Bilinear Groups Research Articles

Decentralized multi-authority anonymous credential system with bundled languages on identifiers in bilinear groups

Decentralized multi-authority anonymous credential system with bundled languages on identifiers in bilinear groups

Practically secure linear-map vector commitment and its applications

The primitive of vector commitment scheme allows a user to commit to an ordered sequence of messages (i.e., a vector) and later open the commitment at any position subset of the vector. The most important and desirable feature of vector commitment schemes is that the size of the opening proof is sublinear in the length of the committed vector. The original vector commitment scheme has now been extended to support several new functionalities like aggregation, updatability and homomorphism, and has applications ranging from verifiable data streaming to stateless cryptocurrency. Among these extensions, the linear-map vector commitment (LVC) scheme enables a user to open a general linear map evaluated on the committed vector, rather than those messages of the committed vector as in the original vector commitment scheme. However, the existing LVC schemes are only proved to be secure under the idealized assumptions, i.e., using the algebraic group model, which might be unpractical in the real world. To this end, we eliminate the use of algebraic group model, and propose a practically secure LVC construction. Our construction achieves practical security by additionally generating degree proofs for polynomials that enable a verifier to check the degree of polynomials publicly. We prove the security of the proposed LVC construction in the standard model under a q-type complexity assumption over bilinear groups. Moreover, we demonstrate how to use the proposed LVC scheme to construct maintainable vector commitments and verifiable data streaming protocols. The theoretical comparison and experimental results indicate that our proposal provides stronger security guarantee, while being competitive in terms of efficiency.

Multi-keyword ranked search scheme for privacy protection in social networks

In a social network friend-matching scenario, a proposed blockchain-based privacy protection scheme with cloud-edge collaboration aims to improve search efficiency while protecting the personal privacy information of dating users. The scheme encrypts and stores massive dating data on the cloud server (CS), and uploading the corresponding keyword index to the nearby edge node (EN) for distributed storage. To enhance the search experience for users, this paper uses the Bisecting K-means clustering algorithm to classify all dating documents, categorizes the keywords with high relevance to form keyword grouping first, and then constructs the inverted index based on the keyword grouping results, so that we can quickly locate the position of the query keywords, and then find the matching document identifiers to speed up the ciphertext search. Simultaneously, this paper introduces the BM25 model to calculate the relevance scores of ciphertext documents to achieve the effect of ranking ciphertext documents. Under the general bilinear group model, the proposed scheme proves selectively secure against selective keyword attacks and plain text attacks. The simulation results indicate that this proposed scheme is a more efficient multi-keyword ranking search scheme for dating data.

A logarithmic-sized accountable ring signature scheme in the standard model

Ring signature and group signature are two major cryptographic primitives providing users anonymity and authentication simultaneously. While both primitives enable any user to sign messages as a member of a set of users, the feature of ring signature is that a signer can choose a group in an ad-hoc manner, which is called a ring, by itself. Conversely, in group signature, a group membership is managed by some trusted third party, which is called a group manager, and an (appropriate) accountability is provided for the group manager to identify illegal anonymous signers. Accountable ring signature (ARS) is a cryptographic primitive combining the features of ring signature and group signature. ARS allows signers to choose their groups (rings) in an ad-hoc manner, and at the same time, maintain accountability by forcing them to select a designated opener who can identify them.In this paper, we propose the first ARS scheme with O(log⁡n) signature size in the standard model (without depending on the random oracle methodology), where n is the size of a ring. More precisely, we propose a new generic construction of ARS based on (standard) signature, (standard) public key encryption, non-interactive zero-knowledge proof system, somewhere perfectly binding hash function, and public key encryption with non-interactive opening. All building blocks for our ARS scheme can be obtained under the decisional linear (DLIN) assumption over bilinear groups.

An improved finegrained ciphertext policy based temporary keyword search on encrypted data for secure cloud storage

We present a temporary keyword search over sensitive and confidential health data in a cloud environment. The cloud constitutes a semi-trusted domain, making it necessary for data owners to secure their data before outsourcing it through techniques like encryption. Attribute-based keyword search techniques tend to perform a search operation using a search token generated by an authorized user. These search tokens can lead to serious privacy threats, as they can extract all ciphertexts that may have been generated along with their keyword. Therefore, restricting search tokens to extract ciphertexts generated within a time interval is a more promising solution. In this paper, we present a novel ciphertext policy fine-grained temporary keyword that prevents the misuse of these search tokens. Further, it mitigates the risk of insider threats within healthcare organizations by limiting the window of opportunity for unauthorized access to minimum. To assess the security, our proposed scheme is formally proven to be secure against Selectively Chosen Keyword Attacks in the generic bilinear group model. Additionally, we demonstrate that the encryption algorithm’s complexity is linear in relation to the number of attributes. Our scheme’s significance and practicality are revealed by the performance evaluation.

A Traceable Universal Designated Verifier Transitive Signature Scheme

A transitive signature scheme enables anyone to obtain the signature on edge (i,k) by combining the signatures on edges (i,j) and (j,k), but it suffers from signature theft and signature abuse. The existing work has solved these problems using a universal designated verifier transitive signature (UDVTS). However, the UDVTS scheme only enables the designated verifier to authenticate signatures, which provides a simple way for the signer to deny having signed some messages. The fact that the UDVTS is not publicly verifiable prevents the verifier from seeking help arbitrating the source of signatures. Based on this problem, this paper proposes a traceable universal designated verifier transitive signature (TUDVTS) and its security model. We introduce a tracer into the system who will trace the signature back to its true source after the verifier has submitted an application for arbitration. To show the feasibility of our primitive, we construct a concrete scheme from a bilinear group pair (G,GT) of prime order and prove that the scheme satisfies unforgeability, privacy, and traceability.

Fog-Enabled Secure and Efficient Fine-Grained Searchable Data Sharing and Management Scheme for IoT-Based Healthcare Systems

In recent times, fog computing has emerged as a helpful extension of cloud computing. It can efficiently handle the prevalent issue of managing silos of data generated by today's digital healthcare services. Moreover, the application of the Internet of Things (IoT) in the development of smart healthcare systems further adds tons of data tirelessly to these silos, thus making the cloud congested. To manage such continuously growing data, the concept of adding a fog layer between the cloud and the end-users (EUs) proved to be beneficial. These intermediary fog nodes (FNs) can handle and store data, and thus facilitate the cloud and alleviate the burden from the EUs. Most of the existing search schemes for encrypted data have been developed for the cloud platform and ignored this helpful extension, which can improve the scheme's efficiency by delegating most of the heavy computations to the intermediary FNs. In this article, a fine-grained searchable data sharing scheme has been proposed using the fog computing platform. The resulting scheme is efficient and lightweight because the FN facilitates EUs by performing computationally intensive tasks on their behalf. A significant reduction in storage and computational cost has been achieved by the proposed scheme at the data owner's end, representing the resource-constrained IoT devices. The storage cost has been reduced to two source group elements, and the computational cost has been reduced to three exponent operations in the source group and one hash operation. Furthermore, the proposed scheme is secure against the selectively chosen keyword attack in the generic bilinear group model.

Possibility of decryption speed-up by parallel processing in CCA secure hashed ElGamal.

In order to prove the ElGamal CCA(Chosen Ciphertext Attack) security in the random oracle model, it is necessary to use the group where ICDH(Interactive Computational Diffie Hellman) assumption holds. Until now, only bilinear group with complex algebraic structure has been known as the ICDH group. In this paper, we introduce the ICDH group with simple algebraic structure. In other words, we prove that ICDH assumption holds in the integer group with composite modulus. On the basis of this, we propose the CCA secure hashed ElGamal and its fast variant to speed up decryption by parallel processing. Our parallel scheme has the fastest decryption among all CCA secure PKE(Public Key Encryption) schemes implemented in integer group and gives the possibility that ElGamal protocol could be practical when the big modulus numbers are used to resist the quantum attack.

Simulation extractable versions of Groth’s zk-SNARK revisited

Zero-knowledge succinct non-interactive arguments of knowledge (zk-SNARKs) are the most efficient proof systems in terms of proof size and verification. Currently, Groth’s scheme from EUROCRYPT 2016, Groth16\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extsf{Groth16}$$\\end{document}, is the state-of-the-art and is widely deployed in practice. Groth16\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extsf{Groth16}$$\\end{document} is originally proven to achieve knowledge soundness, which does not guarantee the non-malleability of proofs. There has been considerable progress in presenting new zk-SNARKs or modifying Groth16\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extsf{Groth16}$$\\end{document} to efficiently achieve strong Simulation extractability, which is shown to be a necessary requirement in some applications. In this paper, we revise the Random oracle based variant of Groth16\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extsf{Groth16}$$\\end{document} proposed by Bowe and Gabizon, BG18, the most efficient one in terms of prover efficiency and CRS size among the candidates, and present a more efficient variant that saves 2 pairings in the verification and 1 group element in the proof. This supersedes our preliminary construction, presented in CANS 2020 (Baghery et al. in CANS 20, volume 12579 of LNCS, Springer, Heidelberg. pp 453-461, 2020), which saved 1 pairing in the verification, and was proven in the generic group model. Our new construction also improves on BG18 in that our proofs are in the algebraic group model with Random Oracles and reduces security to standard computational assumptions in bilinear groups (as opposed to using the full power of the generic group model (GGM)). We implement our proposed simulation extractable zk-SNARK (SE zk-SNARK) along with BG18 in the Arkworks library, and compare the efficiency of our scheme with some related works. Our empirical experiences confirm that our SE zk-SNARK is more efficient than all previous simulation extractable (SE) schemes in most dimensions and it has very close efficiency to the original Groth16\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extsf{Groth16}$$\\end{document}.

S-BDS: An Effective Blockchain-based Data Storage Scheme in Zero-Trust IoT

With the development of the Internet of Things (IoT) , a large-scale, heterogeneous, and dynamic distributed network has been formed among IoT devices. There is an extreme need to establish a trust mechanism between devices, and blockchain can provide a zero-trust security framework for IoT. However, the efficiency of the blockchain is far from meeting the application requirements of the IoT, which has become the biggest resistance to the application of the blockchain in the IoT. Therefore, this paper combines sharding to build an effective Blockchain-based IoT data storage scheme (S-BDS) . Sharding can solve the problem of blockchain capacity and scalability. While the blockchain provides data immutability and traceability for the IoT, it also brings huge demands for data credibility verification. The communication delay in the IoT system seriously affects the security of the system, while the Merkle proof of traditional blockchain occupies a lot of communication resources. This paper constructs Insertable Vector Commitment (IVC) in the bilinear group and replaces the Merkle tree with IVC to store IoT data in the blockchain. The construct has small-sized proof. It also has the ability to record the number of updates, which can prevent replay-attacks. Experiments show that each block processes 1,000 transactions, the proof size of a single data piece is 30% of the original scheme, and proofs from different shards can be aggregated. IVC can effectively reduce communication congestion and improve the stability and security of the IoT system.

Compact Structure-Preserving Signatures with Almost Tight Security

In structure-preserving cryptography, every building block shares the same bilinear groups. These groups must be generated for a specific, a priori fixed security level, and thus, it is vital that the security reduction in all involved building blocks is as tight as possible. In this work, we present the first generic construction of structure-preserving signature schemes whose reduction cost is independent of the number of signing queries. Its chosen-message security is almost tightly reduced to the chosen-plaintext security of a structure-preserving public-key encryption scheme and the security of Groth–Sahai proof system. Technically, we adapt the adaptive partitioning technique by Hofheinz (Eurocrypt 2017) to the setting of structure-preserving signature schemes. To achieve a structure-preserving scheme, our new variant of the adaptive partitioning technique relies only on generic group operations in the scheme itself. Interestingly, however, we will use non-generic operations during our security analysis. Instantiated over asymmetric bilinear groups, the security of our concrete scheme is reduced to the external Diffie–Hellman assumption with linear reduction cost in the security parameter, independently of the number of signing queries. The signatures in our schemes consist of a larger number of group elements than those in other non-tight schemes, but can be verified faster, assuming their security reduction loss is compensated by increasing the security parameter to the next standard level.

Document-Level Relation Extraction with Local Relation and Global Inference

The current popular approach to the extraction of document-level relations is mainly based on either a graph structure or serialization model method for the inference, but the graph structure method makes the model complicated, while the serialization model method decreases the extraction accuracy as the text length increases. To address such problems, the goal of this paper is to develop a new approach for document-level relationship extraction by applying a new idea through the consideration of so-called “Local Relationship and Global Inference” (in short, LRGI), which means that we first encode the text using the BERT pre-training model to obtain a local relationship vector first by considering a local context pooling and bilinear group algorithm and then establishing a global inference mechanism based on Floyd’s algorithm to achieve multi-path multi-hop inference and obtain the global inference vector, which allow us to extract multi-classified relationships with adaptive thresholding criteria. Taking the DocRED dataset as a testing set, the numerical results show that our proposed new approach (LRGI) in this paper achieves an accuracy of 0.73, and the value of F1 is 62.11, corresponding to 28% and 2% improvements by comparing with the classical document-level relationship extraction model (ATLOP), respectively.

(Compact) Adaptively secure FE for attribute-weighted sums from k-Lin

This paper presents the first adaptively simulation secure functional encryption (FE) schemes for attribute-weighted sums. In the proposed FE schemes, attributes are viewed as vectors and weight functions are arithmetic branching programs (ABP). We present two schemes with varying parameters and levels of adaptive simulation security. (a)We first present a one-slot scheme supporting a bounded number of ciphertext queries and an arbitrary polynomial number of secret key queries both before and after the ciphertext queries. This is the best possible level of security one can achieve in the adaptive simulation-based framework. The scheme also achieves indistinguishability-based adaptive security against an unbounded number of ciphertext and secret key queries.(b)Next, bootstrapping from the one-slot scheme, we present an unbounded-slot scheme that can support a bounded number of ciphertext and pre-ciphertext secret key queries while supporting an a-priori unbounded number of post-ciphertext secret key queries. Both schemes enjoy ciphertexts that do not grow with the number of appearances of the attributes within the weight functions. The schemes are built upon prime-order asymmetric bilinear groups and the security is derived under the standard (bilateral) k-Linear (k-Lin) assumption. Our work resolves an open problem posed by Abdalla et al (In: CRYPTO, Springer, New York, 2020), where they presented an unbounded-slot FE scheme for attribute-weighted sum achieving only semi-adaptive simulation security. Technically, we extend the recent adaptive security framework of Lin and Luo (In: EUROCRYPT, Springer, New York, 2020), devised to achieve compact ciphertexts in the context of indistinguishability-based payload-hiding security, to the setting of simulation-based adaptive attribute-hiding security.

A Generic Construction of CCA-Secure Identity-Based Encryption with Equality Test against Insider Attacks

Identity-based encryption with equality test (IBEET) is a generalization of the traditional identity-based encryption (IBE) and public key searchable encryption, where trapdoors enable users to check whether two ciphertexts of distinct identities are encryptions of the same plaintext. By definition, IBEET cannot achieve indistinguishability security against insiders, i.e., users who have trapdoors. To address this issue, IBEET against insider attacks (IBEETIA) was later introduced as a dual primitive. While all users of IBEETIA are able to check whether two ciphertexts are encryptions of the same plaintext, only users who have tokens are able to encrypt plaintexts. Hence, IBEETIA is able to achieve indistinguishability security. On the other hand, the definition of IBEETIA weakens the notion of IBE due to its encryption inability. Nevertheless, known schemes of IBEETIA made use of rich algebraic structures such as bilinear groups and lattices. In this paper, we propose a generic construction of IBEETIA without resorting to rich algebraic structures. In particular, the only building blocks of the proposed construction are symmetric key encryption and pseudo-random permutations in the standard model. If a symmetric key encryption scheme satisfies CCA security, our proposed IBEETIA scheme also satisfies CCA security.

Certificateless Public Key Authenticated Encryption with Keyword Search Achieving Stronger Security

Transforming data into ciphertexts and storing them in the cloud database is a secure way to simplify data management. Public key encryption with keyword search (PEKS) is an important cryptographic primitive as it provides the ability to search for the desired files among ciphertexts. As a variant of PEKS, certificateless public key authenticated encryption with keyword search (CLPAEKS) not only simplifies certificate management but also could resist keyword guessing attacks (KGA). In this paper, we analyze the security models of two recent CLPAEKS schemes and find that they ignore the threat that, upon capturing two trapdoors, the adversary could directly compare them and distinguish whether they are generated using the same keyword. To cope with this threat, we propose an improved security model and define the notion of strong trapdoor indistinguishability. We then propose a new CLPAEKS scheme and prove it to be secure under the improved security model based on the intractability of the DBDH problem and the DDH problem in the targeted bilinear group.

Dual-server certificateless public key encryption with authorized equality test for outsourced IoT data

The Internet of Things (IoT) devices with restricted storage and computing sources are unable to store and handle massive data at local. A promising method is to engage some cloud server for maintaining outsourced encrypted IoT data and responding user request, in the meantime, the privacy of outsourced data can be protected. Existing encryption techniques with equality test allow the authorized cloud server to compare encrypted data and perform data classification. However, these schemes in the single server model cannot resist internal keyword guessing attacks. Also, the existing schemes in public key setting confront the burden of maintaining public key certificates, and the ones in identity-based setting face the key escrow problem. To address these issues, this paper proposes a dual-server certificateless public key encryption scheme supporting authorized equality test (DS-CL-AET) in bilinear groups. Security analysis indicates that the proposed DS-CL-AET scheme offers confidentiality protection for outsourced ciphertext and authentication tokens. Performance analysis demonstrates the practicality of our DS-CL-AET scheme in securing outsourced IoT data in clouds.

An Efficient E2E Crowd Verifiable E-Voting System

Electronic voting (e-voting), compared with article voting, has advantages in several aspects. Among those benefits, the ability to audit the electoral process at every stage is one of the most desired features of an e-voting system. In Eurocrypt 2015, Kiayias, Zacharias, and Zhang proposed a new E2E verifiable e-voting system that for the first time provides E2E verifiability without relying on external sources of randomness or the random oracle model; the main advantage of such system is in the fact that election auditors need only the election transcript and the feedback from the voters to pronounce the election process unequivocally valid. Unfortunately, their system comes with a huge performance and storage penalty for the election authority (EA) compared to other e-voting systems such as Helios. The main reason is that due to the way the EA forms the proof of the tally result, it is required to <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">precompute</i> a number of ciphertexts for each voter and each possible choice of the voter. The performance penalty on the EA appears to be intrinsic to the approach: voters cannot compute an enciphered ballot themselves because there seems to be no way for them to prove that it is a valid ciphertext. In this work, we construct a new e-voting system that retains similar strong E2E characteristics (but against computational adversaries) while completely eliminating the performance and storage penalty of the EA. Our construction has similar performance to Helios and is practical. The privacy of our construction relies on the SXDH assumption over bilinear groups via complexity leveraging.

Privacy-Preserving Spatio-Temporal Keyword Search for Outsourced Location-Based Services

With the popularization of location-based services (LBS), encryption techniques have been utilized to protect data security when outsourcing LBS to cloud. However, existing schemes only consider spatial range search or keyword search, while expressive and practical search over encrypted LBS data is still a challenging problem. In this article, we introduce PrivSTL, a privacy-preserving spatio-temporal keyword search framework over the encrypted LBS data based on attribute-based encryption, linear encryption and RSA encryption. It allows mobile users to submit LBS query with spatial range, time interval and Boolean keyword expression, and provides accurate and authorized search by matching these query conditions and also the access policy. Then we introduce an extended scheme PrivSTG, which utilizes Geohash to divide the locations into grids, and outsources an encrypted index tree to cloud servers. PrivSTG improves the service efficiency by searching only over the ciphertexts in the surrounding grids of mobile user. Finally, we analyze the security of PrivSTL against chosen-plaintext, chosen-keyword and outside keyword-guessing attacks in generic bilinear group model, and show that PrivSTL guarantees the spatio-temporal keyword profile privacy, and also protects the query privacy. The experimental results indicate that our scheme is practical and efficient for outsourced LBS.

Anonymous Identity Based Broadcast Encryption against Continual Side Channel Attacks in the State Partition Model

In the past 10 years, many side-channel attacks have been discovered and exploited one after another by attackers, which have greatly damaged the security of cryptographic systems. Since no existing anonymous broadcast encryption scheme can resist the side-channel attack, the paper presents an anonymous identity-based broadcast encryption against continual side-channel attacks in the state partition model (CLR-SS-AIBBE). Based on split-state technology, the proposed scheme divides the private key into two states, and the decryption operations are correspondingly divided into two steps. Based on the three static hypotheses for a bilinear group with composite order, the proposed scheme can be proved to be fully secure by the dual system encryption technology in the standard model. The leakage ratio about the private key can reach 1/3.

SHT-based public auditing protocol with error tolerance in FDL-empowered IoVs

With the intelligentization of the Internet of Vehicles (IoVs), Artificial Intelligence (AI) technology is becoming more and more essential, especially deep learning. Federated Deep Learning (FDL) is a novel distributed machine learning technology and is able to address the challenges like data security, privacy risks, and huge communication overheads from big raw data sets. However, FDL can only guarantee data security and privacy among multiple clients during data training. If the data sets stored locally in clients are corrupted, including being tampered with and lost, the training results of the FDL in intelligent IoVs must be negatively affected. In this paper, we are the first to design a secure data auditing protocol to guarantee the integrity and availability of data sets in FDL-empowered IoVs. Specifically, the cuckoo filter and Reed-Solomon codes are utilized to guarantee error tolerance, including efficient corrupted data locating and recovery. In addition, a novel data structure, Skip Hash Table (SHT) is designed to optimize data dynamics. Finally, we illustrate the security of the scheme with the Computational Diffie-Hellman (CDH) assumption on bilinear groups. Sufficient theoretical analyses and performance evaluations demonstrate the security and efficiency of our scheme for data sets in FDL-empowered IoVs.