Vector Commitment Research Articles

Aggregatable Subvector Commitment with Efficient Updates

An aggregatable subvector commitment scheme extends a vector commitment scheme by enabling the aggregation of multiple proofs into a single compact subvector proof. However, the existing schemes have to recompute proofs for each position when inserting an element into the vector, incurring significant computational overhead. In this paper, we propose a novel aggregatable subvector commitment scheme based on Newton interpolation, which efficiently supports the addition of new elements. Specifically, the proposed scheme allows incremental updates to the commitment and proofs for each position, avoiding the requirement for full recomputation and thereby significantly reducing computational overhead. Additionally, we employ the Karatsuba algorithm to efficiently perform large-integer multiplication, which improves the aggregation and verification of proofs. Finally, we implement the proposed scheme and conduct a detailed comparison with aSVC. Experimental results demonstrate that the proposed scheme achieves a 48× speedup when adding an element to a 16-length vector, as well as 2.13× and 1.73× speedups for aggregating eight proofs and performing verification, respectively.

Distributed Medical Data Storage Mechanism Based on Proof of Retrievability and Vector Commitment for Metaverse Services.

The metaverse is a unified, persistent, and shared multi-user virtual environment with a fully immersive, hyper-temporal, and diverse interconnected network. When combined with healthcare, it can effectively improve medical services and has great potential for development in realizing medical training, enhanced teaching, and remote surgical treatment. The metaverse provides immersive services for users through massive and multimodal data, and its data scale and data growth rate are bound to show exponential growth. Blockchain-based distributed storage is a fundamental way to keep the metaverse running continuously; however, many blockchains, such as Ethereum and Filecoin, suffer from low transaction throughput and high latency, which seriously affect the efficiency of distributed storage services and make it difficult to apply them to the metaverse environment. To this end, this paper first proposes a network architecture for distributed storage systems based on proof of retrievability to address the problem of centralized decision making and single point of access in centralized storage. The secure data storage of the metaverse health system is ensured. Secondly, we designed two data transmission protocols through vector commitment and encoding functions to achieve the transfer of time cost from the critical path to storage nodes and improve the efficiency of data verification between nodes as well as the scalability of the metaverse health system. Finally, this paper also conducts security analysis and performance analysis of the proposed scheme, and the results show that our scheme is secure and efficient.

Spatio-Temporal Big Data Collaborative Storage Mechanism Based on Incremental Aggregation Subvector Commitment in On-Chain and Off-Chain Systems

As mobile internet and Internet of Things technologies rapidly advance, the amount of spatio-temporal big data have surged, and efficient and secure management solutions are urgently needed. Although cloud storage provides convenience, it also brings significant data security challenges. Blockchain technology is an ideal choice for processing large-scale spatio-temporal big data due to its unique security features, but its storage scalability is limited because the data need to be replicated throughout the network. To solve this problem, a common approach is to combine blockchain with off-chain storage to form a hybrid storage blockchain. However, these solutions cannot guarantee the authenticity, integrity, and consistency of on-chain and off-chain data storage, and preprocessing is required in the setup phase to generate public parameters proportional to the data length, which increases the computational burden and reduces transmission efficiency. Therefore, this paper proposes a collaborative storage mechanism for spatio-temporal big data based on incremental aggregation sub-vector commitments, which uses vector commitment binding technology to ensure the secure storage of on-chain and off-chain data. By generating public parameters of fixed length, the computational complexity is reduced and the communication efficiency is improved while improving the security of the system. In addition, we design an aggregation proof protocol that integrates aggregation algorithms and smart contracts to improve the efficiency of data query and verification and ensure the consistency and integrity of spatio-temporal big data storage. Finally, simulation experiments verify the correctness and security of the proposed protocol, providing a solid foundation for the blockchain-based spatio-temporal big data storage system.

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.

Asynchronous verifiable information dispersal protocol of achieving optimal communication

The evolution of distributed systems necessitates robust protocols to facilitate secure and efficient data storage and retrieval amid challenges like asynchronous communication and adversarial threats. However, achieving the theoretical lower bounds of communication cost in Asynchronous Verifiable Information Dispersal (AVID) protocols remains an unresolved issue, prompting the need for innovation in this domain.In this paper, we propose a new AVID protocol designed to optimize communication cost. In contrast to previous approaches, we leverage vector commitment (VC) technology combined with erasure codes, replacing conventional hash tree structures or error correction codes. This approach results in significant O(logn) communication savings. Additionally, our research reveals that while ensuring simultaneous output from all honest nodes is desirable to satisfy Totality, it is not necessary for all nodes to receive corresponding shares or proofs during the Dispersal phase. This insight allows us to circumvent the common O(n2κ) communication overhead.Our AVID protocol achieves an optimal dispersal cost of O(|M|+n2) compared to the prior best of O(|M|+κn2). Furthermore, each node in our protocol incurs a storage cost of O(|M|/n+κ) bits, while the retrieval cost per client is O(|M|+nκ).

Communication-Efficient Verifiable Data Streaming Protocol in the Multi-User Setting

Verifiable data streaming (VDS) protocols enable end users with limited storage space to continuously stream data items to an untrusted cloud server, while preserving the capacity of verifying the integrity of those retrieved data items for downstream tasks. Although there has been plenty of research around the construction of VDS, we observe that they all focus on the scenario of single-user. When deploying these VDS protocols into more common applications that involve multiple users' data (e.g., network data monitoring and stock trends analysis), the size of the proof used to prove the integrity of retrieved data items grows linearly with the number of involved users. This would bring tremendous communication overhead, especially for lightweight users. To this end, we initiate the study of VDS protocols that are suitable for multi-user (or cross-user) setting. Specifically, we first introduce a new primitive called aggregatable chameleon vector commitment (ACVC) that allows to aggregate multiple proofs from different commitments into a single proof. Then, based on ACVC, we present a communication-efficient VDS protocol for the multi-user setting. That is, when querying data items from multiple users, the size of corresponding proof is constant and independent of the number of involved users. Theoretical analysis indicates that the proposed VDS protocol outperforms previous VDS protocols in terms of communication overhead. We also implement the proposed ACVC, and conduct extensive experiments to demonstrate its practicability.

BUA: a blockchain-based unlinkable authentication scheme for mobile IoT

ABSTRACT Mobile IoT, a pioneering IoT facet, enhances data acquisition. Mutual authentication ensures device validity in mobile IoT. Unlinkable authentication needs for mobile IoT data nodes during device validation. Current methods have issues: Certificate Authority (CA) faces computational load, and blockchain deals with storage and throughput. In this paper, BUA, a blockchain-based unlinkable authentication scheme, applies vector commitment for CA reduction and blockchain data compression. A binary tree auxiliary index, minimizes redundancy in vector commitment verification. This scheme fulfills security goals and boosts performance by 13.24%, surpassing similar proposols.

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.

OWL: A data sharing scheme with controllable anonymity and integrity for group users

As our society becomes digital and communication technology develops, global collaboration is an inevitable trend, where data-sharing is a critical component of cooperation across organizations. Identity privacy and data integrity are vital issues in data-sharing. Existing works struggle to address these problems simultaneously, either privacy leaking or privacy abuse. In this work, we proposed OWL, a data-sharing scheme that (1) provides users on-demand anonymity and (2) allows users to verify data integrity while preserving anonymity. To achieve (1) OWL enables controllable anonymity that allows de-anonymity for the malicious while keeping anonymity to the honest providers based on traceable ring signature technology. To achieve (2), OWL designs a data integrity auditing scheme that uses vector commitment to verify data integrity without privacy leakage. Furthermore, OWL employs the blockchain to store immutable auxiliary information for the integrity and controllable anonymity. We also employ the state channel to resolve the performance bottleneck of blockchain and design methods to improve the usage of the state channel for group users. We prove that OWL achieves controllable anonymity and integrity. Finally, we implement the experiment to evaluate the efficiency of OWL.

Efficient inner product arguments and their applications in range proofs

AbstractInner product arguments allow a prover to prove that the inner product of two committed vectors equals a public scalar. They are used to reduce the complexity of many cryptographic primitives, such as range proofs. Range proofs are deployed in numerous applications to prove that a committed value lies in a certain range. As core building blocks, their complexity largely determines the performance of corresponding applications. In this paper, we have optimised the inner product argument with statement including two vector commitments (IPAtvc) and range proof of Daza et al. (PKC’20), the inner product argument with statement including only one vector commitment (IPAovc) of Bünz et al. (S&P′18). For IPAtvc, we reduce the concrete communication complexity by 2 log2n field elements, where n is the vector dimension. For range proofs, we reduce the concrete communication and prover complexities by about 2 log2m field elements and 11m field multiplications, respectively, where m is the bit length of range. For IPAovc, we exponentially reduce the asymptotic verifier complexity from linear to logarithmic. Due to the asymptotic characteristics, our protocols are highly competitive when the vector dimension or bit length of range is large.

Blockchain-based auditing with data self-repair: From centralized system to distributed storage

Cloud storage provides data owners with massive storage and computing resources. To release from heavy data management and maintenance, more and more data owners are willing to outsource data to cloud. However, the data stored in cloud are out of the control of data owners, and may be corrupted and unretrievable. To solve the above problem, this paper proposes a decentralized auditing scheme BVA for the single cloud storage server, and an extended batch auditing scheme E-BVA for distributed storage. Firstly, BVA and E-BVA utilize vector commitment technology to realize lightweight data integrity auditing for outsourced data. Secondly, to avoid privacy and performance risks caused by the third party auditor, both BVA and E-BVA employ a smart contract on the blockchain as an auditor to perform data integrity auditing. Thirdly, both schemes support the verifiability between outsourced data and their corresponding authenticators, which prevents malicious data owners framing cloud storage servers and avoid subsequent dispute arbitration. Finally, based on regenerating code, E-BVA supports data self-repair of corrupted servers, while protecting the privacy of outsourced data and realizing the lightweight computation. The security and performance analyses demonstrate the security and efficiency of BVA and E-BVA.

A blockchain-based compact audit-enabled deduplication in decentralized storage

Secure deduplication and data auditing are significant in improving the resource utilization and data integrity protection of data outsourcing services. However, existing audit-enabled deduplication schemes cannot implement block-level deduplication over audit tags since they contain file information, and have to bear the consequent storage burden. Also, they suffer from the low coupling problem caused by the difference in optimal data chunking between deduplication and auditing. In this paper, we propose a blockchain-based compact audit-enabled deduplication scheme in decentralized storage. Specifically, we introduce the concept of N-ary tag commitment tree (NTCT), which integrates the information of all data blocks into a file authenticator to support integrity verification and enable block-level deduplication over audit tags. On this basis, we propose a blockchain-based compact audit-enabled deduplication protocol, which adopts an aggregatable vector commitment to generate audit tags, thereby overcoming the low coupling problem between deduplication and auditing. Notably, data users can outsource the task of tag generation to storage servers. Meanwhile, the capabilities of duplication detection, proof of ownership (PoW), and integrity verification are integrated into audit tags to reduce tag redundancy. Furthermore, we present an update protocol to allow data users to achieve a lightweight data update without uploading the entire new data. Finally, security analysis and performance evaluation demonstrate that our scheme is practical.

VRBC: A Verifiable Redactable Blockchain with Efficient Query and Integrity Auditing

Driven by various legal obligations and service requirements, the redactable blockchain was introduced to balance the modifiability and immutability of blockchain technology. However, such a blockchain inevitably generates one or even more acceptable versions for the same block data, enabling malicious full nodes to deceive light/new nodes with old data, and even disrupt the consistency of the blockchain ledger. In this paper, we introduce the concept of verifiable redactable blockchain (VRBC) to provide efficient validity verification for on-chain data. To this end, we design a novel authentication data structure, called blockchain authentication tree (BAT), which employs a chameleon hash function and aggregatable vector commitment to bind continuously-appended blocks. Based on this, we propose an efficient VRBC scheme supporting integrity auditing, which not only allows the light nodes to query and validate on-chain data, but also enables new nodes to check the integrity of the blockchain ledger before synchronizing it, effectively avoiding resource waste and security risks caused by invalid queries and ledger synchronization. Furthermore, we introduce some optimized strategies to improve the performance of our scheme and extend it to transaction-level and permissionless VRBC. Finally, we demonstrate the practicability of our scheme through detailed security analysis and visual performance evaluation.

Publicly Verifiable Databases With All Efficient Updating Operations

The primitive of verifiable database (VDB) can enable a resource-limited client to securely outsource an encrypted database to an untrusted cloud server and the client could efficiently retrieve and update the data at will. Meanwhile, the client can undoubtedly detect any misbehavior by the server if the database has been tampered with. We argue that most of the existing VDB schemes can only support the updating operation of replacement, rather than other common updating operations such as <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">insertion</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">deletion</i> . Recently, the first publicly verifiable VDB schemes that supports all updating operations was proposed based on the idea of hierarchical vector commitment. However, one disadvantage of the proposed VDB scheme is that the computation and storage complexity increases linearly when the client continually inserts data records in the same index of the database. As a result, it remains an open problem how to construct an efficient (and publicly verifiable) VDB scheme that can support all updating operations regardless of the manner of insertion. In this paper, we first introduce a new primitive called committed invertible Bloom filter (CIBF) and utilize it to propose a new publicly verifiable VDB scheme that can support all kinds of updating operations. Additionally, the proposed construction is efficient regardless of the manner of updating operations and thus provides an affirmative answer to the above open problem.

Efficient verifiable databases with additional insertion and deletion operations in cloud computing

Verifiable database (VDB) schemes allow the data owner to outsource a large database to the cloud so that any resource-constraint client could later retrieve the database records and check whether the cloud returns valid records or not. Meanwhile, the database can be updated by the data owner. To the best of our knowledge, there is no secure and efficient VDB scheme supporting public verification and all kinds of update operations (i.e., insertion, modification, and deletion) simultaneously. To resolve this problem, we propose an efficient VDB scheme by incorporating vector commitment (VC) with Merkle Interval Hash Tree (MIHT). To enhance the security (i.e., resist the forward automatic update attack), we re-formalize the syntax of VC and present a new construction of VC based on modified Generalized Bilinear Inversion (mGBI) assumption. Our proposed VC scheme is used for guaranteeing the integrity of data. Like the traditional VC schemes, our proposed scheme remains publicly verifiable. MIHT is a new primitive introduced by us, which is mainly used to support all update operations. Security analysis shows that our proposed VDB scheme can achieve real-world security requirements. The detailed performance analyses and simulations show that our proposed schemes are more practical in the real world.

ELSA: efficient long-term secure storage of large datasets (full version) \u2217

An increasing amount of information today is generated, exchanged, and stored digitally. This also includes long-lived and highly sensitive information (e.g., electronic health records, governmental documents) whose integrity and confidentiality must be protected over decades or even centuries. While there is a vast amount of cryptography-based data protection schemes, only few are designed for long-term protection. Recently, Braun et al. (AsiaCCS’17) proposed the first long-term protection scheme that provides renewable integrity protection and information-theoretic confidentiality protection. However, computation and storage costs of their scheme increase significantly with the number of stored data items. As a result, their scheme appears suitable only for protecting databases with a small number of relatively large data items, but unsuitable for databases that hold a large number of relatively small data items (e.g., medical record databases).In this work, we present a solution for efficient long-term integrity and confidentiality protection of large datasets consisting of relatively small data items. First, we construct a renewable vector commitment scheme that is information-theoretically hiding under selective decommitment. We then combine this scheme with renewable timestamps and information-theoretically secure secret sharing. The resulting solution requires only a single timestamp for protecting a dataset while the state of the art requires a number of timestamps linear in the number of data items. Furthermore, we extend the scheme, that supports a single client, to a multi-client setting. Subsequently, we characterize the arising challenges with respect to integrity and confidentiality and discuss how our multi-client scheme tackles them. We implemented our solution and measured its performance in a scenario where 9600 data items are aggregated, stored, protected, and verified over a time span of 80 years. Our measurements show that our new solution completes this evaluation scenario an order of magnitude faster than the state of the art.

Privacy preserving integrity checking of shared dynamic cloud data with user revocation

In Cloud computing, storage and maintenance of the data are provided as service to the client. Traditionally, when the clients store and maintain their data at their own server, the data are dynamic in nature and are often shared among groups of users. The clients desire the traditional flexibility when they shift their data to the Cloud. Introducing the flexibility of sharing dynamic data with storage outsourced to the Cloud needs addressing new security challenges and requires the provision for user revocation. This paper presents a secure and effective scheme for storage of shared dynamic data in untrusted cloud servers with provisions for privacy preserving integrity check by third-party auditor and for addition and revocation of users. This proposed scheme is based on CDH-based ring signature and vector commitment.

A (Zero-Knowledge) Vector Commitment with Sum Binding and its Applications

Abstract Vector commitment (VC) schemes allow committing to an ordered sequence of ${q}$ values ${(m_1,\cdots ,m_q)}$ in such a way that one can later open the commitment at specific positions. However, the existing VC schemes suffer from two substantial shortcomings that limit their use: (i) the commitments cannot be opened except at some specific positions, and (ii) their security only captures position-binding but offers no privacy: the client may learn additional information about the committed sequence through the proofs and the commitments. To resolve these problems, we first extend VC to a more expressive primitive called VC with sum binding (VCS), in which the commitment can also be opened to the sum of all elements in the committed sequence. VCS additionally satisfies the security of sum binding, which guarantees that the commitment cannot be opened to different sums. To enhance its privacy, we extend VCS to zero-knowledge VCS (ZKVCS), in which commitments and proofs constructed during the protocol execution leak nothing about the committed sequence. We formalize this new property by a standard real/ideal experiment. Meanwhile, the detailed performance analyses and simulations show that our proposed schemes are more practical. Finally, we introduce a novel notion of (zero-knowledge) verifiable database supporting sum and show how to construct it from our (ZK)VCS scheme.

Secure data stream outsourcing with publicly verifiable integrity in cloud storage

Recent technological developments in Internet of Things has led to enormous amount of data stream. Limited by storage and computation capabilities, increasing companies and individuals outsource their data stream to powerful cloud servers, from which they can query the data when it is needed. Nevertheless, it presents a challenge in order to ensure the cloud server can comply with their advertised policies and return the correct query results. In this paper, we focus in particular on the scenario where a data owner wishes to (i) outsource its unbounded data stream to a cloud server; (ii) enable anyone who has the public key to retrieve the outsourced data stream; (iii) ensure public verification of the integrity for query results. To this end, we propose a secure data stream outsourcing scheme with publicly verifiable integrity in cloud storage (DSO-PVI), which builds upon the well-established techniques of Chameleon Vector Commitment (CVC) to guarantee the integrity of query results. Moreover, we introduce a formal security model of DSO-PVI and prove that it is secure against malicious cloud servers. Our analyses and experimental results demonstrate that the proposed scheme is greatly improved in terms of functionality and performance.

Publicly verifiable data transfer and deletion scheme for cloud storage

With the rapid development of cloud storage, more and more resource-constraint data owners can employ cloud storage services to reduce the heavy local storage overhead. However, the local data owners lose the direct control over their data, and all the operations over the outsourced data, such as data transfer and deletion, will be executed by the remote cloud server. As a result, the data transfer and deletion have become two security issues because the selfish remote cloud server might not honestly execute these operations for economic benefits. In this article, we design a scheme that aims to make the data transfer and the transferred data deletion operations more transparent and publicly verifiable. Our proposed scheme is based on vector commitment (VC), which is used to deal with the problem of public verification during the data transfer and deletion. More specifically, our new scheme can provide the data owner with the ability to verify the data transfer and deletion results. In addition, by using the advantages of VC, our proposed scheme does not require any trusted third party. Finally, we prove that the proposed scheme not only can reach the expected security goals but also can satisfy the efficiency and practicality.