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101.
102.
We cryptanalyse here two variants of the McEliece cryptosystem based on quasi-cyclic codes. Both aim at reducing the key size
by restricting the public and secret generator matrices to be in quasi-cyclic form. The first variant considers subcodes of
a primitive BCH code. The aforementioned constraint on the public and secret keys implies to choose very structured permutations.
We prove that this variant is not secure by producing many linear equations that the entries of the secret permutation matrix
have to satisfy by using the fact that the secret code is a subcode of a known BCH code. This attack has been implemented
and in all experiments we have performed the solution space of the linear system was of dimension one and revealed the permutation
matrix. The other variant uses quasi-cyclic low density parity-check (LDPC) codes. This scheme was devised to be immune against
general attacks working for McEliece type cryptosystems based on LDPC codes by choosing in the McEliece scheme more general
one-to-one mappings than permutation matrices. We suggest here a structural attack exploiting the quasi-cyclic structure of
the code and a certain weakness in the choice of the linear transformations that hide the generator matrix of the code. This
cryptanalysis adopts a polynomial-oriented approach and basically consists in searching for two polynomials of low weight
such that their product is a public polynomial. Our analysis shows that with high probability a parity-check matrix of a punctured
version of the secret code can be recovered with time complexity O(n
3) where n is the length of the considered code. The complete reconstruction of the secret parity-check matrix of the quasi-cyclic LDPC
codes requires the search of codewords of low weight which can be done with about 237 operations for the specific parameters proposed. 相似文献
103.
Affine monotone and maximal monotone subspaces are characterized. 相似文献
104.
Jean-Pierre Aubin 《Applied mathematics and computation》2010,217(3):963-971
The advent of techniques to measure velocities of “GPS equipped vehicles” using satellite technology, replacing the density of the road traffic sensors, motivates and justifies the revision of conceptual, mathematical algorithms and software based models. This paper summarizes studies on the traffic evolutions achieving the minimum of a congestion function controlled “macroscopic traffic velocities” called “celerities” instead of founding traffic regulation on the measures of traffic densities. The flux valued function is the Fenchel transform of the fundamental diagram and is a convex decreasing function. We use the properties of capture basins investigated in viability theory, specifically a Lax-Hopf formula characterizing them and the “Max-Plus” morphism of capture basins for deriving the statements proved in this paper. Traffic conditions involve as well boundary conditions or conditions on trajectories inside the domain. 相似文献
105.
In this note, we prove a sharp lower bound for the log canonical threshold of a plurisubharmonic function ${\varphi}$ with an isolated singularity at 0 in an open subset of ${\mathbb{C}^n}$ . This threshold is defined as the supremum of constants c > 0 such that ${e^{-2c\varphi}}$ is integrable on a neighborhood of 0. We relate ${c(\varphi)}$ to the intermediate multiplicity numbers ${e_j(\varphi)}$ , defined as the Lelong numbers of ${(dd^c\varphi)^j}$ at 0 (so that in particular ${e_0(\varphi)=1}$ ). Our main result is that ${c(\varphi)\geqslant\sum_{j=0}^{n-1} e_j(\varphi)/e_{j+1}(\varphi)}$ . This inequality is shown to be sharp; it simultaneously improves the classical result ${c(\varphi)\geqslant 1/e_1(\varphi)}$ due to Skoda, as well as the lower estimate ${c(\varphi)\geqslant n/e_n(\varphi)^{1/n}}$ which has received crucial applications to birational geometry in recent years. The proof consists in a reduction to the toric case, i.e. singularities arising from monomial ideals. 相似文献
106.
Adler Roy L.; Dedieu Jean-Pierre; Margulies Joseph Y.; Martens Marco; Shub Mike 《IMA Journal of Numerical Analysis》2002,22(3):359-390
To study a geometric model of the human spine we are led tofinding a constrained minimum of a real valued function definedon a product of special orthogonal groups. To take advantgeof its Lie group structure we consider Newton's method on thismanifold. Comparisons between measured spines and computed spinesshow the pertinence of this approach. 相似文献
107.
Sergio Guerrero Oleg Yurievich Imanuvilov Jean-Pierre Puel 《Comptes Rendus Mathematique》2006,343(9):573-577
This Note deals with the two-dimensional Navier–Stokes system. In this context, we prove a result concerning its global approximate controllability by means of boundary controls. To cite this article: S. Guerrero et al., C. R. Acad. Sci. Paris, Ser. I 343 (2006). 相似文献
108.
Jean-Pierre Aubin 《Journal of Evolution Equations》2012,12(1):99-117
We assume that the evolution of the population is governed by a controlled McKendrick age-structured partial differential equation where the mortality rate and immigrated population levels are no longer known coefficients, but contingent regulation parameters chosen for a given purpose, for instance, for requiring that the population satisfies prescribed viability constraints depending on time and age. The Lotka renewal equation relating the boundary condition (number of births) to the integral with respect to age of the population is replaced by the introduction of another regulation parameter in the boundary condition, regarded as a natality policy. We may control it by its derivative, regarded as a natality decision. We then construct a regulation map, associating with the population level, the time and the age the subset of natality policies, a mortality rates and an immigration levels needed for governing viable evolutions of the population. 相似文献
109.
Jean-Charles?Majesté Ahmed?Allal Jean-Pierre?MontfortEmail author 《Rheologica Acta》2003,42(5):477-482
The viscoelastic behavior of low molecular weight polymers exhibiting a fairly broad distribution has been deduced from the behavior of narrow samples by way of a linear law as a function of the density of the molecular weight distribution. Rheology of polydisperse linear polymers where the entire distribution of molecular weights is lower than 2 M ehas been investigated using both binary mixtures and a broad sample of polystyrene. A decrease of the friction coefficient and of the viscosity compared to that of a narrow sample with the same M w is observed. Therefore, the low components of broad samples play the role of plasticizers or lubricants which has been investigated in relation with the molecular weight distribution. 相似文献
110.
Alexander I. Popov Alfred J. Smetana Jean-Pierre Kintzinger Thi Thanh-Tam Nguyêen 《Helvetica chimica acta》1980,63(3):668-673
Complexation between crown ethers 12C4, 15C5, 18C6 and cryptand 222, and alkali cations Li+, Na+, K+ in various solvents were studied by 17O-NMR. spectroscopy. Small diamagnetic shifts arising from the cation electric field are observed. They increase according to the sequence K+ < Na+ < Li+. 17O-linewidth are discussed and compared to the 13C relaxation times. Linewidth modification results mainly from modifications of the effective correlation time. In general, for crown ethers, considerable line broadening occurs when the cation fits well into the cavity but line narrowing occurs when the cation is much smaller than the cavity. 相似文献