Bilinear Maps Research Articles

Secure Outsourced Attribute-Based Sharing Framework for Lightweight Devices in Smart Health Systems

The rapid evolution of the Internet of Things has led to the development of smart health. As a form of medical care that uses advanced Internet technology to realize better diagnosis and treatment of patients, smart health transitions medical services move toward real intelligence and greatly helps users. And in smart health, the secure sharing of personal health records (PHRs) is one of the main concerns of patients and medical personnel. Many attribute-based sharing models have been proposed to secure the sharing of PHRs, but there are still two problems to resolve. One is the potential disclosure of the patient data. The attribute-based model achieves flexible access control, but the access policies contain sensitive information of patients. The disclosure of the policy will lead to the leakage of data of the users. The other is the high computational and storage overhead, particularly in smart health systems with limited computing power. In this article, we present a Smart Health-Lightweight Fine-Grained Sharing (SH-LFGS) framework based on attribute-based encryption (ABE). It achieves a fully hidden access policy by adopting Viéte's formula. SH-LFGS introduces an online/offline mechanism in the PHR encryption phase and the outsourced verifiable decryption mechanism. Because the decrypting test requires only one bilinear pair operation, the SH-LFGS can achieve the task of lightweight computation. Analysis of the performance and security of the proposed model confirm its efficiency and security.

Growth of bilinear maps

For a bilinear map ⁎:Rd×Rd→Rd with nonnegative coefficients and a vector s∈Rd of positive entries, among an exponential number of ways combining n instances of s using n−1 applications of ⁎ for a given n, we are interested in the largest entry over all the resulting vectors. An asymptotic behavior is that the n-th root of this largest entry converges to a growth rate λ when n tends to infinity. In this paper, we prove the existence of this limit by a special structure called linear pattern. We also pose a question on the possibility of a relation between the structure and whether λ is algebraic.

SPECIAL VINBERG CONES

The paper is devoted to the generalization of the Vinberg theory of homogeneous convex cones. Such a cone is described as the set of “positive definite matrices” in the Vinberg commutative algebra ℋn of Hermitian T-matrices. These algebras are a generalization of Euclidean Jordan algebras and consist of n × n matrices A = (aij), where aii ∈ ℝ, the entry aij for i < j belongs to some Euclidean vector space (Vij ; \U0001d524) and {a}_{ji}={a}_{ij}^{ast }=mathfrak{g}left({a}_{ij},cdot right)in {V}_{ij}^{ast } belongs to the dual space {V}_{ij}^{ast }. The multiplication of T-Hermitian matrices is defined by a system of “isometric” bilinear maps Vij × Vjk → Vij ; i < j < k, such that |aij ⋅ ajk| = |aij| ⋅ |aik|, alm ∈ Vlm. For n = 2, the Hermitian T-algebra ℋn= ℋ2 (V) is determined by a Euclidean vector space V and is isomorphic to a Euclidean Jordan algebra called the spin factor algebra and the associated homogeneous convex cone is the Lorentz cone of timelike future directed vectors in the Minkowski vector space ℝ1,1⊕ V . A special Vinberg Hermitian T-algebra is a rank 3 matrix algebra ℋ3(V; S) associated to a Clifford Cl(V )-module S together with an “admissible” Euclidean metric \U0001d524S.We generalize the construction of rank 2 Vinberg algebras ℋ2(V ) and special Vinberg algebras ℋ3(V; S) to the pseudo-Euclidean case, when V is a pseudo-Euclidean vector space and S = S0 ⊕ S1 is a ℤ2-graded Clifford Cl(V )-module with an admissible pseudo-Euclidean metric. The associated cone \U0001d4b1 is a homogeneous, but not convex cone in ℋm; m = 2; 3. We calculate the characteristic function of Koszul-Vinberg for this cone and write down the associated cubic polynomial. We extend Baez’ quantum-mechanical interpretation of the Vinberg cone \U0001d4b12 ⊂ ℋ2(V ) to the special rank 3 case.

Blockchain-Aided Privacy-Preserving Outsourcing Algorithms of Bilinear Pairings for Internet of Things Devices

Bilinear pairing is a fundamental operation that is widely used in cryptographic algorithms (e.g., identity-based cryptographic algorithms) to secure IoT applications. Nonetheless, the time complexity of bilinear pairing is <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$O(n^{3})$ </tex-math></inline-formula> , making it a very time-consuming operation, especially for resource-constrained IoT devices. Secure outsourcing of bilinear pairing has been studied in recent years to enable computationally weak devices to securely outsource the bilinear pairing to untrustworthy cloud servers. However, the state-of-art algorithms often require to precompute and store some values, which results in storage burden for devices. In the Internet of Things, devices are generally with very limited storage capacity. Thus, the existing algorithms do not fit the IoT well. In this article, we propose a secure outsourcing algorithm of bilinear pairings, which does not require precomputations. In the proposed algorithm, the outsourcer side’s efficiency is significantly improved compared with executing the original bilinear pairing operation. At the same time, the privacy of the input and output is ensured. Also, we apply the Ethereum blockchain in our outsourcing algorithm to enable fair payments, which ensures that the cloud server gets paid only when he correctly accomplished the outsourced work. The theoretical analysis and experimental results show that the proposed algorithm is efficient and secure.

Implementation of higher-order velocity mapping between marker particles and grid in the particle-in-cell code XGC

The global total- $f$ gyrokinetic particle-in-cell code XGC, used to study transport in magnetic fusion plasmas or to couple with a core gyrokinetic code while functioning as an edge gyrokinetic code, implements a five-dimensional continuum grid to perform the dissipative operations, such as plasma collisions, or to exchange the particle distribution function information with a core code. To transfer the distribution function between marker particles and a rectangular two-dimensional velocity-space grid, XGC employs a bilinear mapping. The conservation of particle density and momentum is accurate enough in this bilinear operation, but the error in the particle energy conservation can become undesirably large and cause non-negligible numerical heating in a steep edge pedestal. In the present work we update XGC to use a novel mapping technique, based on the calculation of a pseudo-inverse, to exactly preserve moments up to the order of the discretization space. We describe the details of the implementation and we demonstrate the reduced interpolation error for a tokamak test plasma using first- and second-order elements with the pseudo-inverse method and comparing with the bilinear mapping.

Fine-Grained Access Control Scheme Based on Improved Proxy Re-Encryption in Cloud

Cloud storage technology has attracted a considerable number of users owing to its exponential growth. Storing data in the cloud can save the resources of local storage configuration and reduce the cost of local hardware investment. However, the data stored in the cloud is out of the physical control (out of control) of the user. Based on the service characteristics of the cloud environment and the security requirements of user privacy data in the cloud environment, this paper proposes an improved identity proxy re-encryption algorithm based on the advanced encryption standard algorithm. The performance of the algorithm is optimized by reducing the number of bilinear mapping operations, whose calculation takes the longest time in the proxy re-encryption scheme. Only two bilinear mapping operations are required in this scheme. In addition, the encrypted data are tested to different degrees. The experimental results show that this scheme satisfies encryption and decryption performance requirements of the user.

Elliptic divisibility sequences over the Edwards model of elliptic curves

In this work, we use division polynomials on Edwards elliptic curves to construct elliptic nets of rank one called elliptic divisibility sequence on this curve. Introduced by Morgan Ward, elliptic divisibility sequence on elliptic curve are used for solving the elliptic curve discrete logarithm problem (ECDLP). Moved on rank 2, Elliptic Nets algorithm via elliptic nets associated to Weierstrass elliptic curves are useful for the computation of bilinear maps (called pairings) defined on the groups of points of elliptic curves and very useful to the construction of cryptographic protocols.

A Dynamic Membership Group-Based Multiple-Data Aggregation Scheme for Smart Grid

In the smart grid, meters report their real-time electricity consumption data to a utility supplier, and the utility supplier can adjust its supply accordingly. However, adversaries can infer users' privacy behaviors based on publicly transferred real-time electricity consumption data. Data aggregation schemes protect users' privacy from being leaked. We find two major problems are unsolved: 1) meter failure problem and 2) dynamic membership problem. To solve these problems, we designed a dynamic membership group-based multiple-data aggregation scheme. First, a group-based key establishment scheme is proposed, meters are divided into groups, meters in a group build keys to encrypt their data, the meter failure problem is alleviated. If one group has broken meters, the other groups will not be affected. Second, the dynamic join, dynamic leave, and meter replacement techniques are proposed, and the dynamic membership is achieved by allowing meters to update their keys. The simulation results show a meter's computation cost and communication cost are the minima among the related works, which makes the proposed scheme more suitable for the IoT scenario. Besides, we designed a data encoding method and a data retrieve method, we designed two attacks: 1) “bilinear map pairing attack” and 2) “zero attack.”

PA-CRT: Chinese Remainder Theorem Based Conditional Privacy-Preserving Authentication Scheme in Vehicular Ad-Hoc Networks

Existing security and identity-based vehicular communication protocols used in Vehicular Ad-hoc Networks (VANETs) to achieve conditional privacy-preserving mostly rely on an ideal hardware device called tamper-proof device (TPD) equipped in vehicles. Achieving fast authentication during the message verification process is usually challenging in such strategies and further they suffer performance constraints from resulting overheads. To address such challenges, this paper proposes a novel Chinese remainder theorem (CRT)-based conditional privacy-preserving authentication scheme for securing vehicular authentication. The proposed protocol only requires realistic TPDs, and eliminates the need for pre-loading the master key onto the vehicle's TPDs. Chinese remainder theorem can dynamically assist the trusted authorities (TAs) whilst generating and broadcasting new group keys to the vehicles in the network. The proposed scheme solves the leakage problem during side channel attacks, and ensures higher level of security for the entire system. In addition, the proposed scheme avoids using the bilinear pairing operation and map-to-point hash operation during the authentication process, which helps achieving faster verification even under increasing number of signature. Moreover, the security analysis shows that our proposed scheme is secure under the random oracle model and the performance analysis shows that our proposed scheme is efficient in reducing computation and communication overheads.

SpyChain: A Lightweight Blockchain for Authentication and Anonymous Authorization in IoD

In this paper, we have proposed a lightweight blockchain based model to provide distributed authentication and anonymous authorization in IoD. We have proposed four different approaches to hide the identity of unmanned aerial vehicles UAV during the message exchanges using the blockchain. Non Interactive Zero Knowledge Proof (NIZKP) with bilinear map has been used to provide anonymity of UAV on the blockchain. The first approach describes a mechanism for the unlinkability of user identities. The second approach provides resistance against malleability attack together with unlinkability. The third approach ensures sender trackability to the receiver. In the fourth scheme, a UAV can delegate its task of tracking transactions to GCS in such a way that GCS can track the transaction of UAV but cannot claim the transaction’s authority. Relevant proofs of security for Signature Unforgeability and Unlinkability in Ciphertext (UN-C) are given to prove the strength of the techniques.

Three Representation Types for Systems of Forms and Linear Maps

We consider systems of bilinear forms and linear maps as representations of a graph with undirected and directed edges. Its vertices represent vector spaces; its undirected and directed edges represent bilinear forms and linear maps, respectively. We prove that if the problem of classifying representations of a graph has not been solved, then it is equivalent to the problem of classifying representations of pairs of linear maps or pairs consisting of a bilinear form and a linear map. Thus, there are only two essentially different unsolved classification problems for systems of forms and linear maps.

Integrity Verification Mechanism of Sensor Data Based on Bilinear Map Accumulator

With the explosive growth in the number of IoT devices, ensuring the integrity of the massive data generated by these devices has become an important issue. Due to the limitation of hardware, most past data integrity verification schemes randomly select partial data blocks and then perform integrity validation on those blocks instead of examining the entire dataset. This will result in that unsampled data blocks cannot be detected even if they are tampered with. To solve this problem, we propose a new and effective integrity auditing mechanism of sensor data based on a bilinear map accumulator. Using the proposed approach will examine all the data blocks in the dataset, not just some of the data blocks, thus, eliminating the possibility of any cloud manipulation. Compared with other schemes, our proposed solution has been proved to be highly secure for all necessary security requirements, including tag forgery, data deletion, replacement, replay, and data leakage attacks. The solution reduces the computational and storage costs of cloud storage providers and verifiers, and also supports dynamic operations for data owners to insert, delete, and update data by using a tag index table (TIT). Compared with existing schemes based on RSA accumulator, our scheme has the advantages of fast verification and witness generation and no need to map data blocks to prime numbers. The new solution supports all the characteristics of a data integrity verification scheme.

A Secure Transmission Method of Network Communication Data Based on Symmetric Key Encryption Algorithm

In order to solve the problems of low transmission efficiency and high transmission bit error rate in traditional transmission methods, a new secure transmission method of network communication data is designed based on symmetric key encryption algorithm. Based on the analysis of the security key theory, the agentless key publishing protocol is adopted to control the access of network communication data, so as to construct the ciphertext protocol. Then the key construction in the encryption process is completed by bilinear mapping method. On this basis, the encryption and decryption algorithm, dynamic key generation module and Shared key update module are combined to realize the secure transmission of network communication data. The experimental results show that the bit error rate of this method was kept below 1%, the time of transmission was below 80 s, and the VIM value exceeded 0.1, indicating that this method has the advantages of high data transmission efficiency, low bit error rate and safer transmission process.

AN IDENTITY-BASED ENCRYPTION SCHEME USING ISOGENY OF ELLIPTIC CURVES

Identity-Based Encryption is a public key cryptosystem that uses the receiver identifier information such as email address, IP address, name and etc, to compute a public and a private key in a cryptosystem and encrypt a message. A message receiver can obtain the secret key corresponding with his privacy information from Private Key Generator and he can decrypt the ciphertext. In this paper, we review Boneh-Franklin’s scheme and use bilinear map and Weil pairing’s properties to propose an identity-based cryptography scheme based on isogeny of elliptic curves.

Identity-based Data Possession Verification Scheme for Multi-Replica Storage in Cloud

In the cloud storage environment, how to efficiently and dynamically complete the integrity verification of multi-user and multi-replica data is a challenging problem. Based on the bilinear mapping signature mechanism and the multi-branch authentication tree, we propose an identity-based integrity verification scheme of multi-replica data for cloud, which solves the problem of large public key storage and management overhead in signature algorithm based on traditional public key cryptosystems. The proof shows that our scheme satisfies the robustness and has the function of protecting privacy. The results of analysis indicate that, compared with the existing similar schemes, our scheme has higher communication efficiency and computing performance.

Efficient Policy-Hiding and Large Universe Attribute-Based Encryption With Public Traceability for Internet of Medical Things

Modern day medical systems are closely integrated and interconnected with other systems, such as those comprising Internet-of-Medical Things (IoMT) devices that facilitate remote healthcare services, say during pandemics (e.g., COVID-19). Attribute-based encryption (ABE) is a promising cryptographic primitive to support fine-grained access control in the ciphertext environment; in other words, ABE can potentially be used to ensure data confidentiality and user privacy in the IoMT ecosystem. In this article, we propose an efficient partially-policy-hidden and large universe ABE scheme with public traceability to construct a practical IoMT system (hereafter referred to as PTIoMT). The system is designed to achieve the following features: 1) the access policy is partially hidden: only nonsensitive attribute labels/names are displayed, while sensitive attribute values are hidden in the encrypted electronic health records (EHRs); 2) the number of the attributes is independent of the public parameters and, thus, can be arbitrarily large; 3) any user who discloses the decryption key can be efficiently tracked; and 4) fewer bilinear pairing operations are required during the decryption process. The security analysis and performance evaluation demonstrate the security and efficiency of PTIoMT.

Algebraic Tensor Products Revisited: Axiomatic Approach

This is an expository paper on tensor products where the standard approaches for constructing concrete instances of algebraic tensor products of linear spaces, via quotient spaces or via linear maps of bilinear maps, are reviewed by reducing them to different but isomorphic interpretations of an abstract notion, viz. the universal property, which is based on a pair of axioms.

高分七号双线阵立体测绘相机系统集成与测试

高分七号双线阵立体测绘相机系统集成与测试

高分七号双线阵立体测绘相机系统集成与测试

高分七号双线阵立体测绘相机系统集成与测试

Efficient Short Group Signatures for Conditional Privacy in Vehicular Ad Hoc Networks via ID Caching and Timed Revocation

Vehicular Ad hoc Networks (VANETs) are a subset of the Internet of Things (IoT) that are used in smart traffic applications. Due to their high speed, mobility, and exposure to the environment, the security requirements for VANETs result in the conflicting design goals of protecting member privacy while also ensuring non-repudiation. Group signature schemes can fulfill these requirements, but often at the cost of expensive bilinear pairing operations. Furthermore, the cost of updating the group key information can be costly. Accordingly, this paper has two goals. First, it presents a group signature scheme that has been modified to remove pairing operations by caching computed values, while still preserving the critical requirement of conditional privacy. Second, this paper presents an argument for the abandonment of perfect forward and backward secrecy in VANET schemes in order to prevent the generation of keys that are never used, or used only once, and reduce the twin burdens of excessive key recalculation and key redistribution on the system.