Unidad docente Matemáticas
http://hdl.handle.net/10017/281
MATEMATIC2024-04-20T01:44:21ZTrace-based cryptanalysis of cyclotomic R_{q,0}xR_q-PLWE for the non-split case
http://hdl.handle.net/10017/60505
Trace-based cryptanalysis of cyclotomic R_{q,0}xR_q-PLWE for the non-split case
Blanco Chacón, Iván; Barbero Lucas, Beatriz; Durán Díaz, José Raúl; Njah Epouse Nchiwo, Rahinatou Yuh
We describe a decisional attack against a version of the PLWE problem
in which the samples are taken from a certain proper subring of large dimension
of the cyclotomic ring Fq[x]/(Φp
k (x)) with k > 1 in the case where q ≡ 1 (mod p)
but Φp
k (x) is not totally split over Fq. Our attack uses the fact that the roots of
Φp
k (x) over suitable extensions of Fq have zero-trace and has overwhelming success
probability as a function of the number of input samples. An implementation in
Maple and some examples of our attack are also provided.
2023-07-19T00:00:00ZEstimation of the spatio-temporal wave grouping properties by using multidimensional discrete and spline methods
http://hdl.handle.net/10017/60272
Estimation of the spatio-temporal wave grouping properties by using multidimensional discrete and spline methods
Nieto Borge, José Carlos; Alcázar Arribas, Juan Gerardo; Orden Martín, David; Marazuela Reca, Sara; Rodríguez, Gerardo
Wave groups can be detected and studied by using the wave envelope. So far, the method used to compute the wave envelope employs the Riesz transform. However, such a technique always produces symmetric envelopes, which is only realistic in the case of linear waves. In this paper we present a new method to compute the wave envelope providing more realistic results. In particular, the method allows to detect non-symmetry in the wave envelope, something useful, for instance, when detecting groups of high waves. The method computes first the local maxima and minima of the sea surface, and then determines the wave envelope by combining discrete methods, namely the use of the Delaunay triangulation, and tensor-product splines. The proposed method has been applied to simulated wave fields, and also to wave elevations data measured by an X-band radar. The obtained results correctly reproduce the behavior of the simulated waves.
2019-09-01T00:00:00ZOn q-Gevrey asymptotics for logarithmic type solutions in singularly perturbed q-difference-differential equations
http://hdl.handle.net/10017/60267
On q-Gevrey asymptotics for logarithmic type solutions in singularly perturbed q-difference-differential equations
Lastra Sedano, Alberto; Malek, Stephane
A family of singularly perturbed q-difference-differential equations under the action of a small complex perturbation parameter is studied. The action of the formal monodromy around the origin is present in the equation, which suggests the construction of holomorphic solutions holding logarithmic terms in both, the formal and the analytic level. We provide both solutions and describe the asymptotic behavior relating them by means of q-Gevrey asymptotic expansions of some positive order, with respect to the perturbation parameter. On the way, the development of a space product of Banach spaces in the Borel plane is needed to provide a fixed point for a coupled system of equations.
2023-12-25T00:00:00ZMeromorphic solutions of q-difference equations
http://hdl.handle.net/10017/60266
Meromorphic solutions of q-difference equations
Lastra Sedano, Alberto; Remy, Pascal
In this article, we construct explicit meromorphic solutions of first order linear q-difference equations in the complex domain and we describe the location of all their zeros and poles. The homogeneous case leans on the study of four fundamental equations, providing the previous informations in the framework of entire or meromorphic coefficients. The inhomogeneous situation, which stems from the homogeneous one and two fundamental equations, is also described in detail. We also address the case of higher-order linear q-difference equations, using a classical factorization argument. All these results are illustrated by several examples.
2023-11-15T00:00:00Z