Generalized cryptanalysis of RSA with small public exponent针对公钥e小于等于N的0.5次幂的RSA算法的广义密码分析

In this paper, we demonstrate that there exist weak keys in the RSA public-key cryptosystem with the public exponent e = N^α ≤ N^0.5. In 1999, Boneh and Durfee showed that when α ≈ 1 and the private exponent d = N^β < N^0.292, the system is insecure. Moreover, their attack is still effective for 0.5 < α < 1.875. We propose a generalized cryptanalytic method to attack the RSA cryptosystem with α ≤ 0.5. For \(c = \left\lfloor {\frac{{1 - \alpha }}{\alpha }} \right\rfloor \) and e^γc ≡ d (mod e^c), when γ, β satisfy \(\gamma < 1 + \frac{1}{c} - \frac{1}{{2\alpha c}}and\beta < \alpha c + \frac{7}{6} - \alpha \gamma c - \frac{1}{3}\sqrt {6\alpha + 6\alpha c + 1 - 6\alpha \gamma c} \), we can perform cryptanalytic attacks based on the LLL algorithm. The basic idea is an application of Coppersmith’s techniques and we further adapt the technique of unravelled linearization, which leads to an optimized lattice. Our advantage is that we achieve new attacks on RSA with α ≤ 0.5 and consequently, there exist weak keys in RSA for most α.     

Design of optimal and robust control with <Emphasis Type="Italic">H</Emphasis> <Subscript>∞</Subscript>/<Emphasis Type="Italic">γ</Emphasis> <Subscript>0</Subscript> performance criterion

For a double-input single-output system, this paper defines a disturbance attenuation level (called H_∞/γ₀ norm) as the maximum-value L₂ norm of the output under an unknown disturbance with a bounded L₂ norm supplied to the first input and an impulsive disturbance in the form of the product of an unknown vector and the delta function supplied the second input, where the squared L₂ norm of the former disturbance plus the quadratic form of the impulsive disturbance vector does not exceed 1. Weight matrix choice in the H_∞/γ₀ norm yields a trade-off between the attenuation level of the L₂ disturbance and the attenuation level of the impulsive disturbance in corresponding channels. For the uncertain systems with dynamic or parametric uncertainty in the feedback loop, a robust H_∞/γ₀ norm is introduced that includes the robust H_∞ and γ₀ norms as special cases. All these characteristics or their upper bounds in the uncertain system are expressed via solutions of linear matrix inequalities. This gives a uniform approach for designing optimal and robust control laws with the H_∞/γ₀, H_∞ and γ₀ performance criteria.     

Noise Level Estimation in High-Dimensional Linear Models

We consider the problem of estimating the noise level σ² in a Gaussian linear model Y = Xβ+σξ, where ξ ∈ ?ⁿ is a standard discrete white Gaussian noise and β ∈ ?^p an unknown nuisance vector. It is assumed that X is a known ill-conditioned n × p matrix with n ≥ p and with large dimension p. In this situation the vector β is estimated with the help of spectral regularization of the maximum likelihood estimate, and the noise level estimate is computed with the help of adaptive (i.e., data-driven) normalization of the quadratic prediction error. For this estimate, we compute its concentration rate around the pseudo-estimate ||Y ? Xβ||²/n.     

Deterministic lateral displacement (DLD) in the high Reynolds number regime: high-throughput and dynamic separation characteristics

Recent progress in the development of biosensors has created a demand for high-throughput sample preparation techniques that can be easily integrated into microfluidic or lab-on-a-chip platforms. One mechanism that may satisfy this demand is deterministic lateral displacement (DLD), which uses hydrodynamic forces to separate particles based on size. Numerous medically relevant cellular organisms, such as circulating tumor cells (10–15 µm) and red blood cells (6–8 µm), can be manipulated using microscale DLD devices. In general, these often-viscous samples require some form of dilution or other treatment prior to microfluidic transport, further increasing the need for high-throughput operation to compensate for the increased sample volume. However, high-throughput DLD devices will require a high flow rate, leading to an increase in Reynolds numbers (Re) much higher than those covered by existing studies for microscale (≤?100 µm) DLD devices. This study characterizes the separation performance for microscale DLD devices in the high-Re regime (10?<?Re?<?60) through numerical simulation and experimental validation. As Re increases, streamlines evolve and microvortices emerge in the wake of the pillars, resulting in a particle trajectory shift within the DLD array. This differs from previous DLD works, in that traditional models only account for streamlines that are characteristic of low-Re flow, with no consideration for the transformation of these streamlines with increasing Re. We have established a trend through numerical modeling, which agrees with our experimental findings, to serve as a guideline for microscale DLD performance in the high-Re regime. Finally, this new phenomenon could be exploited to design passive DLD devices with a dynamic separation range, controlled simply by adjusting the device flow rate.     

Developing heatable microfluidic chip to generate gelatin emulsions and microcapsules

The heatable microfluidic chip developed herein successfully integrates a microheater and flow-focusing device to generate uniform-sized gelatin emulsions under various flow rate ratios (sample phase/oil phase, Q _s/Q _o) and driven voltages. The gelatin emulsions can be applied to encapsulate vitamin C for drug release. Our goal is to create the thermal conditions for thermo-sensitive hydrogel materials in the microfluidic chip and generate continuous and uniform emulsions under any external environment. The gelatin emulsion sizes have a coefficient of variation of <5 % and can be precisely controlled by altering the flow rate ratio (Q _s/Q _o) and driven voltage. The gelatin emulsion diameters range from 45 to 120 μm. Moreover, various sizes of these gelatin microcapsules containing vitamin C were used for drug release. The developed microfluidic chip has the advantages of a heatable platform in the fluid device, active control over the emulsion diameter, the generation of uniform-sized emulsions, and simplicity. This new approach for gelatin microcapsules will provide many potential applications in drug delivery and pharmaceuticals.     

On risk concentration for convex combinations of linear estimators

We consider the estimation problem for an unknown vector β ∈ Rp in a linear model Y = Xβ + σξ, where ξ ∈ Rⁿ is a standard discrete white Gaussian noise and X is a known n × p matrix with n ≥ p. It is assumed that p is large and X is an ill-conditioned matrix. To estimate β in this situation, we use a family of spectral regularizations of the maximum likelihood method β^α(Y) = H ^α(X ^T X) β ^?(Y), α ∈ R⁺, where β ^?(Y) is the maximum likelihood estimate for β and {H ^α(·): R⁺ → [0, 1], α ∈ R⁺} is a given ordered family of functions indexed by a regularization parameter α. The final estimate for β is constructed as a convex combination (in α) of the estimates β^α(Y) with weights chosen based on the observations Y. We present inequalities for large deviations of the norm of the prediction error of this method.     

Finding the Schwarzschild metric from gravity’s Exterior and Interior Effacement algebra

In the author’s previous publications, a recursive linear algebraicmethod was introduced for obtaining (sans gravitational radiation) the full potential expansions for the gravitational metric field components and the Lagrangian for the general N-body system. Two apparent properties of gravity—Exterior Effacement and Interior Effacement—were defined and enforced to obtain the recursive algebra, especially for the motion-independent potential expansions of the general N-body situation. The linear algebraic equations of this method permit determination of the potential coefficients at any order n ^? of the expansions in terms of the lower order coefficients. To illustrate the capabilities of this algebraic method by enforcing exterior and interior effacement, and focusing on only a needed few potential series of the full motion-independent potential expansions, the complete exterior metric field for a single, spherically symmetric mass source is here obtained—the Schwarzschild metric field of general relativity (the Eddington PPN parameter γ = 1) as well as its generalization if the isotropic spatial metric potential’s linearized form is ?g _SS (γ, r) = 1 + 2γ Gm/c ² r +.... with γ ≠ 1 are obtained.     

General Independence Sets in Random Strongly Sparse Hypergraphs

We analyze the asymptotic behavior of the j-independence number of a random k-uniform hypergraph H(n, k, p) in the binomial model. We prove that in the strongly sparse case, i.e., where \(p = c/\left( \begin{gathered} n - 1 \hfill \\ k - 1 \hfill \\ \end{gathered} \right)\) for a positive constant 0 < c ≤ 1/(k ? 1), there exists a constant γ(k, j, c) > 0 such that the j-independence number α _j (H(n, k, p)) obeys the law of large numbers \(\frac{{{\alpha _j}\left( {H\left( {n,k,p} \right)} \right)}}{n}\xrightarrow{P}\gamma \left( {k,j,c} \right)asn \to + \infty \) Moreover, we explicitly present γ(k, j, c) as a function of a solution of some transcendental equation.     

First and Others credit-assignment schema for evaluating the academic contribution of coauthors

Credit-assignment schemas are widely applied by providing fixed or flexible credit distribution formulas to evaluate the contributions of coauthors of a scientific publication. In this paper, we propose an approach named First and Others (F&O) counting. By introducing a tuning parameter α and a weight β, two new properties are obtained: (1) flexible assignment of credits by modifying the formula (with the change of α) and applying preference to the individual author by adjusting the weights (with the change of β), and (2) calculation of the credits by separating the formula for the first author from others. With formula separation, the credit of the second author shows an inflection point according to the change of α. The developed theorems and proofs concerning the modification of α and β reveal new properties and complement the base theory for informetrics. The F&O schema is also adapted when considering the policy of ‘first-corresponding-author-emphasis’. Through a comparative analysis using a set of empirical data from the fields of chemistry, medicine, psychology, and the Harvard survey data, the performance of the F&O approach is compared with those of other methods to demonstrate its benefits by the criteria of lack of fit and coefficient of determination.     

Microfluidic immobilization and subcellular imaging of developing <Emphasis Type="Italic">Caenorhabditis elegans</Emphasis>

Caenorhabditis elegans has been an essential model organism in the fields of developmental biology, neuroscience, and aging. However, these areas have been limited by our ability to visualize and track individual C. elegans worms, especially at the subcellular scale, over the course of their lifetime. Here we present a microfluidic device to culture individual C. elegans in parallel throughout post-embryonic development. The device allows for periodic mechanical immobilization of the worm, enabling 3D imaging at subcellular precision. The immobilization is sufficient to enable fluorescence recovery after photobleaching (FRAP) measurements on organelles and other substructures within the same specific cells throughout larval development, without the use of chemical anesthetics. Using this device, we measure FRAP recovery of two nucleolar proteins in specific intestinal cells within the same worms during larval development. We show that these proteins exhibit different fluorescence recovery as the worm grows, suggesting differential protein interactions during development. We anticipate that this device will help expand the possible uses of C. elegans as a model organism, enabling its use in addressing fundamental questions at the subcellular scale.     

Approximating the Metric TSP in Linear Time

Given a metric graph G=(V,E) of n vertices, i.e., a complete graph with a non-negative real edge cost function satisfying the triangle inequality, the metricity degree of G is defined as \(\beta=\max_{x,y,z\in V}\{\frac{c(x,y)}{c(x,z)+c(y,z)}\}\in[\frac{1}{2},1]\). This value is instrumental to establish the approximability of several NP-hard optimization problems definable on G, like for instance the prominent traveling salesman problem, which asks for finding a Hamiltonian cycle of G of minimum total cost. In fact, this problem can be approximated quite accurately depending on the metricity degree of G, namely by a ratio of either \(\frac{2-\beta}{3(1-\beta)}\) or \(\frac{3\beta^{2}}{3\beta^{2}-2\beta+1}\), for \(\beta<\frac{2}{3}\) or \(\beta\geq \frac{2}{3}\), respectively. Nevertheless, these approximation algorithms have O(n ³) and O(n ^2.5log?^1.5 n) running time, respectively, and therefore they are superlinear in the Θ(n ²) input size. Thus, since many real-world problems are modeled by graphs of huge size, their use might turn out to be unfeasible in practice, and alternative approaches requiring only O(n ²) time are sought. However, with this restriction, all the currently available approaches can only guarantee a 2-approximation ratio for the case β=1, which means a \(\frac{2\beta^{2}}{2\beta^{2}-2\beta+1}\)-approximation ratio for general β<1. In this paper, we show how to elaborate—without affecting the space and time complexity—one of these approaches, namely the classic double-MST heuristic, in order to obtain a 2β-approximate solution. This improvement is effective, since we show that the double-MST heuristic has in general a performance ratio strictly larger than 2β, and we further show that any alternative elaboration of it cannot lead to a performance ratio better than 2β?ε, for any ε>0. Our theoretical results are complemented with an extensive series of experiments, that show the practical appeal of our approach.     

Separation and concentration of <Emphasis Type="Italic">Phytophthora ramorum</Emphasis> sporangia by inertial focusing in curving microfluidic flows

We present an integrated microfluidic system for performing isolation and concentration of Phytophthora ramorum pathogens using a chip whose working principle is based on inertial lateral migration in curving flows. The chip was fabricated from multiple layers of thermoplastic polymers and features an embedded spiral separation channel along with peristaltic microvalves for fluidic operation and process control. A pumping system paired with a fully programmable pressure manifold is used to boost concentration levels by recirculating the sample liquid multiple times through the separation chip, making it possible to reduce sample volumes from 10 to 1 mL or less. The system was calibrated using fluorescent polymer particles with a nominal diameter of 30 µm which is comparable to that of P. ramorum sporangia. The separation process has been shown to be highly effective and more than 99% of the beads can be recovered in the concentrated batch. Experiments conducted with P. ramorum sporangia have shown that a 5.3-fold increase in pathogen content with 95% recovery can be achieved using three subsequent concentration cycles. The utility of the method has been validated by processing a sample derived from infested Rhododendron leaves where a 6.1-fold increase in the concentration of P. ramorum has been obtained after four concentration cycles. Although specifically designed and demonstrated for sporangia of P. ramorum, the method and related design rules can easily be extended to other microbial organisms, effectively supporting bioanalytical applications where efficient, high-throughput separation of target species is of primary concern.     

On-chip PMA labeling of foodborne pathogenic bacteria for viable qPCR and qLAMP detection

Propidium monoazide (PMA) is a membrane impermeable molecule that covalently bonds to double stranded DNA when exposed to light and inhibits the polymerase activity, thus enabling DNA amplification detection protocols that discriminate between viable and non-viable entities. Here, we present a microfluidic device for inexpensive, fast, and simple PMA labeling for viable qPCR and qLAMP assays. The three labeling stages of mixing, incubation, and cross-linking are completed within a microfluidic device that is designed with Tesla structures for passive microfluidic mixing, bubble trappers to improve flow uniformity, and a blue LED to cross-link the molecules. Our results show that the on-chip PMA labeling is equivalent to the standard manual protocols and prevents the replication of DNA from non-viable cells in amplification assays. However, the on-chip process is faster and simpler (30 min of hands-off work), has a reduced likelihood of false negatives, and it is less expensive because it only uses 1/20th of the reagents normally consumed in standard bench protocols. We used our microfluidic device to perform viable qPCR and qLAMP for the detection of S. typhi and E. coli O157. With this device, we are able to specifically detect viable bacteria, with a limit of detection of 7.6 × 10³ and 1.1 × 10³ CFU/mL for S. typhi and E. coli O157, respectively, while eliminating amplification from non-viable cells. Furthermore, we studied the effects of greater flow rates to expedite the labeling process and identified a maximum flow rate of 0.7 μL/min for complete labeling with the current design.     

Sensitive analysis of glutathione in bacteria and HaCaT cells by polydopamine/gold nanoparticle-coated microchip electrophoresis via online pre-concentration of field-amplified sample stacking

In this paper, polydopamine/gold nanoparticles (PDA/Au NPs) were used to construct a functional film on a glass microfluidic channel surface in microchip electrophoresis (MCE) for the separation of reduced glutathione (GSH) and oxidized glutathione (GSSH). The formation of the PDA/Au NPs was characterized by scanning electron microscopy, transmission electron microscope, UV–Vis spectra and ATR-FTIR. An online pre-concentration strategy involving field-amplified sample stacking was used to determine the sensitivity of the assay for measuring GSH and GSSH in bacteria (Escherichia coli, Staphylococcus aureus and Salmonella enterica serovar Typhimurium) and HaCaT cells samples by MCE with laser-induced fluorescence detection. The influences of the separation voltage, the concentration of the running buffer and the pH value of running buffer, were carefully investigated. Using this studied method, GSH and GSSH could be simultaneously pre-concentrated and separated within 70 s. The limits of detection of GSH and GSSH were as low as 0.81 and 0.91 nM, respectively (S/N = 3), which corresponded to approximately 180–301-fold improvements in peak height. Moreover, this method was successfully applied to the analysis of bacteria (E. coli, S. aureus and S. typhimurium) and HaCaT cell samples with a satisfactory recovery rate.     

An integrated microfluidic system using mannose-binding lectin for bacteria isolation and biofilm-related gene detection

Molecular diagnosis of biofilm-related genes (BRGs) in common bacteria that cause periprosthetic joint infections may provide crucial information for clinicians. In this study, several BRGs, including ica, fnbA, and fnbB, were rapidly detected (within 1 h) with a new integrated microfluidic system. Mannose-binding lectin (MBL)-coated magnetic beads were used to isolate these bacteria, and on-chip nucleic acid amplification (polymerase chain reaction, PCR) was then performed to detect BRGs. Both eukaryotic and prokaryotic MBLs were able to isolate common bacterial strains, regardless of their antibiotic resistance, and limits of detection were as low as 3 and 9 CFU for methicillin-resistant Staphylococcus aureus and Escherichia coli, respectively, when using a universal 16S rRNA PCR assay for bacterial identification. It is worth noting that the entire process including bacteria isolation by using MBL-coated beads for sample pre-treatment, on-chip PCR, and fluorescent signal detection could be completed on an integrated microfluidic system within 1 h. This is the first time that an integrated microfluidic system capable of detecting BRGs by using MBL as a universal capturing probe was reported. This integrated microfluidic system might therefore prove useful for monitoring profiles of BRGs and give clinicians more clues for their clinical judgments in the near future.     

Relations between Transition Rates and Quantum Numbers in Gravitational Potentials

This paper forms part of an ongoing investigation to examine the quantum prediction that isolated baryons and electrons in the deep gravity wells of galaxy halos should exhibit reduced interaction cross-sections by virtue of the composition of the gravitational eigenspectra of their wave functions, and thereby identify a possible mechanism responsible for the origin of dark matter, without resorting to new physics or unknown particles. Relevant to this investigation are the electromagnetic state-to-state transition rates of charged particles occupying these gravitational eigenstates (EinsteinA coefficients), and, in the present work, we examine trends in these rates and net state lifetimes for particles in 1/r potential wells for values of the principal quantum number n and the angular momentum quantum number l. We find that transition rates decrease with increasing n and l, and that the rate is more steeply dependent on l when the quantum parameter Δp (≡ Δn ? Δl) is greater, in agreement with earlier work. It is also found that there is an empirical relationship between the total state lifetime τ and the eigenvalues n and l, which is given by τ ∝ n ^α l ^β , where α ≈ 3 and β ≈ 2. The results apply equally to electrical potential wells, where the phenomena of reduced cross-sections and long radiative lifetimes is well known in the case of the Rydberg states of electrons in atoms. More importantly, in the case of gravitational eigenstates discussed here, the quantum prediction of low Einstein A (and therefore B) coefficients ofmany of the stateto-state transitions will mean that a particle whose eigenspectral composition consists of many of these weakly interacting states will be less likely to undergo scattering processes such as Compton scattering. Trends in the Einstein coefficients over the range of component eigenstates are required for calculating the net visibility and interaction rates of the generalized wave functions representing charged particles in macroscopic gravitational fields.     

Polar Codes with Higher-Order Memory

We introduce a construction of a set of code sequences {C_n^(m) : n ≥ 1, m ≥ 1} with memory order m and code length N(n). {C_n^(m)} is a generalization of polar codes presented by Ar?kan in [1], where the encoder mapping with length N(n) is obtained recursively from the encoder mappings with lengths N(n ? 1) and N(n ? m), and {C_n^(m)} coincides with the original polar codes when m = 1. We show that {C_n^(m)} achieves the symmetric capacity I(W) of an arbitrary binary-input, discrete-output memoryless channel W for any fixed m. We also obtain an upper bound on the probability of block-decoding error P_e of {C_n^(m)} and show that \({P_e} = O({2^{ - {N^\beta }}})\) is achievable for β < 1/[1+m(? ? 1)], where ? ∈ (1, 2] is the largest real root of the polynomial F(m, ρ) = ρ^m ? ρ^{m ? 1} ? 1. The encoding and decoding complexities of {C_n^(m)} decrease with increasing m, which proves the existence of new polar coding schemes that have lower complexity than Ar?kan’s construction.     

Attracting ellipsoids and synthesis of oscillatory regimes

An approach to stabilization of nonlinear oscillations in multidimensional spaces is proposed on the basis of the V.I. Zubov’s stability theory for invariant sets. As a special case, the derived controls make it possible to excite self-oscillating regimes in specified state subspaces R ^2k ? R ²ⁿ with simultaneous oscillation damping on Cartesian products R ^2n?2k .     

Stochastic problems in <Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> and <Emphasis Type="Italic">H</Emphasis><Subscript>2</Subscript>/<Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> control

We consider stochastic control systems subjected simultaneously to stochastic and determinate perturbations. Stochastic perturbations are assumed to be state-multiplicative stochastic processes, while determinate perturbations can be any processes with finite energy on infinite time interval. The results of the determinate H _∞-theory are compared to their stochastic analogs. The determinate and stochastic theories are linked together by the lemma that establishes the equivalence between the stability and boundness of the ‖L‖_∞ < γ norm of the perturbation operator L, from one side, and the solvability of certain linear matrix inequalities (LMIs), from the other side. As soon as the stochastic version of the lemma is proven, the γ-controller analysis and design problems are solved, in general, identically in the frame of the united LMI methodology.     

Inertial migration of single particle in a square microchannel over wide ranges of <Emphasis Type="Italic">Re</Emphasis> and particle sizes

Inertial migration of particles has been widely used in inertial microfluidic systems to passively manipulate cells/particles. However, the migration behaviors and the underlying mechanisms, especially in a square microchannel, are still not very clear. In this paper, the immersed boundary-lattice Boltzmann method (IB-LBM) was introduced and validated to explore the migration characteristics and the underlying mechanisms of an inertial focusing single particle in a square microchannel. The grid-independence analysis was made first to highlight that the grid number across the thin liquid film (between a particle and its neighboring channel wall) was of significant importance in accurately capturing the migrating particle’s dynamics. Then, the inertial migration of a single particle was numerically investigated over wide ranges of Reynolds number (Re, from 10 to 500) and particle sizes (diameter-to-height ratio a/H, from 0.16 to 0.5). It was interesting to find that as Re increased, the channel face equilibrium (CFE) position moved outward to channel walls at first, and then inflected inwards to the channel center at high Re (Re?>?200). To account for the physical mechanisms behind this behavior, the secondary flow induced by the inertial focusing single particle was further investigated. It was found that as Re increased, two vortices appeared around the particle and grew gradually, which pushed the particle away from the channel wall at high Re. Finally, a correlation was proposed based on the numerical data to predict the critical length L_c (defined to describe the size of fluid domain that was strongly influenced by the particle) according to the particle size a/H and Re.