Elliptic Curve Discrete Logarithm Problem over Small Degree Extension Fields

In 2008 and 2009, Gaudry and Diem proposed an index calculus method for the resolution of the discrete logarithm on the group of points of an elliptic curve defined over a small degree extension field $\mathbb{F}_{q^{n}}$ . In this paper, we study a variation of this index calculus method, improving the overall asymptotic complexity when $n = \varOmega(\sqrt [3]{\log_{2} q})$ . In particular, we are able to successfully obtain relations on $E(\mathbb{F}_{q^{5}})$ , whereas the more expensive computational complexity of Gaudry and Diem’s initial algorithm makes it impractical in this case. An important ingredient of this result is a variation of Faugère’s Gröbner basis algorithm F4, which significantly speeds up the relation computation. We show how this index calculus also applies to oracle-assisted resolutions of the static Diffie–Hellman problem on these elliptic curves.     

Four-Dimensional Gallant–Lambert–Vanstone Scalar Multiplication

The GLV method of Gallant, Lambert, and Vanstone (CRYPTO 2001) computes any multiple kP of a point P of prime order n lying on an elliptic curve with a low-degree endomorphism Φ (called GLV curve) over $\mathbb{F}_{p}$ as $$kP = k_1P + k_2\varPhi(P) \quad\text{with } \max \bigl\{ |k_1|,|k_2| \bigr\} \leq C_1\sqrt{n} $$ for some explicit constant C ₁>0. Recently, Galbraith, Lin, and Scott (EUROCRYPT 2009) extended this method to all curves over $\mathbb{F}_{p^{2}}$ which are twists of curves defined over $\mathbb{F}_{p}$ . We show in this work how to merge the two approaches in order to get, for twists of any GLV curve over $\mathbb{F}_{p^{2}}$ , a four-dimensional decomposition together with fast endomorphisms Φ,Ψ over $\mathbb{F}_{p^{2}}$ acting on the group generated by a point P of prime order n, resulting in a proven decomposition for any scalar k∈[1,n] given by $$kP=k_1P+ k_2\varPhi(P)+ k_3\varPsi(P) + k_4\varPsi\varPhi(P) \quad \text{with } \max_i \bigl(|k_i| \bigr)< C_2\, n^{1/4} $$ for some explicit C ₂>0. Remarkably, taking the best C ₁,C ₂, we obtain C ₂/C ₁<412, independently of the curve, ensuring in theory an almost constant relative speedup. In practice, our experiments reveal that the use of the merged GLV–GLS approach supports a scalar multiplication that runs up to 1.5 times faster than the original GLV method. We then improve this performance even further by exploiting the Twisted Edwards model and show that curves originally slower may become extremely efficient on this model. In addition, we analyze the performance of the method on a multicore setting and describe how to efficiently protect GLV-based scalar multiplication against several side-channel attacks. Our implementations improve the state-of-the-art performance of scalar multiplication on elliptic curves over large prime characteristic fields for a variety of scenarios including side-channel protected and unprotected cases with sequential and multicore execution.     

WCDMA Multiclass Downlink Capacity and Interference Statistics of Cigar-Shaped Microcells in Highways

In this paper, the multiclass downlink capacity and the interference statistics of the sectors of a cigar-shaped microcells using wideband code-division multiple-access with soft handover mode are analyzed. The two-slope propagation model with log-normal shadowing is used in the analysis where a model of 8 cigar-shaped microcells is utilized. The performance of the downlink is studied for different [sector range R, standard deviation of the shadowing ( $\sigma _{1}$ and $\sigma _{2})$ and propagation exponents ( $\text{ s}_{1}$ and $\text{ s}_{2})$ ]. It is found that increasing the sector range from 500 to 1,000 m will increase the sector downlink capacity. Also, it is found that increasing the value of the propagation parameters ( $\sigma _{1}$ and $\sigma _{2})$ will reduce the downlink sector capacity. It is noticed that, the effect of changing the propagation exponent $\text{ s}_{1}$ is null while increasing the propagation exponent $\text{ s}_{2}$ will increase the downlink capacity.     

Soft X-ray Absorption and Photoemission Spectroscopy Study of Cobalt-Based Thermoelectric Oxides: \hbox{Ca}_3\hbox{Co}_4\hbox{O}_9, \hbox{Ca}_3\hbox{Co}_2\hbox{O}_6, and \hbox{Bi}_{2}\hbox{Sr}_{2}\hbox{Co}_2\hbox{O}_{y}

The electronic structures of Co-based potential thermoelectric (TE) oxides, including $\hbox{Ca}_3\hbox{Co}_4\hbox{O}_9$ and $\hbox{Bi}_{2}\hbox{Sr}_{2}\hbox{Co}_2\hbox{O}_{y}$ (y = 8 + δ) single crystals and polycrystalline $\hbox{Ca}_3\hbox{Co}_2\hbox{O}_6$ , have been investigated by employing soft x-ray absorption spectroscopy (XAS) and photoemission spectroscopy (PES). Co 2p XAS measurements show that Co ions are nearly trivalent ( $\hbox{Co}^{3+}$ ) in all of these Co-based TE oxides with a small mixture of $\hbox{Co}^{4+}$ ions in $\hbox{Bi}_{2}\hbox{Sr}_{2}\hbox{Co}_2\hbox{O}_{y}$ . Valence-band PES and O 1s XAS measurements show that the occupied Co 3d states are located at the top of the valence bands and that the lowest unoccupied states have the primarily Co 3d character, respectively. These findings suggest the importance of the Co 3d electronic structures in determining TE properties of these Co-based oxides.     

Efficient Reverse Converters for 4-Moduli Sets {2^{2n-1}-1, 2^{n}, 2^{n}+1, 2^{n}-1} and {2^{2n-1}, 2^{2n-1}-1, 2^{n}+1, 2^{n}-1} Based on CRTs Algorithm

Speed and complexity of a reverse converter are two important factors that affect the performance of a residue number system. In this paper, two efficient reverse converters are proposed for the 4-moduli sets {2 \(^{2n-1}-1\) , 2 \(^{n}\) , 2 \(^{n}+1\) , 2 \(^{n}-1\) } and {2 \(^{2n-1}\) , 2 \(^{2n-1}-1\) , 2 \(^{n}+1\) , 2 \(^{n}-1\) } with 5 \(n\) -bit and 6 \(n\) -bit dynamic range, respectively. The proposed reverse converter for moduli set {2 \(^{2n-1}-1\) , 2 \(^{n}\) , 2 \(^{n}+1\) , 2 \(^{n}-1\) } has been designed based on CRT and New CRT-I algorithms and in two-level structure. Also, an efficient reverse converter for moduli set {2 \(^{2n-1}\) , 2 \(^{2n-1}-1\) , 2 \(^{n}+1\) , 2 \(^{n}-1\) } has been designed by applying New CRT-I algorithm. The proposed reverse converters are based on adders and hence can be simply implemented by VLSI circuit technology. The proposed reverse converters offer less delay and hardware cost when compared with the recently introduced reverse converters for the moduli sets {2 \(^{n}+1\) , 2 \(^{n}-1\) ,2 \(^{n}\) , 2 \(^{2n+1}-1\) } and {2 \(^{n}+1\) , 2 \(^{n}-1\) , 2 \(^{2n}\) , 2 \(^{2n+1}-1\) }.     

A novel image segmentation model with an edge weighting function

A variational model for image segmentation consists of a data term and a regularization term. Usually, the data term is chosen as squared $\text{ L }_{2}$ norm, and the regularization term is determined by the prior assumption. In this paper, we present a novel model in the framework of MAP (maximum a posteriori). A new iteratively reweighted $\text{ L }_{2}$ norm is used in the data term, which shares the advantages of $\text{ L }_{2}$ and mixed $\text{ L }_{21}$ norm. An edge weighting function is addressed in the regularization term, which enforces the ability to reduce the outlier effects and preserve edges. An improved region-based graph cuts algorithm is proposed to solve this model efficiently. Numerical experiments show our method can get better segmentation results, especially in terms of removing outliers and preserving edges.     

Extended Robust \mathcal{H}_{2} and \mathcal{H}_{\infty} Filter Design for Discrete Time-Invariant Linear Systems with Polytopic Uncertainty

This paper is concerned with the problem of robust $\mathcal{H}_{2}$ and $\mathcal{H}_{\infty}$ filter design for discrete-time linear time-invariant systems with polytopic parameter uncertainties. Less conservative robust $\mathcal{H}_{2}$ and $\mathcal{H}_{\infty}$ filter design procedures are proposed in terms of single-parameter minimization problems with linear matrix inequality constraints. To this end, we generalize the filter structures available in the literature to date in such a way that the filter’s next state is built by summing the filter’s states over several samples from the past to the present. For stability of the filtering error system, the homogeneous polynomial parameter-dependent Lyapunov functions are employed. Finally, illustrative examples are given to demonstrate the merits of the proposed methods.     

Decentralized \mathcal{L}_{2}–\mathcal{L}_{\infty} Filtering for Interconnected Markovian Jump Systems with Delays

This paper deals with the problem of decentralized $\mathcal{L}_{2}$ – $\mathcal{L}_{\infty}$ filtering for a class of interconnected (or large-scale) Markovian jump systems with constant time delays. The purpose is to present delay-dependent conditions for the existence of mode-dependent decentralized filters, which guarantees that the filtering error system is stochastically stable with a prescribed $\mathcal{L}_{2}$ – $\mathcal{L}_{\infty}$ disturbance attenuation level. Such a purpose is achieved by using a mode-dependent centralized Lyapunov functional together with the so-called Jensen’s inequality. The obtained synthesis conditions are expressed in terms of linear matrix inequalities (LMIs), which leads to a convex design method for the concerned filters. An example including numerical and simulation results is provided finally to illustrate the effectiveness of the proposed design method.     

A Rate \text{ M }_{\mathrm{T}} Full Diversity STF Block Coded 4\times 4 MIMO-OFDM System with Reduced Complexity

Multiple input multiple output (MIMO) communication systems with orthogonal frequency division multiplexing (OFDM) has a great role to play for 4G broadband wireless communications. In this paper, a space time frequency (STF) code is presented with reduced decoder complexity and to achieve code rate $\text{ M }_\mathrm{T}$ with full diversity of $\text{ M }_{\mathrm{T}} \text{ M }_{\mathrm{R}} \text{ N }_{\mathrm{b}}$ L i.e., product of number of transmit antennas ( $\text{ M }_\mathrm{T}$ ), receive antennas $(\text{ M }_{\mathrm{R}})$ , fading blocks $(\text{ N }_{\mathrm{b}})$ and channel taps (L). The maximum achievable diversity with high rate of STF block coded MIMO-OFDM is analyzed and verified by simulation results. The decoder complexity is resolved by employing several approaches like maximum likelihood (ML), sphere decoder (SD) and array processing. The performance of STF code is compared with existing layered algebraic STF code in terms of decoder complexity and bit error rate (BER). Further, the closed form expressions for BER performance of STFBC MIMO-OFDM systems are derived and evaluated for frequency selective block fading channels with MPSK constellations.     

Anisotropic Thermopower of the Kondo Insulator \hbox {CeRu}_4\hbox {Sn}_6

The intermetallic compound \(\hbox {CeRu}_4\hbox {Sn}_6\) has been tentatively classified as Kondo insulator. This class of material, especially non-cubic representatives, is not yet fully understood. Here we report thermopower measurements on single-crystalline \(\hbox {CeRu}_4\hbox {Sn}_6\) between 2 K and 650 K, along the main crystallographic directions. Large positive thermopower is observed in the directions along which the hybridization is strong and a Kondo insulating gap forms. A negative contribution to the thermopower dominates for the crystallographic \(c\) axis where hybridization is weak and metallicity prevails.     

Electronic Structure and Thermoelectric Properties of Pseudoquaternary \hbox{Mg}_{2}\hbox{Si}_{1-x-y}\hbox{Sn}_{x}\hbox{Ge}_{y}-Based Materials

A theoretical study is presented on complex pseudoternary Bi-doped \(\hbox{Mg}_{2}\hbox{Si}_{1-x-y}\hbox{Sn}_{x}\hbox{Ge}_{y}\) materials, which have recently been revealed to reach high thermoelectric figures of merit (ZT) of ～1.4. Morphological characterization by scanning electron microscopy and energy-dispersive x-ray spectroscopy indicated that the investigated samples were multiphase and that the alloy with nominal composition \(\hbox{Mg}_{2}\hbox{Si}_{0.55}\hbox{Sn}_{0.4}\hbox{Ge}_{0.05}\) contained three phases: \(\hbox{Mg}_{2}\hbox{Si}_{0.35}\hbox{Sn}_{0.6}\hbox{Ge}_{0.05}\) (Sn-rich phase), \(\hbox{Mg}_{2}\hbox{Si}_{0.65}\hbox{Sn}_{0.3}\hbox{Ge}_{0.05}\) (Si-rich phase), and \(\hbox{Mg}_{2}\hbox{Si}_{0.15}\hbox{Sn}_{0.5}\hbox{Ge}_{0.35}\) (Ge-rich phase). The electronic structure of all these phases was calculated in the framework of the fully charge self-consistent Korringa–Kohn–Rostoker method with the coherent potential approximation (KKR-CPA) to treat chemical disorder. Electron transport coefficients such as the electrical conductivity, thermopower, and the electronic part of the thermal conductivity were studied by combining the KKR-CPA technique with Boltzmann transport theory. The two-dimensional (2D) plots (as a function of electron carrier concentration and temperature), computed for the thermopower and power factor, well support the large thermoelectric efficiency detected experimentally. Finally, employing the experimental value of the lattice thermal conductivity as an adjustable parameter, it is shown that ZT ≈ 1.4 can be reached for an optimized Bi content near T ≈ 900 K in case of the nominal composition as well as the Sn-rich phase. The question of the effect of disorder on the convergence of the conduction bands and thus the electron transport properties is addressed through detailed examination of the Fermi surfaces.     

Effect of the stoichiometric composition of the Si(111)\sqrt {21} × \sqrt {21} -(Au, Ag) surface phase on substrate conductivity

The conductivity of a silicon substrate with a Si(111) $\sqrt {21} $ × $\sqrt {21} $ -(Au, Ag) surface phase is studied. It is found that the surface conductivity of such a substrate varies depending on the ratio of the amounts of gold and silver in the given structure. An analysis of the behavior of the Si(111) $\sqrt {21} $ × $\sqrt {21} $ -(Au, Ag) surface conductivity during silver adsorption indicates the effect of a space-charge layer in the surface region of the substrate on the measurement results.     

A 5 GHZ CMOS Power VCO with Novel Frequency-Modulation for RF Transmitter

A 5 GHz transformer-feedback power oscillator with novel frequency modulation (FM) up to 10 MHz is presented in this paper. The novel FM is achieved by a CMOS transistor between transformer and ground, which is designed for varying the equivalent inductance and mutual inductance of the transformer and shows no DC connection with the oscillation circuit. The major frequency tuning is realized by the variable capacitor which is controlled by a phase lock loop. The RF VCO with 210 MHz tuning range operates in class-E mode to achieve a cost-effective transmitter, which demonstrates a high DC-to-RF conversion efficiency of 39 %. A RF power of 15.1 dBm and phase noise better than \(-\) 109 dBc/Hz @ 100 kHz from the central frequency of 5.5 GHz is obtained with the biasing conditions V \(_\mathrm{ds}\) = 1.8 V and V \(_\mathrm{gs}\) = 0.65 V. The VCO also demonstrates an ultra-low voltage operation capability: with V \(_\mathrm{ds}\) = V \(_\mathrm{gs}\) = 0.6 V and DC power consumption of 9 mW, the output power is 4.5 dBm and the phase noise better than \(-\) 93 dBc/Hz @ 100 kHz. The die size of the transformer-feedback power oscillator is only \(0.4\times 0.6\) mm \(^{2}\) .     

Thiele’s continued fractions in digital implementation of noninteger differintegrators

A rational approximation is the preliminary step of all the indirect methods for implementing digital fractional differintegrators s ^??, with ${\nu \in \mathbb{R}, 0<|\nu| <1 }$ , and where ${s \in \mathbb{C}}$ . This paper employs the convergents of two Thiele??s continued fractions as rational approximations of s ^??. In a second step, it uses known s-to-z transformation rules to obtain a rational, stable, and minimum-phase z-transfer function, with zeros interlacing poles. The paper concludes with a comparative analysis of the quality of the proposed approximations in dependence of the used s-to-z transformations and of the sampling period.     

Performance Analysis of Microwave Radio Refractivity on Radio Field Strength and Radio Horizon Distance Over Akure,Nigeria

Surface radio refractivity studies are being carried out in Akure, \((7.15^{\circ }\hbox {N}, 5.12^{\circ }\hbox {E})\) South-Western Nigeria, by in-situ measurement of atmospheric pressure, temperature, and relative humidity using Wireless Weather Station (Integrated Sensor Suit, ISS). Five years of measurement (January, 2007–December, 2011) were used to compute the surface radio refractivity and its diurnal, daily, seasonal and yearly variations are analyzed. The results were then used to compute radio horizon distance \((\hbox {R}_\mathrm{DH})\) and examine the field strength (FSV) variability. Results obtained show that the surface radio refractivity, \(\hbox {N}_\mathrm{s}\) , varies with the time of the day as well as the seasons of the year. High values of \(\hbox {N}_\mathrm{s}\) were recorded in the morning and evening hours while the values were minima around 1,500 h local time. An average value of surface radio refractivity of 364.74 N-units was obtained for this location. The annual maximum mean of FSV is 15.24 dB and the minimum is 2.20 dB. This implies that the output of a receiving antenna in Akure may generally be subject to variations not less than 2 dB in a year, but can be as high as 15 dB.     

Method for Designing Efficient Mixed Radix Multipliers

The multiplication of two signed inputs, \(A {\times } B\) , can be accelerated by using the iterative Booth algorithm. Although high radix multipliers require summing a smaller number of partial products, and consume less power, its performance is restricted by the generation of the required hard multiples of B ( \(\pm \phi B\) terms). Mixed radix architectures are presented herein as a method to exploit the use of several radices. In order to implement efficient multipliers, we propose to overlap the computation of the \(\pm \phi B\) terms for higher radices with the addition of the partial products associated to lower radices. Two approaches are presented which have different advantages, namely a combinatory design and a synchronous design. The best solutions for the combinatory mixed radix multiplier for \(64\times 64\) bits require \(8.78\) and \(6.55~\%\) less area and delay in comparison to its counterpart radix-4 multiplier, whereas the synchronous solution for \(64\times 64\) bits is almost \(4{\times }\) smaller in comparison with the combinatory solution, although at the cost of about \(5.3{\times }\) slowdown. Moreover, we propose to extend this technique to further improve the multipliers for residue number systems. Experimental results demonstrate that best proposed modulo \(2^{n}{-}1\) and \(2^{n}{+}1\) multiplier designs for the same width, \(64{\times }64\) bits, provide an Area-Delay-Product similar for the case of the combinatory approach and \(20~\%\) reduction for the synchronous design, when compared to their respective counterpart radix-4 solutions.     

An Ideal Multi-secret Sharing Scheme Based on Connectivity of Graphs

Secure communication has become more and more important for many modern communication applications. In a secure communication, every pair of users need to have a secure communication channel (each channel is controlled by a server) In this paper, using monotone span programs we devise an ideal linear multi-secret sharing scheme based on connectivity of graphs. In our proposed scheme, we assume that every pair of users, \(p\) and \(q\) , use the secret key \(s_{pq} \) to communicate with each other and every server has a secret share such that a set of servers can recover \(s_{pq} \) if the channels controlled by the servers in this set can connect users, \(p\) and \(q\) . The multi-secret sharing scheme can provide efficiency for key management. We also prove that the proposed scheme satisfies the definition of a perfect multi-secret sharing scheme. Our proposed scheme is desirable for secure and efficient secure communications.     

A New Algorithm Based on Linearized Bregman Iteration with Generalized Inverse for Compressed Sensing

This paper aims to solve the basis pursuit problem $\min_{u\in\mathbb{R}^{n}}\{\|u\|_{1}: Au=f\}$ in compressed sensing when A is any matrix, there are two contributions in this paper. First, we provide a simplified iterative formula that combines original linearized Bregman iteration together with a soft threshold and iterative formula for generalized inverse of matrix $A\in\mathbb{R}^{m\times n}$ . Furthermore, we also discuss its convergence. Compared to the original linearized Bregman method, the proposed simplified iterative scheme possesses obvious advantage. The workload and computing time are greatly reduced, when m?n and $\operatorname{rank}(A)\ll m$ , especially. But the requirement of high accuracy cannot be achieved. So, we need to select the proper number of inner loop to achieve the goal of balancing the workload and the accuracy of the simplified iterative formula. Second, we propose a new chaotic iterative algorithm based on the simplified iteration. Under the same iterations, the computing time of the simplified iteration with q=1 (q is the number of inner loops) is almost the same as that of the chaotic method, but the precision of the latter is better than that of the former because it utilized more information; and the accuracy of the chaotic method achieves that of A ^? linearized Bregman iteration, while the computing time of the former is less than one half of the latter. In conclusion, the calculating efficiency of our two methods as regards A ^? iteration is improved, and specially the chaotic iteration is more competitive. Numerical results on compressed sensing are presented that demonstrate that our methods can be significantly more effective than the original linearized Bregman iterations, even when matrix A is ill-conditioned.     

Optimization of fiber Raman amplifier by reduction of four wave mixing effect

We analyzed the four wave mixing (FWM) effect by propagating two channels through the same backward pumped fiber Raman amplifier (FRA) with variations in FRA parameters. It is observed that FWM increases with increase in signal input power as well as pump power. The FWM effect is also analyzed for Raman constant \(({f}_{\text{ r }})\) to obtain the optimum value of \(({f}_{\text{ r }})\) , and it is found that to have minimum FWM, the optimum value of Raman constant comes out to be 0.18. This Raman amplifier can be used for wavelength division multiplexed application with constant broadband gain.     

Formation of a Buffer Layer for Graphene on C-Face SiC{0001}

Graphene films prepared by heating the SiC $ (000\bar{1}) $ surface (the C-face of the {0001} surface) in a Si-rich environment have been studied using low-energy electron diffraction (LEED) and low-energy electron microscopy. Upon graphitization, an interface with $ \sqrt {43} \times \sqrt {43} - R \pm 7.6^\circ $ symmetry is observed by in situ LEED. After oxidation, the interface displays $ \sqrt 3 \times \sqrt 3 - R 30^\circ $ symmetry. Electron reflectivity measurements indicate that these interface structures arise from a graphene-like “buffer layer” that forms between the graphene and the SiC, similar to that observed on Si-face SiC. From a dynamical LEED structure calculation for the oxidized C-face surface, it is found to consist of a graphene layer sitting on top of a silicate (Si₂O₃) layer, with the silicate layer having the well-known structure as previously studied on bare SiC $ (000\bar{1}) $ surfaces. Based on this result, the structure of the interface prior to oxidation is discussed.