2,370 research outputs found
A geometric view of cryptographic equation solving
This paper considers the geometric properties of the Relinearisation algorithm and of the XL algorithm used in cryptology for equation solving. We give a formal description of each algorithm in terms of projective geometry, making particular use of the Veronese variety. We establish the fundamental geometrical connection between the two algorithms and show how both algorithms can be viewed as being equivalent to the problem of finding a matrix of low rank in the linear span of a collection of matrices, a problem sometimes known as the MinRank problem. Furthermore, we generalise the XL algorithm to a geometrically invariant algorithm, which we term the GeometricXL algorithm. The GeometricXL algorithm is a technique which can solve certain equation systems that are not easily soluble by the XL algorithm or by Groebner basis methods
Two philosophies for solving non-linear equations in algebraic cryptanalysis
Algebraic Cryptanalysis [45] is concerned with solving of particular systems of multivariate non-linear equations which occur in cryptanalysis. Many different methods for solving such problems have been proposed in cryptanalytic literature: XL and XSL method, Gröbner bases, SAT solvers, as well as many other. In this paper we survey these methods and point out that the main working principle in all of them is essentially the same. One quantity grows faster than another quantity which leads to a “phase transition” and the problem becomes efficiently solvable. We illustrate this with examples from both symmetric and asymmetric cryptanalysis. In this paper we point out that there exists a second (more) general way of formulating algebraic attacks through dedicated coding techniques which involve redundancy with addition of new variables. This opens numerous new possibilities for the attackers and leads to interesting optimization problems where the existence of interesting equations may be somewhat deliberately engineered by the attacker
Mixed-signal circuits and boards for high safety applications
A design methodology for analogue on-line test is presented by means of a real circuit implementation. The test strategy is based on monitoring via a very small analogue checker the inputs of all operational ampliers of a fully di erential circuit. The self-checking properties of the functional circuit are evaluated for a hard/soft fault model. Since the analogue checker outputs a double-rail error indication, the compatibility with digital checkers is ensured and the design of self-checking mixed-signal circuits becomes very simple. The mixed-signal approach is extended toboards through the IEEE Std. 1149.1 digital test bus and a layout rule to avoid interconnect di erential shorts.
Study of the optimal conditions for NV- center formation in type 1b diamond, using photoluminescence and positron annihilation spectroscopies
We studied the parameters to optimize the production of negatively-charged
nitrogen-vacancy color centers (NV-) in type~1b single crystal diamond using
proton irradiation followed by thermal annealing under vacuum. Several samples
were treated under different irradiation and annealing conditions and
characterized by slow positron beam Doppler-broadening and photoluminescence
(PL) spectroscopies. At high proton fluences another complex vacancy defect
appears limiting the formation of NV-. Concentrations as high as 2.3 x 10^18
cm^-3 of NV- have been estimated from PL measurements. Furthermore, we inferred
the trapping coefficient of positrons by NV-. This study brings insight into
the production of a high concentration of NV- in diamond, which is of utmost
importance in ultra-sensitive magnetometry and quantum hybrid systems
applications
Using LDGM Codes and Sparse Syndromes to Achieve Digital Signatures
In this paper, we address the problem of achieving efficient code-based
digital signatures with small public keys. The solution we propose exploits
sparse syndromes and randomly designed low-density generator matrix codes.
Based on our evaluations, the proposed scheme is able to outperform existing
solutions, permitting to achieve considerable security levels with very small
public keys.Comment: 16 pages. The final publication is available at springerlink.co
Coherent low-energy charge transport in a diffusive S-N-S junction
We have studied the current voltage characteristics of diffusive mesoscopic
Nb-Cu-Nb Josephson junctions with highly-transparent Nb-Cu interfaces. We
consider the low-voltage and high-temperature regime eV<\epsilon_{c}<k_{B}T
where epsilon_{c} is the Thouless energy. The observed excess current as well
as the observed sub-harmonic Shapiro steps under microwave irradiation suggest
the occurrence of low-energy coherent Multiple Andreev Reflection (MAR).Comment: 4 pages, 4 figures, final versio
Synchronization of Hamiltonian motion and dissipative effects in optical lattices: Evidence for a stochastic resonance
We theoretically study the influence of the noise strength on the excitation
of the Brillouin propagation modes in a dissipative optical lattice. We show
that the excitation has a resonant behavior for a specific amount of noise
corresponding to the precise synchronization of the Hamiltonian motion on the
optical potential surfaces and the dissipative effects associated with optical
pumping in the lattice. This corresponds to the phenomenon of stochastic
resonance. Our results are obtained by numerical simulations and correspond to
the analysis of microscopic quantities (atomic spatial distributions) as well
as macroscopic quantities (enhancement of spatial diffusion and pump-probe
spectra). We also present a simple analytical model in excellent agreement with
the simulations
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