ResearchPad - algebraic-geometry https://www.researchpad.co Default RSS Feed en-us © 2020 Newgen KnowledgeWorks <![CDATA[Robustness and parameter geography in post-translational modification systems]]> https://www.researchpad.co/article/elastic_article_14658 Biological organisms are often said to have robust properties but it is difficult to understand how such robustness arises from molecular interactions. Here, we use a mathematical model to study how the molecular mechanism of protein modification exhibits the property of multiple internal states, which has been suggested to underlie memory and decision making. The robustness of this property is revealed by the size and shape, or “geography,” of the parametric region in which the property holds. We use advances in reducing model complexity and in rapidly solving the underlying equations, to extensively sample parameter points in an 8-dimensional space. We find that under realistic molecular assumptions the size of the region is surprisingly small, suggesting that generating multiple internal states with such a mechanism is much harder than expected. While the shape of the region appears straightforward, we find surprising complexity in how the region grows with increasing amounts of the modified substrate. Our approach uses statistical analysis of data generated from a model, rather than from experiments, but leads to precise mathematical conjectures about parameter geography and biological robustness.

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<![CDATA[Security analysis of elliptic curves with embedding degree 1 proposed in PLOS ONE 2016]]> https://www.researchpad.co/article/5c75ac88d5eed0c484d089b5

Wang et al. proposed a method for obtaining elliptic curves with embedding degree 1 for securing critical infrastructures, and presented several elliptic curves generated by their method with torsion points of 160 bits and 189 bits orders. They also presented some experimental results and claimed that their implementation of an elliptic curve generated with their method is faster than an implementation for embedded devices presented by Bertoni et al. In this paper, we point out that the security and efficiency claims given by Wang et al. are flawed. Specifically, we show that it is possible to solve finite field discrete logarithm problems defined over their elliptic curves in practice. On the elliptic curves with torsion points of 160 bits orders generated by Wang et al., their instances of finite field discrete logarithm problems are solved in around 4 hours by using a standard desktop PC. On the torsion points of 189 bits orders, their instances are solved in around 10 days by using two standard desktop PCs. The hardness of the finite field discrete logarithm problems is one of the most important bases of security; therefore, their elliptic curves should not be used for cryptographic purposes.

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<![CDATA[Using supervised learning to select audit targets in performance-based financing in health: An example from Zambia]]> https://www.researchpad.co/article/5c59ff00d5eed0c4841358af

Independent verification is a critical component of performance-based financing (PBF) in health care, in which facilities are offered incentives to increase the volume of specific services but the same incentives may lead them to over-report. We examine alternative strategies for targeted sampling of health clinics for independent verification. Specifically, we empirically compare several methods of random sampling and predictive modeling on data from a Zambian PBF pilot that contains reported and verified performance for quantity indicators of 140 clinics. Our results indicate that machine learning methods, particularly Random Forest, outperform other approaches and can increase the cost-effectiveness of verification activities.

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<![CDATA[A quadratic trigonometric spline for curve modeling]]> https://www.researchpad.co/article/5c40f762d5eed0c48438600c

An imperative curve modeling technique has been established with a view to its applications in various disciplines of science, engineering and design. It is a new spline method using piecewise quadratic trigonometric functions. It possesses error bounds of order 3. The proposed curve model also owns the most favorable geometric properties. The proposed spline method accomplishes C2 smoothness and produces a Quadratic Trigonometric Spline (QTS) with the view to its applications in curve design and control. It produces a C2 quadratic trigonometric alternative to the traditional cubic polynomial spline (CPS) because of having four control points in its piecewise description. The comparison analysis of QTS and CPS verifies the QTS as better alternate to CPS. Also, the time analysis proves QTS computationally efficient than CPS.

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<![CDATA[Cryptanalysis and improvement of an elliptic curve based signcryption scheme for firewalls]]> https://www.researchpad.co/article/5c1c0af5d5eed0c484426fcd

In network security, firewall is a security system that observes and controls the network traffic based on some predefined rules. A firewall sets up a barrier between internal network and another outside unsecured network, such as the Internet. A number of signcryption schemes for firewall are proposed over the years, many of them are proved to have security flaws. In this paper, an elliptic curve based signcryption scheme for firewalls is analyzed. It is observed that the scheme is not secure and has many security flaws. Anyone who knows the public parameters, can modify the message without the knowledge of sender and receiver. The claimed security attributes of non-repudiation, unforgeability, integrity and authentication are compromised. After successful cryptanalysis of this scheme, we proposed a modified version of the scheme.

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<![CDATA[Elliptic Curve Cryptography-Based Authentication with Identity Protection for Smart Grids]]> https://www.researchpad.co/article/5989db00ab0ee8fa60bc6352

In a smart grid, the power service provider enables the expected power generation amount to be measured according to current power consumption, thus stabilizing the power system. However, the data transmitted over smart grids are not protected, and then suffer from several types of security threats and attacks. Thus, a robust and efficient authentication protocol should be provided to strength the security of smart grid networks. As the Supervisory Control and Data Acquisition system provides the security protection between the control center and substations in most smart grid environments, we focus on how to secure the communications between the substations and smart appliances. Existing security approaches fail to address the performance-security balance. In this study, we suggest a mitigation authentication protocol based on Elliptic Curve Cryptography with privacy protection by using a tamper-resistant device at the smart appliance side to achieve a delicate balance between performance and security of smart grids. The proposed protocol provides some attractive features such as identity protection, mutual authentication and key agreement. Finally, we demonstrate the completeness of the proposed protocol using the Gong-Needham- Yahalom logic.

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<![CDATA[Constructing Pairing-Friendly Elliptic Curves under Embedding Degree 1 for Securing Critical Infrastructures]]> https://www.researchpad.co/article/5989daf1ab0ee8fa60bc1380

Information confidentiality is an essential requirement for cyber security in critical infrastructure. Identity-based cryptography, an increasingly popular branch of cryptography, is widely used to protect the information confidentiality in the critical infrastructure sector due to the ability to directly compute the user’s public key based on the user’s identity. However, computational requirements complicate the practical application of Identity-based cryptography. In order to improve the efficiency of identity-based cryptography, this paper presents an effective method to construct pairing-friendly elliptic curves with low hamming weight 4 under embedding degree 1. Based on the analysis of the Complex Multiplication(CM) method, the soundness of our method to calculate the characteristic of the finite field is proved. And then, three relative algorithms to construct pairing-friendly elliptic curve are put forward. 10 elliptic curves with low hamming weight 4 under 160 bits are presented to demonstrate the utility of our approach. Finally, the evaluation also indicates that it is more efficient to compute Tate pairing with our curves, than that of Bertoni et al.

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<![CDATA[A General Mathematical Algorithm for Predicting the Course of Unfused Tetanic Contractions of Motor Units in Rat Muscle]]> https://www.researchpad.co/article/5989da90ab0ee8fa60b9fc1f

An unfused tetanus of a motor unit (MU) evoked by a train of pulses at variable interpulse intervals is the sum of non-equal twitch-like responses to these stimuli. A tool for a precise prediction of these successive contractions for MUs of different physiological types with different contractile properties is crucial for modeling the whole muscle behavior during various types of activity. The aim of this paper is to develop such a general mathematical algorithm for the MUs of the medial gastrocnemius muscle of rats. For this purpose, tetanic curves recorded for 30 MUs (10 slow, 10 fast fatigue-resistant and 10 fast fatigable) were mathematically decomposed into twitch-like contractions. Each contraction was modeled by the previously proposed 6-parameter analytical function, and the analysis of these six parameters allowed us to develop a prediction algorithm based on the following input data: parameters of the initial twitch, the maximum force of a MU and the series of pulses. Linear relationship was found between the normalized amplitudes of the successive contractions and the remainder between the actual force levels at which the contraction started and the maximum tetanic force. The normalization was made according to the amplitude of the first decomposed twitch. However, the respective approximation lines had different specific angles with respect to the ordinate. These angles had different and non-overlapping ranges for slow and fast MUs. A sensitivity analysis concerning this slope was performed and the dependence between the angles and the maximal fused tetanic force normalized to the amplitude of the first contraction was approximated by a power function. The normalized MU contraction and half-relaxation times were approximated by linear functions depending on the normalized actual force levels at which each contraction starts. The normalization was made according to the contraction time of the first contraction. The actual force levels were calculated initially from the recorded tetanic curves and subsequently from the modeled curves obtained from the summation of all models of the preceding contractions (the so called “full prediction”). The preciseness of the prediction was verified by two coefficients estimating the error between the modeled and the experimentally recorded curves. The proposed approach was tested for 30 MUs from the database and for three additional MUs, not included in the initial set. It was concluded that this general algorithm can be successfully used for modeling of a unfused tetanus course of a single MU of fast and slow type.

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<![CDATA[An Extended Chaotic Maps-Based Three-Party Password-Authenticated Key Agreement with User Anonymity]]> https://www.researchpad.co/article/5989daacab0ee8fa60ba98b0

User anonymity is one of the key security features of an authenticated key agreement especially for communicating messages via an insecure network. Owing to the better properties and higher performance of chaotic theory, the chaotic maps have been introduced into the security schemes, and hence numerous key agreement schemes have been put forward under chaotic-maps. Recently, Xie et al. released an enhanced scheme under Farash et al.’s scheme and claimed their improvements could withstand the security loopholes pointed out in the scheme of Farash et al., i.e., resistance to the off-line password guessing and user impersonation attacks. Nevertheless, through our careful analysis, the improvements were released by Xie et al. still could not solve the problems troubled in Farash et al‥ Besides, Xie et al.’s improvements failed to achieve the user anonymity and the session key security. With the purpose of eliminating the security risks of the scheme of Xie et al., we design an anonymous password-based three-party authenticated key agreement under chaotic maps. Both the formal analysis and the formal security verification using AVISPA are presented. Also, BAN logic is used to show the correctness of the enhancements. Furthermore, we also demonstrate that the design thwarts most of the common attacks. We also make a comparison between the recent chaotic-maps based schemes and our enhancements in terms of performance.

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<![CDATA[Multi-Objective Aerodynamic Optimization of the Streamlined Shape of High-Speed Trains Based on the Kriging Model]]> https://www.researchpad.co/article/5989db53ab0ee8fa60bdca65

Minimizing the aerodynamic drag and the lift of the train coach remains a key issue for high-speed trains. With the development of computing technology and computational fluid dynamics (CFD) in the engineering field, CFD has been successfully applied to the design process of high-speed trains. However, developing a new streamlined shape for high-speed trains with excellent aerodynamic performance requires huge computational costs. Furthermore, relationships between multiple design variables and the aerodynamic loads are seldom obtained. In the present study, the Kriging surrogate model is used to perform a multi-objective optimization of the streamlined shape of high-speed trains, where the drag and the lift of the train coach are the optimization objectives. To improve the prediction accuracy of the Kriging model, the cross-validation method is used to construct the optimal Kriging model. The optimization results show that the two objectives are efficiently optimized, indicating that the optimization strategy used in the present study can greatly improve the optimization efficiency and meet the engineering requirements.

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<![CDATA[When Do Short-Wave Cones Signal Blue or Red? A Solution Introducing the Concept of Primary and Secondary Cone Outputs]]> https://www.researchpad.co/article/5989daf0ab0ee8fa60bc0d94

A recent paper by Oh and Sakata investigates the “incompletely solved mystery” of how the three cone responses map onto perceived hue, and particularly the S cone’s well-known problematic contribution to blueness and redness. Citing previous workers, they argue the twentieth century traditional multistage model does not satisfactorily account for color appearance. In their experiment, increasing S cone excitation with shortening wavelength from about 480–460 nm increased perceived blueness up to the unique Blue point at 470 nm, when (a) it began decreasing and (b) redness perception began increasing. The authors asked, What mechanism can be responsible for such functions? I demonstrate a solution. First, it is shown the problem does not lie in the traditional opponent color chromatic responses yellow-blue, red-green (y-b, r-g, which accurately predict the above functions), but in the traditional multistage model of mapping cone responses to chromatic response functions. Arguably, this is due to the S cone’s hypothetically signaling both blueness and redness by the same mechanism rather than by different, independent, mechanisms. Hence a new distinction or mechanism is proposed for a more accurate model, that introduces the new terms primary and secondary cone outputs. However, this distinction requires that the cones S, M, L each directly produce one of the three spectral chromatic responses b, g, y. Such a model was recently published, based on extremely high correlation of SML cone responsivities with the three spectral (bgy) chromatic responses. This model encodes the former directly onto the latter one-to-one as cone primary outputs, whilst S and L cones have a further or secondary function where each produces one of the two spectral lobes of r chromatic response. The proposed distinction between primary and secondary cone outputs is a new concept and useful tool in detailing cone outputs to chromatic channels, and provides a solution to the above “incompletely solved mystery.” Thus the S cone has a primary output producing the total b chromatic response and a secondary output that shares with the L cone the production of r chromatic response, thus aligning with Oh and Sokata’s results. The model similarly maps L cone to yellowness as primary output and to redness as secondary output.

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<![CDATA[Topology of Innovation Spaces in the Knowledge Networks Emerging through Questions-And-Answers]]> https://www.researchpad.co/article/5989dac4ab0ee8fa60bb1df2

The communication processes of knowledge creation represent a particular class of human dynamics where the expertise of individuals plays a substantial role, thus offering a unique possibility to study the structure of knowledge networks from online data. Here, we use the empirical evidence from questions-and-answers in mathematics to analyse the emergence of the network of knowledge contents (or tags) as the individual experts use them in the process. After removing extra edges from the network-associated graph, we apply the methods of algebraic topology of graphs to examine the structure of higher-order combinatorial spaces in networks for four consecutive time intervals. We find that the ranking distributions of the suitably scaled topological dimensions of nodes fall into a unique curve for all time intervals and filtering levels, suggesting a robust architecture of knowledge networks. Moreover, these networks preserve the logical structure of knowledge within emergent communities of nodes, labeled according to a standard mathematical classification scheme. Further, we investigate the appearance of new contents over time and their innovative combinations, which expand the knowledge network. In each network, we identify an innovation channel as a subgraph of triangles and larger simplices to which new tags attach. Our results show that the increasing topological complexity of the innovation channels contributes to network’s architecture over different time periods, and is consistent with temporal correlations of the occurrence of new tags. The methodology applies to a wide class of data with the suitable temporal resolution and clearly identified knowledge-content units.

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<![CDATA[A Temporal Credential-Based Mutual Authentication with Multiple-Password Scheme for Wireless Sensor Networks]]> https://www.researchpad.co/article/5989db4fab0ee8fa60bdb909

Wireless sensor networks (WSNs), which consist of a large number of sensor nodes, have become among the most important technologies in numerous fields, such as environmental monitoring, military surveillance, control systems in nuclear reactors, vehicle safety systems, and medical monitoring. The most serious drawback for the widespread application of WSNs is the lack of security. Given the resource limitation of WSNs, traditional security schemes are unsuitable. Approaches toward withstanding related attacks with small overhead have thus recently been studied by many researchers. Numerous studies have focused on the authentication scheme for WSNs, but most of these works cannot achieve the security performance and overhead perfectly. Nam et al. proposed a two-factor authentication scheme with lightweight sensor computation for WSNs. In this paper, we review this scheme, emphasize its drawbacks, and propose a temporal credential-based mutual authentication with a multiple-password scheme for WSNs. Our scheme uses multiple passwords to achieve three-factor security performance and generate a session key between user and sensor nodes. The security analysis phase shows that our scheme can withstand related attacks, including a lost password threat, and the comparison phase shows that our scheme involves a relatively small overhead. In the comparison of the overhead phase, the result indicates that more than 95% of the overhead is composed of communication and not computation overhead. Therefore, the result motivates us to pay further attention to communication overhead than computation overhead in future research.

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<![CDATA[Parallel point-multiplication architecture using combined group operations for high-speed cryptographic applications]]> https://www.researchpad.co/article/5989db59ab0ee8fa60bdf18b

In this paper, we propose a novel parallel architecture for fast hardware implementation of elliptic curve point multiplication (ECPM), which is the key operation of an elliptic curve cryptography processor. The point multiplication over binary fields is synthesized on both FPGA and ASIC technology by designing fast elliptic curve group operations in Jacobian projective coordinates. A novel combined point doubling and point addition (PDPA) architecture is proposed for group operations to achieve high speed and low hardware requirements for ECPM. It has been implemented over the binary field which is recommended by the National Institute of Standards and Technology (NIST). The proposed ECPM supports two Koblitz and random curves for the key sizes 233 and 163 bits. For group operations, a finite-field arithmetic operation, e.g. multiplication, is designed on a polynomial basis. The delay of a 233-bit point multiplication is only 3.05 and 3.56 μs, in a Xilinx Virtex-7 FPGA, for Koblitz and random curves, respectively, and 0.81 μs in an ASIC 65-nm technology, which are the fastest hardware implementation results reported in the literature to date. In addition, a 163-bit point multiplication is also implemented in FPGA and ASIC for fair comparison which takes around 0.33 and 0.46 μs, respectively. The area-time product of the proposed point multiplication is very low compared to similar designs. The performance (1Area×Time=1AT) and Area × Time × Energy (ATE) product of the proposed design are far better than the most significant studies found in the literature.

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<![CDATA[An Enhanced Biometric Based Authentication with Key-Agreement Protocol for Multi-Server Architecture Based on Elliptic Curve Cryptography]]> https://www.researchpad.co/article/5989db37ab0ee8fa60bd378f

Biometric based authentication protocols for multi-server architectures have gained momentum in recent times due to advancements in wireless technologies and associated constraints. Lu et al. recently proposed a robust biometric based authentication with key agreement protocol for a multi-server environment using smart cards. They claimed that their protocol is efficient and resistant to prominent security attacks. The careful investigation of this paper proves that Lu et al.’s protocol does not provide user anonymity, perfect forward secrecy and is susceptible to server and user impersonation attacks, man-in-middle attacks and clock synchronization problems. In addition, this paper proposes an enhanced biometric based authentication with key-agreement protocol for multi-server architecture based on elliptic curve cryptography using smartcards. We proved that the proposed protocol achieves mutual authentication using Burrows-Abadi-Needham (BAN) logic. The formal security of the proposed protocol is verified using the AVISPA (Automated Validation of Internet Security Protocols and Applications) tool to show that our protocol can withstand active and passive attacks. The formal and informal security analyses and performance analysis demonstrates that the proposed protocol is robust and efficient compared to Lu et al.’s protocol and existing similar protocols.

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<![CDATA[Security enhanced multi-factor biometric authentication scheme using bio-hash function]]> https://www.researchpad.co/article/5989db59ab0ee8fa60bdf1c7

With the rapid development of personal information and wireless communication technology, user authentication schemes have been crucial to ensure that wireless communications are secure. As such, various authentication schemes with multi-factor authentication have been proposed to improve the security of electronic communications. Multi-factor authentication involves the use of passwords, smart cards, and various biometrics to provide users with the utmost privacy and data protection. Cao and Ge analyzed various authentication schemes and found that Younghwa An’s scheme was susceptible to a replay attack where an adversary masquerades as a legal server and a user masquerading attack where user anonymity is not provided, allowing an adversary to execute a password change process by intercepting the user’s ID during login. Cao and Ge improved upon Younghwa An’s scheme, but various security problems remained. This study demonstrates that Cao and Ge’s scheme is susceptible to a biometric recognition error, slow wrong password detection, off-line password attack, user impersonation attack, ID guessing attack, a DoS attack, and that their scheme cannot provide session key agreement. Then, to address all weaknesses identified in Cao and Ge’s scheme, this study proposes a security enhanced multi-factor biometric authentication scheme and provides a security analysis and formal analysis using Burrows-Abadi-Needham logic. Finally, the efficiency analysis reveals that the proposed scheme can protect against several possible types of attacks with only a slightly high computational cost.

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<![CDATA[Cryptanalysis and Improvement of a Biometric-Based Multi-Server Authentication and Key Agreement Scheme]]> https://www.researchpad.co/article/5989db4bab0ee8fa60bda3b7

With the security requirements of networks, biometrics authenticated schemes which are applied in the multi-server environment come to be more crucial and widely deployed. In this paper, we propose a novel biometric-based multi-server authentication and key agreement scheme which is based on the cryptanalysis of Mishra et al.’s scheme. The informal and formal security analysis of our scheme are given, which demonstrate that our scheme satisfies the desirable security requirements. The presented scheme provides a variety of significant functionalities, in which some features are not considered in the most of existing authentication schemes, such as, user revocation or re-registration and biometric information protection. Compared with several related schemes, our scheme has more secure properties and lower computation cost. It is obviously more appropriate for practical applications in the remote distributed networks.

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<![CDATA[Dynamic behaviors of a modified SIR model in epidemic diseases using nonlinear incidence and recovery rates]]> https://www.researchpad.co/article/5989db51ab0ee8fa60bdc3e9

The transmission of infectious diseases has been studied by mathematical methods since 1760s, among which SIR model shows its advantage in its epidemiological description of spread mechanisms. Here we established a modified SIR model with nonlinear incidence and recovery rates, to understand the influence by any government intervention and hospitalization condition variation in the spread of diseases. By analyzing the existence and stability of the equilibria, we found that the basic reproduction number R0 is not a threshold parameter, and our model undergoes backward bifurcation when there is limited number of hospital beds. When the saturated coefficient a is set to zero, it is discovered that the model undergoes the Saddle-Node bifurcation, Hopf bifurcation, and Bogdanov-Takens bifurcation of codimension 2. The bifurcation diagram can further be drawn near the cusp type of the Bogdanov-Takens bifurcation of codimension 3 by numerical simulation. We also found a critical value of the hospital beds bc at R0<1 and sufficiently small a, which suggests that the disease can be eliminated at the hospitals where the number of beds is larger than bc. The same dynamic behaviors exist even when a ≠ 0. Therefore, it can be concluded that a sufficient number of the beds is critical to control the epidemic.

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<![CDATA[Special Relativity at the Quantum Scale]]> https://www.researchpad.co/article/5989da73ab0ee8fa60b95a70

It has been suggested that the space-time structure as described by the theory of special relativity is a macroscopic manifestation of a more fundamental quantum structure (pre-geometry). Efforts to quantify this idea have come mainly from the area of abstract quantum logic theory. Here we present a preliminary attempt to develop a quantum formulation of special relativity based on a model that retains some geometric attributes. Our model is Feynman's “checker-board” trajectory for a 1-D relativistic free particle. We use this model to guide us in identifying (1) the quantum version of the postulates of special relativity and (2) the appropriate quantum “coordinates”. This model possesses a useful feature that it admits an interpretation both in terms of paths in space-time and in terms of quantum states. Based on the quantum version of the postulates, we derive a transformation rule for velocity. This rule reduces to the Einstein's velocity-addition formula in the macroscopic limit and reveals an interesting aspect of time. The 3-D case, time-dilation effect, and invariant interval are also discussed in term of this new formulation. This is a preliminary investigation; some results are derived, while others are interesting observations at this point.

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<![CDATA[A New Ticket-Based Authentication Mechanism for Fast Handover in Mesh Network]]> https://www.researchpad.co/article/5989db25ab0ee8fa60bd029b

Due to the ever-growing popularity mobile devices of various kinds have received worldwide, the demands on large-scale wireless network infrastructure development and enhancement have been rapidly swelling in recent years. A mobile device holder can get online at a wireless network access point, which covers a limited area. When the client leaves the access point, there will be a temporary disconnection until he/she enters the coverage of another access point. Even when the coverages of two neighboring access points overlap, there is still work to do to make the wireless connection smoothly continue. The action of one wireless network access point passing a client to another access point is referred to as the handover. During handover, for security concerns, the client and the new access point should perform mutual authentication before any Internet access service is practically gained/provided. If the handover protocol is inefficient, in some cases discontinued Internet service will happen. In 2013, Li et al. proposed a fast handover authentication mechanism for wireless mesh network (WMN) based on tickets. Unfortunately, Li et al.’s work came with some weaknesses. For one thing, some sensitive information such as the time and date of expiration is sent in plaintext, which increases security risks. For another, Li et al.’s protocol includes the use of high-quality tamper-proof devices (TPDs), and this unreasonably high equipment requirement limits its applicability. In this paper, we shall propose a new efficient handover authentication mechanism. The new mechanism offers a higher level of security on a more scalable ground with the client’s privacy better preserved. The results of our performance analysis suggest that our new mechanism is superior to some similar mechanisms in terms of authentication delay.

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