Bilinear Maps Research Articles

3D Object Representation Learning: A Set-to-Set Matching Perspective.

In this paper, we tackle the 3D object representation learning from the perspective of set-to-set matching. Given two 3D objects, calculating their similarity is formulated as the problem of set-to-set similarity measurement between two set of local patches. As local convolutional features from convolutional feature maps are natural representations of local patches, the set-to-set matching between sets of local patches is further converted into a local features pooling problem. To highlight good matchings and suppress the bad ones, we exploit two pooling methods: 1) bilinear pooling and 2) VLAD pooling. We analyze their effectiveness in enhancing the set-to-set matching and meanwhile establish their connection. Moreover, to balance different components inherent in a bilinear-pooled feature, we propose the harmonized bilinear pooling operation, which follows the spirits of intra-normalization used in VLAD pooling. To achieve an end-to-end trainable framework, we implement the proposed harmonized bilinear pooling and intra-normalized VLAD as two layers to construct two types of neural network, multi-view harmonized bilinear network (MHBN) and multi-view VLAD network (MVLADN). Systematic experiments conducted on two public benchmark datasets demonstrate the efficacy of the proposed MHBN and MVLADN in 3D object recognition.

Medi-Block record: Secure data sharing using block chain technology

With the advances in the era of Artificial intelligence, block chain, cloud computing, big data has the need for secure, decentralized medical record storage and retrieval systems, while cloud storage resolves storage issues but it is difficult to realize the secure sharing of records over the network. The decentralized nature of block chain technology resolves the problem of authentication dependent on third party and imparts secure transmission. This paper proposed block chain based distributed authentication mechanism process and network architecture. Medi-Block presents a tamperproof and anonymous identity management model for medical record sharing for hospitals and patients, utilizing the concept of bilinear mapping for the authentication phase and eliminating third party trust issues. It implements two-way authentications between the patients and the hospital. The effectiveness of the proposed authentication scheme is analyzed by BAN logic, storage overhead and computing cost. The results presented in the paper demonstrate how a block chain platform based on BAN logic can enable medical data sharing while also meeting various security requirements during the authentication phase. Furthermore, reducing average communication time and cost in terms of accessibility meets the requirements of medical data record sharing for integrity, privacy, and availability.

PFLUA-DIoT: A Pairing Free Lightweight and Unlinkable User Access Control Scheme for Distributed IoT Environments

The Internet of Things (IoT) connects enormous objects through various sensors to facilitate daily life by interconnecting the information space with the decision-makers. Security and privacy are, however, the main concerns in IoT due to the openness of communication channels and the unattended nature of common sensors. To provide security and privacy for sensors and users in IoT-based systems; in 2019, Zhou <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al.</i> proposed an unlinkable authentication scheme using bilinear pairings. However, the vulnerability of their scheme against sensor node impersonation attack as proved in this article renders the scheme of their work impractical and insecure. A pairing free lightweight and unlinkable authentication scheme for distributed IoT devices (PFLUA-DIoT) is then proposed in this article. The security of PFLUA-DIoT is proved using the formal method along with a discussion on its provision of security features. The performance and security comparisons show that PFLUA-DIoT provides known security features and provides better performance. Due to the avoidance of bilinear pairing-based expensive operations, PFLUA-DIoT completes authentication in less than half running time as compared with their and related schemes. Therefore, the PFLUA-DIoT can address the security and privacy issues of IoT, practically and efficiently.

Eigenmeasures and stochastic diagonalization of bilinear maps

A new stochastic approach is presented to understand general spectral type problems for (not necessarily linear) functions between topological spaces. In order to show its potential applications, we construct the theory for the case of bilinear forms acting in couples of a Banach space and its dual. Our method consists of using integral representations of bilinear maps that satisfy particular domination properties, which is shown to be equivalent to having a certain spectral structure. Thus, we develop a measure‐based technique for the characterization of bilinear operators having a spectral representation, introducing the notion of eigenmeasure, which will become the central tool of our formalism. Specific applications are provided for operators between finite and infinite dimensional linear spaces.

On the classification of bilinear maps with radical of a fixed codimension

ABSTRACT Let be an n-dimensional linear space over an algebraically closed base field. We provide a general method for classifying, up to equivalence, all bilinear maps such that , in case a classification of bilinear maps when is known. This is equivalent to giving a procedure to classify (up to isomorphism) all n-dimensional algebras with annihilator of dimension n−m from a given classification of m-dimensional algebras. As an example of application, we consider the case in which m = 2.

Vehicle plate localization and extraction based on hough transform and bilinear operations

&lt;p&gt;In general, the extraction of the vehicle plate is a previous step of plate recognition, and it actively studied for several decades. Plate localization is used in various security and traffic applications. In this paper, the proposed method is efficient to localize a plate for the multinational countries. The proposed method consists of three levels. The first level is the preprocessing&lt;strong&gt; &lt;/strong&gt;that contains several steps. The digital camera capture images have been taken about twenty meters from the car with zooming two to three meters. Images are resampled using the zooming technique (bilinear interpolation) that makes the dimension of image (1024 x 768) pixels. The resampled images are resized to (940x 730). These images are converted to grayscale (green channel), and the bilateral filter is applied for removing noise. The second level is plate detection that adopts morphological operations, image subtraction, and vertical edge detection (Sobel). At the last Connected component analysis and Hough transform are used. The third level is the Deskew plate that notifies the plate may skew so that Hough transform is used to detect the largest line segment. Then, the images are rotated using bilinear interpolation. About 860 images are tested for different countries (Iraq, Belarus, Armenia, Hungary), and the accuracy is 98.99 % for extraction of the plate and 100% for the Deskew plate. Thus, the proposed system shows high efficiency in achievement.&lt;/p&gt;

Interaction solutions to the (2+1)-dimensional generalized Bogoyavlensky-Konopelchenko-like equation

By using the generalized bilinear operations with a prime number p=3, a (2+1)-dimensional gBK-like equation is introduced. classes of interaction solutions of the (2+1)-dimensional gBK-like equation are generated through symbolic computation with maple. Some images were plotted to illustrate the dynamical movement of the solutions with specific values of the involved parameters.

An Efficient Identity-Based Conditional Privacy-Preserving Authentication Scheme for Secure Communication in a Vehicular Ad Hoc Network

The security and privacy issues in vehicular ad hoc networks (VANETs) are often addressed with schemes based on either public key infrastructure, group signature, or identity. However, none of these schemes appropriately address the efficient verification of multiple VANET messages in high-density traffic areas. Attackers could obtain sensitive information kept in a tamper-proof device (TPD) by using a side-channel attack. In this paper, we propose an identity-based conditional privacy-preserving authentication scheme that supports a batch verification process for the simultaneous verification of multiple messages by each node. Furthermore, to thwart side-channel attacks, vehicle information in the TPD is periodically and frequently updated. Finally, since the proposed scheme does not utilize the bilinear pairing operation or the Map-To-Point hash function, its performance outperforms other schemes, making it viable for large-scale VANETs deployment.

White noise differential equations for vector-valued white noise functionals

In this paper, a framework of vector-valued white noise functionals has been constructed as a Gel’fand triple $${\mathcal {W}}_{\alpha }\otimes {\mathcal {E}} \subset \varGamma (H)\otimes K \subset ( {\mathcal {W}}_{\alpha }\otimes {\mathcal {E}})^*$$ . Base on the Gel’fand triple, a new notion of Wick product of vector-valued white noise functionals induced by a bilinear mapping $${\mathfrak {B}}:{\mathcal {E}}^*\times {\mathcal {E}}^*\rightarrow {\mathcal {E}}$$ is introduced and called a $${\mathfrak {B}}$$ -Wick product. We establish the unique existence of solution of an abstract functional differential equation base on the Gel’fand triple. For our purpose, we improve slightly the well-known analytic characterization theorem for S-transform, and the convergence theorem in terms of S-transform for a sequence of vector-valued generalized white noise functionals. As an application, we study the Wick type differential equations for vector-valued white noise functionals, and as examples we discuss the Wick type differential equations for certain operator algebra valued white noise functionals which naturally includes random matrices of white noise functionals.

Attribute-Based Encryption With Parallel Outsourced Decryption for Edge Intelligent IoV

Edge intelligence is an emerging concept referring to processes in which data are collected and analyzed and insights are delivered close to where the data are captured in a network using a selection of advanced intelligent technologies. As a promising solution to solve the problems of insufficient computing capacity and transmission latency, the edge intelligence-empowered Internet of Vehicles (IoV) is being widely investigated in both academia and industry. However, data sharing security in edge intelligent IoV is a challenge that should be solved with priority. Although attribute-based encryption (ABE) is capable of addressing this challenge, many time-consuming modular exponential operations and bilinear pair operations as well as serial computing cause ABE to have a slow decryption speed. Consequently, it cannot address the response time requirement of edge intelligent IoV. Given this problem, an ABE model with parallel outsourced decryption for edge intelligent IoV, called ABEM-POD , is proposed. It includes a generic parallel outsourced decryption method for ABE based on Spark and MapReduce. This method is applicable to all ABE schemes with a tree access structure and can be applied to edge intelligent IoV. Any ABE scheme based on the proposed model not only supports parallel outsourced decryption but also has the same security as the original scheme. In this paper, ABEM-POD has been applied to three representative ABE schemes, and the experiments show that the proposed ABEM-POD is efficient and easy to use. This approach can significantly improve the speed of outsourced decryption to address the response time requirement for edge intelligent IoV.

ECS‐CP‐ABE: A lightweight elliptic curve signcryption scheme based on ciphertext‐policy attribute‐based encryption to secure downlink multicast communication in edge envisioned advanced metering infrastructure networks

AbstractAs an integral part of the smart grid, advanced metering infrastructure (AMI) implements two‐way communication to enable the smart grid achieving the desired performance improvements over the legacy grid. Integrating communication in addition to the inherited weakness of the power grid paves the way to countless number of security threats to target its communication networks, therefore ensuring secure data exchange is a key concern for AMI networks. In this regard, many schemes are proposed in the literature to secure this two‐way communication, however, very little effort has been focused on multicast transmissions carried out between the control center and a group of smart meters. In order to empower efficient, authentic, and confidential data exchange, this article proposes a new signcryption scheme for multicast downlink communication in edge envisioned AMI networks. The proposed scheme is constructed based on ciphertext‐policy attribute‐based encryption to attain secure fine‐grained access control for the multirecipient communication between the utility control center and a group of smart meters. The novelty of our scheme lies behind the fact that it is an elliptic curve cryptosystem that is pairing free, in opposite to most ABE schemes. Instead of the complex bilinear pairing operations, we exploited faster elliptic curve point multiplication operations to construct the proposed signcryption model. we demonstrate the strength of our protocol in defending against passive, collusion, reply, data modification, and signature forgery attacks. Simulation results prove the efficiency of our protocol in terms of messages size and computation complexity when compared with other schemes.

Certificateless Homomorphic Signature Scheme for Network Coding

Homomorphic signature is an extremely important public key authentication technique for network coding to defend against pollution attacks. As a public key cryptographic primitive, it also encounters the same problem of how to confirm the relationship between some public key $pk$ and the identity $ID$ of its owner. In the setting of distributed network coding, the intermediate and destination nodes need to use the public key of source node S to check the validity of vector-signature pairs. Therefore, the binding of S and its corresponding public key becomes crucial. The popular and traditional solution is based on certificates which are issued by a trusted certification authority (CA) center. However, the generation and management of certificates is extremely cumbersome. Hence, in recent work, Lin et al. proposed a new notion of identity-based homomorphic signature, which intends to avoid using certificates. But the key escrow problem is inevitable for identity-based primitives. In this article, we propose another new notion (for network coding): certificateless homomorphic signature (CLHS), which is a compromise for the above two techniques. In particular, we first describe the definition and security model of certificateless homomorphic signature. Then based on bilinear map and the computational Diffie-Hellman (CDH) assumption, give a concrete implementation and detailedly analyze its security. Finally, performance analysis illustrates that our construction is practical.

Introducing totally nonparallel immersions

An immersion of a smooth n-dimensional manifold M→Rq is called totally nonparallel if, for every distinct x,y∈M, the tangent spaces at f(x) and f(y) contain no parallel lines; equivalently, they span a 2n-dimensional space. Given a manifold M, we seek the minimum dimension TN(M) such that there exists a totally nonparallel immersion M→RTN(M). In analogy with the totally skew embeddings studied by Ghomi and Tabachnikov, we find that totally nonparallel immersions are related to the generalized vector field problem, the immersion and embedding problems for real projective spaces, and nonsingular symmetric bilinear maps.Our study of totally nonparallel immersions follows a recent trend of studying conditions which manifest on the configuration spaceFk(M) of k-tuples of distinct points of M; for example, k-regular embeddings, k-skew embeddings, k-neighborly embeddings, and several others. Typically, a map satisfying one of these configuration space conditions induces some Sk-equivariant map on the configuration space Fk(M) (or on a bundle thereof) and obstructions can be computed in the form of Stiefel-Whitney classes. However, the existence problem for such conditions is relatively unstudied.Our main result is a Whitney-type theorem: every smooth n-manifold M admits a totally nonparallel immersion into R4n−1, one dimension less than given by genericity. We begin by studying the local problem, which requires a thorough understanding of the space of nonsingular symmetric bilinear maps, after which the main theorem is established using the removal-of-singularities h-principle technique due to Gromov and Eliashberg. When combined with a recent non-immersion theorem of Davis, we obtain the exact value TN(RPn)=4n−1 when n is a power of 2. This is the first optimal-dimension result for any closed manifold M besides S1, for any of the recently-studied configuration space conditions.

Recognition method of thermal infrared images of plant canopies based on the characteristic registration of heterogeneous images

Canopy thermal infrared imaging reflects the temperature change in the crop canopy, which is closely related to the stomatal conductance and water utilization characteristics of the crop. Thermal infrared imaging is an effective and nondestructive way to study the early detection of crop diseases. However, efficiently extracting the thermal infrared canopy region of the crops is an important factor restricting the study of canopy temperature changes. The grayscale distribution of the edges of the crop canopy thermal infrared image is uneven with strong noise and cannot be extracted effectively using the traditional image segmentation method. Thus, a recognition method for the thermal infrared images of plant canopies based on heterogeneous image characteristic registration was proposed to overcome the shortcomings above. First, the Gauss membership function was selected to construct the network recognition rules on the basis of the three-layer backward reasoning of the adaptive BP neural network to recognize the visible light reference images of the plant canopies. Second, the optimal registration parameters of the affine transformation were calculated for registering the canopy region of the reference image and that of the initial thermal infrared image. Third, a recognition model for the thermal infrared images of plant canopies was established based on bilinear mapping factors. Finally, information entropy and mutual information were used to evaluate the effectiveness of the recognition model. The results showed that the initial temperature range of the original thermal infrared image was 20.46–36.40 °C. After removing the background interference of the thermal infrared canopy of the crop, the temperature range of the target image was 20.46–26.65 °C, and the average temperature after extraction was 2.04 °C lower than that before extraction. In addition, the entropy difference between the canopy of the thermal infrared image identified by the proposed model in this study and the standard recognition method was within the range of 0.01–0.06, indicating the effectiveness of the recognition model for the plant canopy. Therefore, this study provided an efficient method for obtaining the canopy temperature characteristics of crops.

On the Properties of the Arens Regularity of Bounded Bilinear Mappings

On the Properties of the Arens Regularity of Bounded Bilinear Mappings

Two-Lipschitz operator ideals

We introduce and investigate the concept of two-Lipschitz operator ideal between pointed metric spaces and Banach spaces. We show the basics of this new theory and we give a procedure to create a two-Lipschitz operator ideal from a linear operator ideal. We apply our result to the ideals of strongly p-summing and compact linear operator to obtain their corresponding two-Lipschitz operator ideal. Also, we establish a natural relation between two-Lipschitz and bilinear maps and show that the two-Lipschitz factorable p-dominated operators are those which are associated to the well-known p-semi-integral bilinear operators.

$n$-factorization Property of Bilinear Mappings

In this paper, we define a new concept of factorization for a bounded bilinear mapping $f:Xtimes Yto Z$, depended on a natural number $n$ and a cardinal number $kappa$; which is called $n$-factorization property of level $kappa$. Then we study the relation between $n$-factorization property of level $kappa$ for $X^*$ with respect to $f$ and automatically boundedness and $w^*$-$w^*$-continuity and also strong Arens irregularity. These results may help us to prove some previous problems related to strong Arens irregularity more easier than old. These include some results proved by Neufang in ~cite{neu1} and ~cite{neu}. Some applications to certain bilinear mappings on convolution algebras, on a locally compact group, are also included. Finally, some solutions related to the Ghahramani-Lau conjecture is raised.

BAGKD: A Batch Authentication and Group Key Distribution Protocol for VANETs

As an important application of mobile ad hoc networks, VANETs play an important role in intelligent transportation. However, with the development of mobile communication technology, as well as the needs of intelligent transportation, both security and efficiency are required for realtime authentication and communication. Traditional authentication and key distribution schemes suffer from network failure and high response latency. To solve the above problems, this article proposes a BAGKD protocol to achieve robust and efficient networking for the security and efficiency of VANETs. In our protocol, bilinear mapping is used to realize batch authentication, which can improve authentication efficiency and reduce message errors caused by factors such as high speed of vehicles. The group key distribution mechanism can update the group key dynamically, which reduces the risk of group key leakage effectively. For the sake of privacy protection, vehicles utilize pseudonyms issued by a trusted authority to communicate with RSUs. The security of BAGKD protocol is verified by simulation in our experiments on AVISPA. In addition, when compared to three existing protocols based on bilinear mapping, our proposed BAGKD outperforms them in terms of efficiency and communication overhead while maintaining security. The simulation results further confirm that BAGKD is suitable for short-range communication scenarios such as VANETs.

A verifiable and privacy‐preserving multidimensional data aggregation scheme in mobile crowdsensing

AbstractMobile crowdsensing has become a popular data collection paradigm and has been extensively studied. Since the analysis of sensory data usually reveals privacy of mobile users, data aggregation technology is widely used to avoid privacy disclosure. However, traditional privacy‐preserving data aggregation schemes cannot provide aggregate statistics of multidimensional data in fine‐grained areas or resist collusive attacks. Moreover, the cloud platform is not fully trusted, and it is challenging to verify the correctness of data aggregation results. To provide privacy‐preserving multidimensional statistics within fine‐grained areas and verify results of data aggregation, we propose a verifiable privacy‐preserving data aggregation scheme in this article, which is based on data double‐masking, Shamir's secret sharing, and bilinear mapping. Specifically, a key agreement is utilized to establish mask seeds for users, while the users are required to extend mask values and generate the verification key with bilinear mapping. The cloud platform aggregates masked data and provides proof of computational results. Theoretical analysis demonstrates our scheme can protect data and location privacy, verify the aggregation results, and improve the rubustness to failure. The simulation results show that the computational overhead of mobile devices by using the proposed anticollusion scheme is better than that of homomorphic encryption. In addition, the computational complexity of task requesters is less than that of the PVPA scheme for verification of multidimensional aggregation results.

A Novel Pairing-Free Lightweight Authentication Protocol for Mobile Cloud Computing Framework

The mobile cloud computing (MCC) refers to an infrastructure that integrates cloud computing and mobile computing, and it has changed a great deal, the service provisioning of applications, which requires to get the data processed after collection from vast sensor and Internet-of-Things-based network. The ever increasing number of handheld mobile gadgets has exacerbated the need for robust and efficient authenticated key agreements. We could witness a number of MCC-based multiserver authentication schemes lately to foster the secure adaptation of the technology; however, the demonstrated solutions are either insecure or employing too costly bilinear pairing operations for implementation. In view of limitations, as illustrated in previous studies, we propose a novel pairing-free multiserver authentication protocol for MCC environment based on an elliptic curve cryptosystem that is not only efficient, but also free from security loopholes as demonstrated. The performance evaluation section discusses and distinguishes the findings among latest studies. The strength of the contributed scheme is proved theoretically under formal security model.