There are many cryptographic constructions in which one uses a random power or multiple of an element in a group or a ring. We describe a fast method to compute random powers and multiples in certain important situations including powers in the Galois field F2n , multiples on Koblitz elliptic curves, and multiples in NTRU convolution polynomial rings. The underlying idea is to form a random exp...

Les références principales pour l’interprétation du produit de mélange de deux séries en termes d’automates et les applications aux identités syntaxiques sont [Lo 2002] 1.3 et [J 1980]. Dans le cours du 14 mars les exemples suivant sont traités: 1. Mélange de deux éléments de K < X > 2. L’identité x∗0x(x1 · · ·xn) = x∗0x1x∗0x2 · · ·x∗0xnx∗0 3. L’identité (x0 + x1)∗ = x∗0xx∗1 4. L’identité (1 + ...

Le molluscum contagiosum est une tumeur cutanée bénigne d'origine virale. L'agent responsable est un Poxvirus à ADN fréquemment retrouvé chez les enfants de 3 à 16 ans, les immunodéprimés et plus rarement chez les adultes immunocompétents. Le syndrome d'hyper immunoglobulinémie E ou de Job-Buckley fait partie des déficits immunitaires primitifs complexes, caractérisé par l'association constante...

Internal multiples have long been recognized as a problem in seismic imaging. Some theoretical developments have been made to attenuate them, but there is no 3D theory as yet that is valid for a wide range of velocity models. The goal of this paper is to present such a theory. Through the development of this theory we show that, unless certain simplifying assumptions are made about the velocity...

where [a, b, . . .] denotes the least common multiple of a, b, . . . . For the first term above represents the density of the multiples of a1 , the second represents the density of those multiples of a 2 that are not multiples of a 1 , and so on . Now suppose we start from an infinite sequence a,, a2 , . . . (arranged in increasing order) instead of from a finite set . It is plain that A(ai, a2...

Predictive multiple suppression methods consist of two main steps: a prediction step, in which multiples are predicted from the seismic data, and a subtraction step, in which the predicted multiples are matched with the true multiples in the data. The last step appears crucial in practice: an incorrect adaptive subtraction method will cause multiples to be sub-optimally subtracted or primaries ...

Algebraic attacks on LFSR-based stream ciphers recover the secret key by solving an overdefined system of multivariate algebraic equations. They exploit multivariate relations involving key bits and output bits and become very efficient if such relations of low degrees may be found. Low degree relations have been shown to exist for several well known constructions of stream ciphers immune to al...

Primaries (signal) and multiples (noise) often exhibit different kinematics and amplitudes (i.e., patterns) in time and space. Multidimensional prediction-error filters (PEFs) approximate these patterns to separate noise and signal in a least-squares sense. These filters are time-space variant to handle the nonstationarity of multioffset seismic data. PEFs for the primaries and multiples are es...

Receiver-side water-column multiples acquired with ocean-bottom seismic sensors can be used for elastic imaging of the subsurface, which can provide additional information relative to more conventional acoustic imaging. These multiples can be separated from primaries contained in ocean-bottom seismic data using techniques such as up/down decomposition. In elastic imaging, the down-going wavefie...