Bilinear Maps Research Articles

EKV-VBQ: Ensuring Verifiable Boolean Queries in Encrypted Key-Value Stores

To address the deficiencies in privacy-preserving expressive query and verification mechanisms in outsourced key-value stores, we propose EKV-VBQ, a scheme designed to ensure verifiable Boolean queries over encrypted key-value data. We have integrated blockchain and homomorphic Xor operations and pseudo-random functions to create a secure and verifiable datastore, while enabling efficient encrypted Boolean queries. Additionally, we have designed a lightweight verification protocol using bilinear map accumulators to guarantee the correctness of Boolean query results. Our security analysis demonstrates that EKV-VBQ is secure against adaptive chosen label attacks (IND-CLA) and guarantees Integrity and Unforgeability under the bilinear q-strong Diffie–Hellman assumption. Our performance evaluations showed reduced server-side storage overhead, efficient proof generation, and a significant reduction in user-side computational complexity by a factor of log n. Finally, GPU-accelerated optimizations significantly enhance EKV-VBQ’s performance, reducing computational overhead by up to 50%, making EKV-VBQ highly efficient and suitable for deployment in environments with limited computational resources.

Bilinear Perceptual Fusion Algorithm Based on Brain Functional and Structural Data for ASD Diagnosis and Regions of Interest Identification.

Autism spectrum disorder (ASD) is a serious mental disorder with a complex pathogenesis mechanism and variable presentation among individuals. Although many deep learning algorithms have been used to diagnose ASD, most of them focus on a single modality of data, resulting in limited information extraction and poor stability. In this paper, we propose a bilinear perceptual fusion (BPF) algorithm that leverages data from multiple modalities. In our algorithm, different schemes are used to extract features according to the characteristics of functional and structural data. Through bilinear operations, the associations between the functional and structural features of each region of interest (ROI) are captured. Then the associations are used to integrate the feature representation. Graph convolutional neural networks (GCNs) can effectively utilize topology and node features in brain network analysis. Therefore, we design a deep learning framework called BPF-GCN and conduct experiments on publicly available ASD dataset. The results show that the classification accuracy of BPF-GCN reached 82.35%, surpassing existing methods. This demonstrates the superiority of its classification performance, and the framework can extract ROIs related to ASD. Our work provides a valuable reference for the timely diagnosis and treatment of ASD.

Multimorphisms on pre-Riesz spaces of continuous functions

In the theory of vector lattices, mostly three classes of lattice ordered algebras are investigated, called f-algebras, d-algebras, and almost-f-algebras. Each class is endowed with a different type of positive bilinear map as the multiplication, namely with bi-orthomorphisms, bi-Riesz homomorphisms, and orthosymmetric maps, respectively. On the space C(K), with K a compact Hausdorff space, representations as weighted composition or integral operators are known. We give generalized definitions of the above mentioned maps in the setting of partially ordered vector spaces, where we deal with n-linear maps. We generalize the representations to the case of certain subspaces of some C(K) space, with K a compact Hausdorff space. With the representations at hand, we deduce basic properties of these maps. The results also cover the case of order unit spaces, which can be seen as order dense subspaces of some C(K) space via the functional representation.

Empowering Data Owners: An Efficient and Verifiable Scheme for Secure Data Deletion

Cloud services have attracted numerous enterprises, organizations, and individual users due to their exceptional computing power and almost limitless storage capacity. A vast amount of business data and private data are continuously uploaded to the cloud platform, driven by a series of attractive services offered by the cloud. Unfortunately, once data is uploaded to the cloud, its owner has no way of ensuring that it is actually deleted as intended. This obviously increases the concerns of data owners about the security of their data, because it is related to the privacy of users. Therefore, there must be a reliable solution to prove that data is deleted as requested by users, to prevent data leakage or abuse. In existing data deletion schemes, most are designed based on cryptographic knowledge rather than erasure or overwrite techniques, in order not to cause incalculable damage to the storage medium. However, most cryptographic-based data deletion schemes, particularly attribute-based encryption, involve numerous complex bilinear mapping operations, which are expensive for most devices. To address this issue, the paper proposes an Efficient and Verifiable Scheme for Secure Data Deletion (EVSD). Firstly, Elliptic Curve Cryptography (ECC) is introduced to achieve efficient encryption of data. Then, leveraging Linear Secret Sharing Scheme (LSSS), fine-grained data deletion policies supporting logical operations are implemented. Finally, the deletion of the data is efficiently verified using the root of the Merkle Hash Tree (MHT) generated by the defined illegal and legal attributes, while the deletion proof is also generated. Satisfactorily, security analysis shows that the EVSD scheme is much more advantageous compared to existing schemes, and a trait likewise is also observed in the performance evaluation.

Anonymous data sharing scheme for resource-constrained internet of things environments

With the rapid development of Internet of Things (IoT) technology in industrial, agricultural, medical and other fields, IoT terminal devices face security and privacy challenges when sharing data. Among them, ensuring data confidentiality, achieving dual-side privacy protection, and performing reliable data integrity verification are basic requirements. Especially in resource-constrained environments, limitations in the storage, computing, and communication capabilities of devices increase the difficulty of implementing these security safeguards. To address this problem, this paper proposes a resource-constrained anonymous data-sharing scheme (ADS-RC) for the IoT. In ADS-RC, we use elliptic curve operations to replace computation-intensive bilinear pairing operations, thereby reducing the computational and communication burden on end devices. We combine an anonymous verifiable algorithm and an attribute encryption algorithm to ensure double anonymity and data confidentiality during the data-sharing process. To deal with potential dishonest behavior, this solution supports the revocation of malicious user permissions. In addition, we designed a batch data integrity verification algorithm and stored verification evidence on the blockchain to ensure the security and traceability of data during transmission and storage. Through experimental verification, the ADS-RC scheme achieves reasonable efficiency in correctness, security and efficiency, providing a new solution for data sharing in resource-constrained IoT environments.

A Privacy-Preserving Friend Matching Scheme Based on Attribute Encryption in Mobile Social Networks

In mobile social networks, users can easily communicate with others through smart devices. Therefore, the protection of user privacy in social networks is becoming a significant subject. To solve this problem, this paper proposes a fine-grained data access control scheme that uses attributes to match friends. In our scheme, the friend-making parties generate friend preference and self-description lists, respectively, realizing attribute hiding by converting friendship preference into ciphertext access control policies and self-description into attribute keys. The social platform matches user profiles to quickly eliminate unmatched users and avoids invalid decryption. In order to reduce the computational burden and communication cost of mobile devices, we adopt an algorithm mechanism for outsourcing decryption. When the user meets the matching conditions, the algorithm outsources the bilinear pair operation with large computation to the friend server. After that, the user finally decrypts the ciphertext. Security analysis shows that our scheme is safe and effective. In addition, performance evaluation shows that the proposed scheme is efficient and practical.

Hierarchical Identity-Based Authenticated Encryption with Keyword Search over encrypted cloud data

With the rapid development of cloud computing technology, cloud storage services are becoming more and more mature. However, the storage of sensitive data on remote servers poses privacy risks and is presently a source of concern. Searchable Encryption (SE) is an effective method for protecting sensitive data while preserving server-side searchability. Hierarchical Public key Encryption with Keyword Search (HPEKS), a new variant of SE, allows users with higher access permission to search over encrypted data sent to lower-level users. To the best of our knowledge, there exist only four HPEKS schemes in the literature. Two of them are in traditional public-key setting, and the remaining ones are identity-based public key cryptosystems. Unfortunately, all of the four existing HPEKS schemes are vulnerable against inside Keyword Guessing Attacks (KGAs). Moreover, all of the existing HPEKS schemes are based on the computationally expensive bilinear pairing operation which dramatically increases the computational costs. To overcome these issues, in this paper, we introduce the notion of Hierarchical Identity-Based Authenticated Encryption with Keyword Search (HIBAEKS). We formulate a security model for HIBAEKS and propose an efficient pairing-free HIBAEKS scheme. We then prove that the proposed HIBAEKS scheme is secure under the defined security model and is resistant against KGAs. Finally, we compare our proposed scheme with related constructions regarding security requirements, computational and communication costs to indicate the overall superiority of our proposed scheme.

Growth of bilinear maps II: bounds and orders

Growth of bilinear maps II: bounds and orders

Recurrent event query decoder for document-level event extraction

Document-level event extraction is a challenging task in natural language processing, as it involves multiple events within a document and scattered event arguments across sentences. To tackle these challenges, we propose a recurrent event query decoder, i.e., a recurrent module that dynamically updates event queries to capture cross-event dependencies. Our approach then generates arguments by extracting role-argument relations using bilinear mapping, which helps address the issue of scattered arguments. Experimental results demonstrate that our proposed approach outperforms state-of-the-art models on a large-scale public dataset and actual application data, achieving significant improvements in F1-score. In domain-specific event extraction applications, our method achieves higher accuracy with fewer resources compared to general-purpose large language models.

Improved RSA dynamic cryptographic accumulator-based anonymous batch authentication scheme for Internet of Vehicles

The Internet of Vehicles (IoV) provides various services to vehicles through information sharing to ensure road safety and improve traffic efficiency. However, malicious attackers can challenge the privacy and security systems of the IoV by conducting security attacks. Currently, many schemes use bilinear pairing or elliptic curves to construct authentication systems, ensuring anonymity of vehicle identities and message security. However, these schemes suffer drawbacks such as low computational efficiency and high communication overhead in highly dynamic IoV. Therefore, we propose a new efficient certificateless message authentication scheme. The proposed scheme constructs a lightweight security authentication protocol by improving the RSA dynamic accumulator and combining it with non-interactive discrete logarithm zero-knowledge proofs. In addition, our scheme eliminates the need for bilinear pairing operations, thereby reducing computational overhead. Simultaneously, it enables real-time tracking and revocation of malicious vehicle identities. Security analysis shows that our scheme can be reduced to a secure S-RSA assumption under the random oracle model, meeting various security requirements of the IoV. Performance analysis shows that our scheme diminishes not only the computational overhead but also the communication overhead.

A quantum-secure certificateless aggregate signature protocol for vehicular ad hoc networks

Vehicular ad hoc networks (VANETs) have revolutionized communication between vehicles and infrastructure, notably enhancing traffic management and passenger safety. However, VANETs are vulnerable to security threats, especially regarding data authenticity. Aggregate signature is a powerful technique that reduces computational and communication burdens by aggregating multiple signatures from different signers into a single signature. Traditional aggregate signature schemes, based on large prime number decomposition and the discrete logarithm problem, cannot effectively resist quantum attacks. This paper introduces a novel quantum secure certificateless aggregate signature (QSCLAS) scheme designed to enhance data security and privacy in VANETs. Our proposed scheme employs the number theory research unit (NTRU) algorithm. As a lattice-based cryptographic algorithm, NTRU is renowned for its security against quantum computer attacks, making it an essential component of our quantum-secure solution. By eliminating the need for expensive bilinear pairing operations, our proposed scheme achieves high efficiency and practicality in resource-limited VANETs environments. The security analysis demonstrates our scheme's resilience against both Type-I and Type-II adversaries in the random oracle model under the small integer solution (SIS) problem on the NTRU lattice. Furthermore, compared with existing approaches, the results illustrate that our proposed scheme offers significant advantages in signature generation and verification cost, as well as lower transmission overhead than other lattice-based schemes, thereby making it highly suitable for VANETs environments.

Broadcast Encryption using Sum-Product decomposition of Boolean functions

The problem of Broadcast Encryption (BE) consists in broadcasting an encrypted message to a large number of users or receiving devices in such a way that the emitter of the message can control which of the users can or cannot decrypt it. Since the early 1990s, the design of BE schemes has received significant interest and many different concepts were proposed. A major breakthrough was achieved by Naor, Naor and Lotspiech (CRYPTO 2001) by partitioning cleverly the set of authorized users and associating a symmetric key to each subset. Since then, while there have been many advances in public-key based BE schemes, mostly based on bilinear maps, little was made on symmetric cryptography. In this paper, we design a new symmetric-based BE scheme, named Σ Π BE, that relies on logic optimization and consensual security assumptions. It is competitive with the work of Naor et al. and provides a different tradeoff: the bandwidth requirement is significantly lowered at the cost of an increase in the key storage.

Unbounded non-zero inner product encryption

In a non-zero inner product encryption (NIPE) scheme, ciphertexts and keys are associated with vectors from an inner-product space. Decryption of a ciphertext for x→ is allowed by a key for y→ if and only if the inner product 〈x→,y→〉≠0. Existing constructions of NIPE assume the length of the vectors are fixed apriori. We present the first constructions of unbounded non-zero inner product encryption (UNIPE) with constant sized keys. Unbounded here refers to the size of vectors not being pre-fixed during setup. Both constructions, based on bilinear maps, are proven selectively secure under the decisional bilinear Diffie-Hellman (DBDH) assumption.Our constructions are obtained by transforming the unbounded inner product functional encryption (IPFE) schemes of Dufour-Sans and Pointcheval (ACNS 2019), one in the strict domain setting and the other in the permissive domain setting. Interestingly, in the latter case, we prove security from DBDH, a static assumption while the original IPFE scheme relied on an interactive parameterised assumption. In terms of efficiency, features of the IPFE constructions are retained after transformation to NIPE. Notably, the public key and decryption keys have constant size.

Effective privacy preserving in cloud computing using position aware Merkle tree model

In this research manuscript, a new protocol is proposed for predicting the available space in the cloud and verifying the security of stored data. The protocol is utilized for learning the available data, and based on this learning, the available storage space is identified, after which the cloud service providers allow for data storage. The Integrity verification separates the private and the public data, which avoids privacy issues. The integration of the private data is done with the help of cloud service providers with respect to the third-party auditing (TPA). Earlier, public key cryptography and bilinear map technologies have been combined by the researchers, but the computation time and costs were high. To secure the integrity of the data storage, the client should execute several computations. Therefore, this research suggests a reliable and effective method called position-aware Merkle tree (PMT), which is implemented for ensuring data integrity. The proposed system uses a PMT that enables the TPA to perform multiple auditing tasks with high efficiency, less computational cost and computation time. Simulation results clearly shows that the developed PMT method consumed 0.00459 milliseconds of computation time, which is limited when compared to the existing models.

Redact4Trace: A solution for auditing the data and tracing the users in the redactable blockchain

With the introduction of the General Data Protection Regulation and the advent of the Blockchain 3.0 era, redactable blockchain have become a popular area of research. However, auditing harmful data on redactable blockchain has become an urgent problem to be solved to promote redactable blockchain. Moreover, tracing the identity of users who submit harmful data is a concerning problem that urgently needs to be solved. To address these issues, we propose Redact4Trace, a solution for tracing and auditing data in redactable blockchains. In Redact4Trace, transactions are the unit for minor data editing and redaction, ensuring fine-grained data editing and access. We have designed a data auditing scheme based on the unique characteristics of redactable blockchains. This scheme, which uses a chameleon hash, depends only on the transaction’s hash and effectively protects user privacy. We have also designed an identity tracing scheme based on bilinear maps. Users must use the bilinear mapping to compute address information and store it in the transaction for identity tracing. If the identity information in the transaction is altered, our backup scheme based on the discrete logarithm problem can still trace the user’s identity effectively. Security analyses and experimental results confirm that Redact4Trace is both secure and efficient.

Covariant Derivatives on Homogeneous Spaces: Horizontal Lifts and Parallel Transport

We consider invariant covariant derivatives on reductive homogeneous spaces corresponding to the well-known invariant affine connections. These invariant covariant derivatives are expressed in terms of horizontally lifted vector fields on the Lie group. This point of view allows for a characterization of parallel vector fields along curves. Moreover, metric invariant covariant derivatives on a reductive homogeneous space equipped with an invariant pseudo-Riemannian metric are characterized. As a by-product, a new proof for the existence of invariant covariant derivatives on reductive homogeneous spaces and their the one-to-one correspondence to certain bilinear maps is obtained.

GBP: Graph convolutional network embedded in bilinear pooling for fine-grained encoding

In fine-grained recognition, classical high-order coding has inherent contradiction between visual burstiness and feature redundancy, the core of which is the inherent instability of high-order features. Existing methods mainly use EIG and SVD decomposition to maintain feature stability, but this process increases feature redundancy. To address this problem, this paper proposes a Graph Bilinear Pooling (GBP) model to obtain stable fine-grained features through the effective aggregation ability of graph networks. GBP avoids explicit feature decomposition and reconciles the contradiction between visual burstiness and feature redundancy. First, GBP transforms images into a graph spectrum through feature correlation measurement. Then, an improved multi-head graph convolution structure is proposed by using Graph Isomorphism Networks (GIN) to realize feature aggregation. Finally, bilinear pooling operations are performed between graph convolution feature maps and original feature maps to obtain more compact and stable fine-grained feature representations. Experiments on CUB, Cars, and Aircrafts datasets demonstrate that the accuracy of the proposed method is 87.8 %, 93.5 %, and 89.6 % respectively, with a feature representation of 2048 dimensions. Compared to the baseline, the feature number is only 25 % of the baseline model, and the accuracy is increased by 2.6 %, 1.7 %, and 1.3 % respectively. These results demonstrate the effectiveness of graph neural network embedding in improving feature stability.

A traceable and revocable broadcast encryption scheme for preventing malicious encryptors in Medical IoT

Medical data sharing is essential for the advancement of medical research, but the existence of malicious encryptors and malicious users poses a major challenge to the seamless sharing of information among healthcare providers. We proposed a traceable and revocable broadcast encryption scheme for preventing malicious encryptors in the Medical Internet of Things (MIoT). In 2023, Wang et al. first proposed the concept of malicious encryptor for broadcast encryption and trator tracing, and they constructed a scheme for preventing this attack. The malicious encryptor is reasonable in real broadcast encryption systems because the encryptor is not always the same as the digital content provider. When digital content providers for medical institutions want to share sensitive medical data, the employees may implement encryption. Then the employees may plant some trapdoors and sell to the black market, which can be used to construct pirated boxes. To resist malicious encryptor attacks, we rely on the uniform distribution of the output of the secure cryptographic hash function to generate the randomness needed for encryption. To prevent malicious users from selling their private keys to attackers, we set up public tracing and revocation mechanisms. Meanwhile, we enable digital content providers to share common encrypted data to different groups of authorized users protected by privacy, while also sharing individual data to designated consumers of those groups. Under the decision q-parallel BDHE assumption without random oracles, our construction is demonstrated to be adaptive IND-CPA secure. Since we have a compact communication bandwidth, a constant user secret key size, and only three bilinear operations are needed for decryption to recover the encrypted broadcast message, our scheme does not add much overhead and is therefore practical.

A secure and efficient heterogeneous ID‐based signcryption for unmanned aerial vehicular networking system

AbstractIn the last decade, Internet of Things opened the door to applications of unmanned aerial vehicles (UAVs). Since the data is transferred on a public channel, therefore security, privacy, and efficiency are the main concerns of UAVs communication. Signcryption is a technique to execute encryption and signature in one step. However, the usual signcryption is not applicable to UAVs with constrained nature of resources and ground station. Moreover, in particular, UAVs and ground station need a heterogeneous signcryption for UAVs to establish communication with the ground station. But, the bilinear bilinear mapping is a very costly operation, so we need pairless identity based heterogeneous signcryption. The proposed design is unforgeable and secure against chosen message attacks. The experiment shows the efficiency of the proposed method. It takes less communication and computation costs.

Cryptanalysis and improvement of “group public key encryption scheme supporting equality test without bilinear pairings”

Public key encryption with equality test (PKEET) is a novel primitive which supports equality comparisons on two encrypted messages. Currently, most of the existing PKEET schemes are based on bilinear pairing and require heavy computational overheads. To address this issue, Shen et al. recently proposed an efficient group public key encryption supporting equality test without bilinear pairings scheme. Compared with other schemes, their scheme reduces the usage of expensive bilinear pairing operations and enjoys higher computation efficiency. They claimed that their scheme achieved one-wayness security in the random oracle model and resisted offline message recovery attack. In this letter, we analyze Shen et al.'s scheme through two concrete attacks and demonstrate that their scheme can not support the above two security requirements. An improved scheme is provided to overcome the security vulnerabilities in their scheme. Performance analysis shows that our improved scheme has certain advantages in both computation overhead and storage overhead.