on the code structure (that is on the sparse parity check equations) and must be avoided. A constant time decoder is easy to emulate, but its running time depends on the worst case rather than on the average case. So far implementations were focused on minimizing the average cost. We show that the tuning of the algorithm is not the same to reduce the maximal number of iterations as for reducing the average cost. This provides some indications on how to engineer the QC-MDPC-McEliece scheme to resist a timing side-channel attack.Comment: 5 pages, conference ISIT 201

On the asymptotics of a Robin eigenvalue problem

The considered Robin problem can formally be seen as a small perturbation of a Dirichlet problem. However, due to the sign of the impedance value, its associated eigenvalues converge point-wise to $-\infty$ as the perturbation goes to zero. We prove that in this case, Dirichlet eigenpairs are the only accumulation points of the Robin eigenpairs with normalized eigenvectors. We then provide a criteria to select accumulating sequences of eigenvalues and eigenvectors and exhibit their full asymptotic with respect to the small parameter

The Factorization method for three dimensional Electrical Impedance Tomography

The use of the Factorization method for Electrical Impedance Tomography has been proved to be very promising for applications in the case where one wants to find inhomogeneous inclusions in a known background. In many situations, the inspected domain is three dimensional and is made of various materials. In this case, the main challenge in applying the Factorization method consists in computing the Neumann Green's function of the background medium. We explain how we solve this difficulty and demonstrate the capability of the Factorization method to locate inclusions in realistic inhomogeneous three dimensional background media from simulated data obtained by solving the so-called complete electrode model. We also perform a numerical study of the stability of the Factorization method with respect to various modelling errors.Comment: 16 page

On simultaneous identification of a scatterer and its generalized impedance boundary condition

We consider the inverse scattering problem consisting in the identification of both an obstacle and two functional coefficients of a generalized boundary condition prescribed on its boundary, from far--fields due to several plane waves. After proving a uniqueness result for such inverse problem, we define and compute appropriate derivative of the far--field with respect to an obstacle with non constant impedances. A steepest descent method is then applied to retrieve both the obstacle and the functional impedances from the measured far--fields. The feasability of the method is demonstrated with the help of some 2D numerical experiments

Analysis of the factorization method for a general class of boundary conditions

SubmittedInternational audienceWe analyze the factorization method (introduced by Kirsch in 1998 to solve inverse scattering problems at fixed frequency from the farfield operator) for a general class of boundary conditions that generalizes impedance boundary conditions. For instance, when the surface impedance operator is of pseudo-differential type, our main result stipulates that the factorization method works if the order of this operator is different from one and the operator is Fredholm of index zero with non negative imaginary part. We also provide some validating numerical examples for boundary operators of second order with discussion on the choice of the testing function

Identification of generalized impedance boundary conditions: some numerical issues

We are interested in the identification of a Generalized Impedance Boundary Condition from the far fields created by one or several incident plane waves at a fixed frequency. We focus on the particular case where this boundary condition is expressed as a second order surface operator: the inverse problem then amounts to retrieve the two functions $\lambda$ and $\mu$ that define this boundary operator. We first derive a new type of stability estimate for the identification of $\lambda$ and $\mu$ from the far field when inexact knowledge of the boundary is assumed. We then introduce an optimization method to identify $\lambda$ and $\mu$, using in particular a $H^1$-type regularization of the gradient. We lastly show some numerical results in two dimensions, including a study of the impact of some various parameters, and by assuming either an exact knowledge of the shape of the obstacle or an approximate one.Ce travail concerne l'identification d'une condition aux limites d'impédance généralisée (GIBC) sur le bord d'un objet diffractant à partir du champ lointain créé par une ou plusieurs ondes planes, dans le cas particulier où cette condition est caractérisée par un opérateur d'ordre 2 sur le bord, défini par deux fonctions $\lambda$ et $\mu$ à identifier. Nous commençons par établir une estimation originale de stabilité des fonctions $\lambda$ et $\mu$ cherchées vis à vis du champ lointain, en présence d'une erreur commise sur la forme de l'obstacle. Nous introduisons ensuite une méthode d'optimisation pour identifier $\lambda$ et $\mu$, une régularisation de type $H^1$ du gradient étant utilisée. Nous montrons enfin des résultats numériques de reconstruction en deux dimensions incluant une étude de sensibilité par rapport aux différents paramètres, en supposant une connaissance exacte ou approchée de la forme de l'obstacle

A Custom EIT System Based On Off-The-Shelf Equipment

The construction of an EIT system using a commercially available current source and EEG amplifier is discussed. The Keithley 6221 current source offers functionality equivalent to that of existing bespoke systems, alongside the ease of use of a commercial system. When combined with a BioSemi EEG amplifier, a full EIT system is produced. Analysis of the signal quality of the source and imaging experiments on a saline tank verify the feasibility of the approach

Assessment of sub-shelf melting parameterisations using the ocean–ice-sheet coupled model NEMO(v3.6)–Elmer/Ice(v8.3)

Oceanic melting beneath ice shelves is the main driver of the current mass loss of the Antarctic ice sheet and is mostly parameterised in stand-alone ice-sheet modelling. Parameterisations are crude representations of reality, and their response to ocean warming has not been compared to 3-D ocean–ice-sheet coupled models. Here, we assess various melting parameterisations ranging from simple scalings with far-field thermal driving to emulators of box and plume models, using a new coupling framework combining the ocean model NEMO and the ice-sheet model Elmer/Ice. We define six idealised one-century scenarios for the far-field ocean ranging from cold to warm, and representative of potential futures for typical Antarctic ice shelves. The scenarios are used to constrain an idealised geometry of the Pine Island glacier representative of a relatively small cavity. Melt rates and sea-level contributions obtained with the parameterised stand-alone ice-sheet model are compared to the coupled model results. The plume parameterisations give good results for cold scenarios but fail and underestimate sea level contribution by tens of percent for warm(ing) scenarios, which may be improved by adapting its empirical scaling. The box parameterisation with five boxes compares fairly well to the coupled results for almost all scenarios, but further work is needed to grasp the correct number of boxes. For simple scalings, the comparison to the coupled framework shows that a quadratic as opposed to linear dependency on thermal forcing is required. In addition, the quadratic dependency is improved when melting depends on both local and non-local, i.e. averaged over the ice shelf, thermal forcing. The results of both the box and the two quadratic parameterisations fall within or close to the coupled model uncertainty. All parameterisations overestimate melting for thin ice shelves while underestimating melting in deep water near the grounding line. Further work is therefore needed to assess the validity of these melting parameteriations in more realistic set-ups