Blockchain Papers

Amit Kumar Tyagi, N. Sreenath

No abstract is available for this record.

Jun Shen, Xiaofeng Chen, Jianghong Wei, Fuchun Guo · 5 authors

Cloud auditing enables the integrity verification of cloud data without the necessity of data retrieval, which significantly promotes the storage service of cloud computing. Auditing with ownership transfer is a variation where both cloud data and the tags for integrity verification can be transferred. In some scenarios, like joint-stock enterprise acquisition and electronic medical records migration, we argue that auditing and transferring data belonging to multiple owners are significantly important. However, to the best of our knowledge, there exists no such protocol in multi-ownership scenarios in the literature. In this paper, we propose a blockchain-based accountable auditing protocol with multi-ownership transfer for the first time. One distinguishable property is the simultaneous achievement of verifiability, accountability and multi-ownership transferability, merely with very little extra cost. Specifically, we construct a novel tag structure based on homomorphic authenticators and compact multi-signatures, enabling integrity verification and multi-ownership transfer. Subsequently, we record the information concerning data generation and ownership transfer on immutable blockchains to make these procedures accountable. Furthermore, we present a comprehensive analysis and extensive experiments to demonstrate the security and efficiency of the proposed protocol.

Hiren Dutta, Parama Bhaumik

The industry is transitioning to a decentralized, self-managed supply chain network based on use case development. Finance, manufacturing, shipping, auto, food, and real estate supply chains are decentralizing information exchange. IoT data goes to a decentralized network, where transactions are executed without a central authority. This architecture faces difficulties including centralized trust management, interoperability, reusability, privacy, and access control for IoT data sharing. Decentralized group formation and information visibility limits might be mission-critical for the banking, finance, and insurance industries. In past work, we advocated decentralized trust management, reusability, and interoperability. This work addresses privacy, access control, permission, and information exchange transparency without compromising decentralization. In a decentralized context, our technique and proof of concept build trust.

Miguel Pincheira, Elena Donini, Massimo Vecchio, Salil S. Kanhere

The data economy is based on data and information sharing and tremendously impacts society as it facilitates innovative collaborations and decision-making strategies. Nonetheless, most dataset-sharing solutions rely on a centralized authority that rules data ownership, availability, and accessibility. Recent works have explored the integration of distributed storage and blockchain to enhance decentralization, data access, and smart contracts for automating the interactions between actors and data. However, current solutions propose a smart contract design limiting the system's scalability in terms of actors and shared datasets. Furthermore, little is known about the performance of these architectures when using distributed storage instead of centralized storage approaches. This paper proposes a scalable architecture called DeBlock for data sharing in a trusted way among unreliable actors. The architecture integrates a public blockchain that provides a transparent record of datasets and interactions, with a distributed storage for data storage in a completely decentralized way. Furthermore, the architecture provides a smart-contract design for a transparent catalog of datasets, actors, and interactions with efficient search and retrieval capabilities. To assess the system's feasibility, robustness, and scalability, we implement a prototype using the Ethereum blockchain and leveraging two decentralized storage protocols, Swarm and IPFS. We evaluate the performance of our proposed system in different scenarios (e.g., varying the amount and size of the shared datasets). Our results demonstrate that our proposal outperforms benchmarks in gas consumption, latency, and resource requirements, especially when increasing the number of actors and shared datasets.

Sana Alam, Shehnila Zardari, Jawwad Ahmed Shamsi

In the Social Internet of Things (SIoT), trust refers to the decision-making process used by the trustor (Service Requesters (SRs) or Service Consumers (SCs)) to decide whether or not to entrust the trustee (Service Providers (SPs)) with specific services. Trust is the key factor in SIoT domain. The designing of a two-way, two-stage parameterized feedback-based, service-driven, attacks-resistant trust and reputation system for SIoT accompanied by a penalty mechanism for dishonest SPs and SRs is our main contribution that mitigates the trust-related issues occurring during service provisioning and service acquisition amongst various entities (SPs or SRs) and enhances trust amongst them. Our proposed methodology examines a SP’s local trust, global trust, and reputation by taking into account “Social Trust” and “Quality of Service (QoS)” factors”. Two—Stage Parameterized feedback” is incorporated in our proposed strategy to better manage “intention” and “ability” of SRs and provides early identification of suspicious SRs. This feature compels SRs to act honestly and rate the corresponding SPs in a more accurate way. Our recommended paradigm sorts SPs into three SP status lists (White List, Grey List, and Black List) based on reputation values where each list has a threshold with respect to the maximum service fee that can be charged. SPs in White List charge the most per service. SPs in other lists have a lower selection probability. Every feedback updates the SP’s trust and reputation value. Sorting SPs increases resistance against On Off Attack, Discriminatory Attack, Opportunistic Service Attack, and Selective Behavior Attacks. SPs must operate honestly and offer the complete scope of stated services since their reputation value relies on all their global trust values (Tglobal) for various services. Service requests may be accepted or denied by SPs. “Temporarily banned” SRs can only request unblocked services. SRs lose all privileges once on a “permanently banned” list. If local and global trust values differ by more than the threshold, the SR is banned. Our method also provides resistance against Bad Mouthing Attack, Ballot Stuffing Attack. Good Mouthing Attack/Self—Propagating Attack. Experiments indicate our trust and reputation management system recognizes and bans fraudulent SRs. “Dishonest SPs” are “blacklisted,” which affects their reputation, trust, and service charges.

Shuang Yao, Dawei Zhang

<abstract><p>With the continuous development of Internet of Things, finance, big data and many other fields, blockchain has been widely used in these areas for transactions, data sharing, product traceability and so on. Numerous assets have appeared in the blockchain, and there are some levels of conflicts among privacy protection of these assets, transaction transparency and auditability in blockchain; so how to provide privacy preserving, make public verifications and audit the encrypted assets are challenging problems. In this paper, we propose a privacy-preserving transaction scheme with public verification and reliable audit in blockchain. First, we provide privacy preserving of transaction contents based on homomorphic encryption. It is flexible, as we decouple user identity and transaction contents. Then, we propose and design a multiplicative zero-knowledge proof with formal security analysis. Furthermore, several verification rules are defined by us in the scheme, such as balance verification and multiplicative verification based on the proposed multiplicative zero-knowledge proof. Our scheme enables reliable and offline auditing for each transaction, and we aggregate the zero-knowledge proofs to save the ledger space. Finally, we make a security analysis of our proposal in terms of transaction confidentiality, public verification and audit reliability, and we give a performance analysis of the proposed scheme.</p></abstract>

Miquel À. Cabot-Nadal, M. Magdalena Payeras–Capellà, Macià Mut–Puigserver, Alberto Soto

Lots of business processes can be benefited of the use of blockchain-based technologies. The distributed nature of the blockhain overcome a part of the reliability issues related to centralised systems. Recently the use of NFTs has been spread to multiple applications. The EIP-721 standard proposal defines the interface of non-fungible tokens (NFTs). This type of token was designed with the aim of creating interchangeable tokens but with the peculiarity of being unique and non-fungible and with the impossibility to be damaged or destroyed. For this reason, the EIP-721 standard has almost limitless applications: it can represent ownership of digital or physical assets, unlock access to certain services, … In short, it can represent any single object or right that we can transfer between a sender and a receiver. In this paper we present a study on the transferability of the NFTs and its implications in the generation of secure applications. Currently, the NFTs can be transferred with the consent of the owner (by himself or by an authorised party) but the receiver of the token cannot decline the reception of the token, that will be transferred to his wallet. Therefore, we propose in this paper the enhancement of the NFT standard that allows the rejection of reception of tokens, obtaining a kind of token that can be used in a secure way in all kinds of applications that require the selective reception of the tokens.

Kuo‐Hui Yeh, Guan-Yan Yang, Chanapha Butpheng, Lin-Fa Lee · 5 authors

Blockchain technology has recently attracted tremendous interest due to its potential to revolutionize the industry by achieving decentralization while increasing the number of data sources, transparency, reliability, auditability, and trustworthiness. However, one of the major barriers to the widespread adoption of blockchain applications is the lack of mutual consensus and management across blockchains. Cross-blockchain consensus refers to one blockchain network reaching a consensus with another blockchain network to provide the ability to interact and share data. In this paper, we propose a secure management scheme with symmetric cross-blockchain communication and certificateless signature primitives, in which two heterogeneous blockchains are linked by a relay chain to simultaneously deliver cross-blockchain transaction security, achieve compatibility among various blockchains, and ensure the consistency of data exchanged, in practice. Additionally, our evaluation and security analysis shows the practicability and security of our proposed management scheme and demonstrates that a common test platform based on Ethereum can achieve acceptable computation costs.

Ghassan Al-Sumaidaee, Rami Alkhudary, Željko Žilić, Andraws Swidan

No abstract is available for this record.

Garima Verma

The storage of Electronic Health Records (EHRs) on mobile cloud environments has undergone a paradigm shift in recent years, with mobile devices integrating with cloud computing to improve medical data transfers between patients and healthcare providers. This sophisticated paradigm allows for minimal operational costs, significant flexibility, and the use of electronic health records (EHRs). However, for e-health systems, this new paradigm poses concerns regarding data privacy and network security. It’s a challenging problem to exchange EHRs consistently among mobile users while maintaining high-security levels in the mobile cloud. It’s a challenging problem to exchange EHRs consistently among mobile users while maintaining high-security levels in the mobile cloud. Here, this paper intends to introduce a novel blockchain technology for secure health data in the cloud, which aids in ensuring authentication and offers integrity to medical records. Here, blockchain with optimal encryption is deployed via an improved blowfish model that also guarantees authentication features. Further, the optimal key generation is carried out by a new approach termed as Elephant Herding Optimization with Opposition-based Learning (EHO-OBL). Thus, the data integrity is maintained by the developed approach, and at last, the supremacy of the presented approach is proved concerning various measures. Accordingly, the key generation time of the proposed method has attained less value, and it was 51.04%, 91.48%, 92.64%, 91.48%, 89.99%, 91.06% and 91.48% better than traditional Blowfish, Rivest–Shamir–Adleman (RSA), Advanced Encryption Standard (AES), Elliptic-Curve Cryptography (ECC), Elephant Herding Optimization (EHO), Moth-Flame Optimization (MFO) and Whale Optimization (WOA) models, for file size of 10 kb.

Shamama Anwar, Ruchika Tulsyan, Souvik Saha, Sudip Kumar Sahana

Over the last decade, data sharing has become eminent in each aspect of the daily routine chores of industries and research alike. Traditionally, all data sharing platform depend on trusted third parties (TTP), owing to which they lack trust, security, immutability and transparency. But, with the advent of blockchain technology, the data sharing has got a whole new dimensionality. Blockchain is a distributed and decentralized ledger that records the source of a digital resources. The secure features of blockchain have helped it gain popularity and application in a variety of domains including sustainable manufacturing. It can aid in customer and product tracking, supply chain, quality checks, etc. Blockchain can further strengthen how products can be designed, engineered, manufactured, dispatched and tracked in the revolutionized Industry 4.0 initiative. All these activities involve sharing of voluminous data. Hence, this paper presents an efficient data-sharing system which takes the advantage of the transparency as well as the security provided by a blockchain. AnonChain (Anonymous Chain) is a file sharing platform that integrates Inter Planetary File Sharing (IPFS) with the blockchain technology to provide secure and anonymous file sharing.

Sameer Al-Jeshi, Ahmed Tarfa, Hasan Al-Aswad, Wael Elmedany · 5 authors

The Financial Technologies (Fintech) plays a major role in transforming traditional financial institutions. Although it disrupts them, fintech enables these traditional financial institutions to reduce costs, introduce innovative solutions and gain a competitive edge over rivals and develop new digital technology and infrastructure, which increase the dependency on digital systems. The stronger dependence on these new technologies widens the cyber threat landscape towards digital systems/assets and these institutions. This landscape is rapidly increasing and getting more complex. Threat actors are becoming more organized, sophisticated, and cyber-crime has been commercialized. WannaCry, one of the recent large-scale cyber-attacks with global impact was an example of how vulnerabilities can be used in attacks for financial gains. This paper aims to critically analyze the spectrum of cyber threats facing the digital financial sector and illustrate the distributed ledger as an appealing solution which protects the database with its immutable property, as one of the most important assets to digital banking and its’ data. A blockchain model is illustrated to show how the technology can lead to safer implementation, enhanced operations, and to reduced exposure to cyber threats.

Fabian Honecker, Julian Dreyer, Ralf Tönjes

Modern Public Key Infrastructures (PKIs) allow users to create and maintain centrally stored cryptographic certificates. These infrastructures use a so-called certificate chain. At the root of the chain, a root Certification Authority (CA) is responsible for issuing the base certificate. Every verification and certification step within the chain is based upon the security of said root CA. Thus, its operation security is of great concern. Since the root certificates are stored locally on the root CA, any Denial of Service (DoS) attack may render the whole certificate chain, which is based on of the attacked root CA, inoperable. Therefore, this article evaluates different approaches to a decentralized data storage system that is based on the Distributed Ledger Technology (DLT). To show the real-world potential of the proposed approaches, we also evaluate the different technologies using a novel PKI mechanism called Near Field Communication Key Exchange (NFC-KE). The results indicate that modern distributed data storage solutions such as Interplanetary Filesystem (IPFS) and SIA can have significant performance and decentralization benefits in comparison to purely Blockchain-based technologies like Hyperledger Fabric. However, they lack any Smart Contract functionality, which requires a software developer to implement verification mechanisms in centralized software solutions.

Mahdi Movahedian Moghaddam, Hossein Albakri, Kourosh Parand

Abstract Today, with the growth of cryptocurrencies, the importance of keeping them has increased. Wallets are one of the ways to keep cryptocurrencies safe. One of the techniques for securing cryptocurrency wallets is the use of multi-signature technique. This technique is based on a concept called secret sharing. In order to ensure the security of these wallets, the secret sharing scheme is used, which uses the Lagrange interpolation algorithm. This algorithm has a challenge in terms of time complexity, and in this research, we introduced two parallel approaches to reduce this time complexity based on graphical processor units (GPU) and distributed systems. In addition to reducing the time complexity, the distributed approach was able to help us increase the security of the algorithm. The speedup obtained from the execution on the interpolation of 16384 points in the GPU-based approach was equal to 45214 and in the distributed approach, in the execution resulting from 4 to 128 processes was equal to 7.81.

Julius Köpke, Giovanni Meroni, Mattia Salnitri

Collaborative business processes can be seen as smart contracts, as they are oftentimes adopted to express agreements among different organizations. Indeed, they provide mechanisms to formalize the obligations of each involved party. For instance, collaborative business processes can specify when a certain task should be executed, under which conditions a service should be offered to the other participants, and how physical objects and information should be manipulated. In this setting, to prevent misuse of smart contracts and services and information provided, it is paramount to guarantee by design that security requirements are fulfilled. With the rise in popularity of blockchains, several approaches exploiting the trusted smart contract execution environment offered by this technology to enforce collaborative business processes have been proposed. Yet, the complexity of business processes, security requirements, and blockchain applications calls for an engineering approach that guides the design of secure business processes. Such an approach should both take advantage of the possibilities offered by blockchain technology to enforce some security requirements (e.g., non-repudiation), and take into account the limitations blockchain poses for other security requirements (e.g., confidentiality). However, we are not aware of any existing work that aims at addressing such issues following a similar approach. In this article, we propose SecBPMN2BC: a model-driven approach to designing business processes with security requirements that are meant to be deployed on blockchains. SecBPMN2BC consists of: (i) an extension of BPMN 2.0 that allows designing secure smart contracts; (ii) a set of algorithms and their implementation that check incompatible security requirements and help the design of smart contracts; (iii) a workflow that guides the application of the method. The method has been validated with a survey conducted on security and BPMN experts.

Shaoliang Peng, Wenxuan Bao, Hao Liu, Xia Xiao · 9 authors

In the era of big data, data is playing an increasingly important role in scientific study, and reliable storage and secure sharing of data have become a research hotspot. At present, centralized solutions based on data centers and cloud storage have problems with data-right confirmation and center trust. A large number of decentralized storage solutions are public systems, in which blockchain technology, as a tool for value exchange, does not solve the problems of data verification and system supervision. We propose a peer-to-peer storage system with identity access, which achieves data validation, cross-organizational data retrieval, trusted authorization, and sharing based on the consortium blockchain. Our solution proposes a peer-to-peer data storage scheme based on the consortium blockchain and a set of identity authentication mechanisms compatible with the consortium blockchain. Based on this, we propose a blockchain-based permission control scheme and a set of retrieval, authorization, and sharing processes. Finally, we implemented and tested the system to prove the feasibility of the scheme.

Cristhian Martinez-Rendon, J. L. Gonzalez‐Compean, Dante D. Sánchez‐Gallegos, Jesús Carretero

This paper presents a continuous delivery/continuous verifiability ( CD/CV ) method for IoT dataflows in edge–fog–cloud. A CD model based on extraction, transformation, and load (ETL) mechanism as well as a directed acyclic graph ( DAG ) construction, enable end-users to create efficient schemes for the continuous verification and validation of the execution of applications in edge–fog–cloud infrastructures. This scheme also verifies and validates established execution sequences and the integrity of digital assets . CV model converts ETL and DAG into business model, smart contracts in a private blockchain for the automatic and transparent registration of transactions performed by each application in workflows/pipelines created by CD model without altering applications nor edge–fog–cloud workflows. This model ensures that IoT dataflows delivers verifiable information for organizations to conduct critical decision-making processes with certainty. A containerized parallelism model solves portability issues and reduces/compensates the overhead produced by CD/CV operations. We developed and implemented a prototype to create CD/CV schemes, which were evaluated in a case study where user mobility information is used to identify interest points, patterns, and maps. The experimental evaluation revealed the efficiency of CD/CV to register the transactions performed in IoT dataflows through edge–fog–cloud in a private blockchain network in comparison with state-of-art solutions.

Nabeel Khan, Hanan Aljoaey, Mujahid Tabassum, Ali Farzamnia · 6 authors

Since cloud computing is an essential component of any modern company (usually accounting for a considerable share of information technology (IT) infrastructure investment), consumers rely on cloud services. Data privacy and security are worries when data remains in third-party storage. Existing document version control systems are centralized and at risk from data loss, as seen by higher time utilization and incorrect document update procedures that allow modifications to a document without the awareness of other network operators. Underutilized peer resources might be leveraged to construct storage. According to this argument, an elevated level of data security may be obtained by encrypting the data and dispersing it among numerous nodes. In this study, we attempted to review the security of cloud systems when using the blockchain Ethereum, and cloud computing was briefly discussed with its advantages and disadvantages. The idea of a decentralized cloud was briefly demonstrated with blockchain technology. Furthermore, previous papers were reviewed and presented in tabular form. This dictated that there are still research gaps in the field of blockchain-based cloud computing systems. This study proposed a model for secured data storage over a decentralized cloud by blockchain Ethereum.

Mohit Bhasi Thazhath, Jan Michalak, Thang Hoang

The audit log is a crucial component to monitor fine-grained operations over sensitive data (e.g., personal, health) for security inspection and assurance. Since such data operations can be highly sensitive, it is vital to ensure that the audit log achieves not only validity and immutability, but also confidentiality against active threats to standard data regulations (e.g., HIPAA) compliance. Despite its critical needs, state-of-the-art privacy-preserving audit log schemes (e.g., Ghostor (NSDI '20), Calypso (VLDB '19)) do not fully obtain a high level of privacy, integrity, and immutability simultaneously, in which certain information (e.g., user identities) is still leaked in the log. In this paper, we propose Harpocrates, a new privacy-preserving and immutable audit log scheme. Harpocrates permits data store, share, and access operations to be recorded in the audit log without leaking sensitive information (e.g., data identifier, user identity), while permitting the validity of data operations to be publicly verifiable. Harpocrates makes use of blockchain techniques to achieve immutability and avoid a single point of failure, while cryptographic zero-knowledge proofs are harnessed for confidentiality and public verifiability. We analyze the security of our proposed technique and prove that it achieves non-malleability and indistinguishability. We fully implemented Harpocrates and evaluated its performance on a real blockchain system (i.e., Hyperledger Fabric) deployed on a commodity platform (i.e., Amazon EC2). Experimental results demonstrated that Harpocrates is highly scalable and achieves practical performance.

Yongbo Jiang, Gongxue Sun, Tao Feng

With the increasing value of various kinds of data in the era of big data, the demand of different subjects for data transactions has become more and more urgent. In this paper, a blockchain-based data transaction protection scheme is proposed to realize the secure transaction sharing among data. This paper carries out the following work: by analyzing the existing data transaction models, we find the data security and transaction protection problems, establish a third-party-free data transaction platform using blockchain, protect users’ data security by combining AES and improved homomorphic encryption technology, and upload the encrypted data to the Interplanetary File System (IPFS) for distributed storage. Finally, we use the powerful functions of the IPFS, combined with inadvertent transmission protocol, two-way authentication, zero-knowledge proof, and other security verification for data transactions. The security analysis proves that this scheme has higher security despite the time overhead, and we will continue to optimize the scheme to improve efficiency in the future.

Vittorio Capocasale, Danilo Gotta, Guido Perboli

Blockchain is a technology that creates trust among non-trusting parties without relying on any intermediaries. Consequently, it has attracted the interest of companies operating in a multitude of sectors. However, due to the number of different blockchain solutions that have emerged in the last few years and their rapid changes, it is challenging for such companies to orient their technological decisions. This paper presents a comparative analysis of the key dimensions—namely, governance, maturity, support, latency, privacy, interoperability, flexibility, efficiency, resiliency, and scalability—of some of the most-used permissioned blockchain platforms. Moreover, we present the results of a performance evaluation considering the following frameworks: Hyperledger Fabric 2.2, Hyperledger Sawtooth 1.2, and ConsenSys Quorum 21.1 (with both the GoQuorum client and the Hyperledger Besu client). The platforms were tested under similar conditions, and official releases were used, such that our findings provide a reference for companies establishing their technological orientation.

Wen-Xin Yuan, Bin Yan, Wen Li, Liu-Yao Hao · 5 authors

No abstract is available for this record.

Maha Helal, Anas Ratib Alsoud, Hazzaa Alshareef

Abstract Blockchain technology is meant to perform a potential act to intensify the performance of several information systems. In this view, the platforms and the applications adapted for blockchain must be competitive to communicate and connect. The current blockchain platforms have many limitations, such as interoperability issues in divergent systems. The present platforms of blockchain applications work only within their networks. Blockchain interoperability allows data and values to be sent across various networks. The fundamental technology may be homogeneous, still, it relies on third-party intermediaries using the centralized mechanism to retrieve or exchange data from various interacting blockchain networks. The existing intermediaries incorporate security and trust by maintaining a centralized ledger to monitor ‘account balances’ and verify a transaction’s authenticity. The incompetence of individual and independent blockchains to interact with each other is an ingrained issue in decentralized systems. Cross-Chain Interoperability Protocol (CCIP) and similar mechanisms support networks like Fabric, Ripple and Ethereum to interrelate and interoperate each other. It is identified that the shortfall in such significant inter-blockchain communication creates a hassle for the mainstream adoption of blockchain. The article discusses different techniques and methods that provide cross-chain interoperability, its significant features and its applications in blockchain technology. It proposes the Inter-operable Blockchain Framework Design (IBFD), a cross blockchain architecture for interoperability of blockchain networks.

Tim Güneysu, Philip Hodges, Georg Land, Mike Ounsworth · 6 authors

Certificate authorities in public key infrastructures typically require entities to prove possession of the secret key corresponding to the public key they want certified. While this is straightforward for digital signature schemes, the most efficient solution for public key encryption and key encapsulation mechanisms (KEMs) requires an interactive challenge-response protocol, requiring a departure from current issuance processes. In this work we investigate how to non-interactively prove possession of a KEM secret key, specifically for lattice-based KEMs, motivated by the recently proposed KEMTLS protocol which replaces signature-based authentication in TLS 1.3 with KEM-based authentication. Although there are various zero-knowledge (ZK) techniques that can be used to prove possession of a lattice key, they yield large proofs or are inefficient to generate. We propose a technique called verifiable generation, in which a proof of possession is generated at the same time as the key itself is generated. Our technique is inspired by the Picnic signature scheme and uses the multi-party-computation-in-the-head (MPCitH) paradigm; this similarity to a signature scheme allows us to bind attribute data to the proof of possession, as required by certificate issuance protocols. We show how to instantiate this approach for two lattice-based KEMs in Round 3 of the NIST post-quantum cryptography standardization project, Kyber and FrodoKEM, and achieve reasonable proof sizes and performance. Our proofs of possession are faster and an order of magnitude smaller than the previous best MPCitH technique for knowledge of a lattice key, and in size-optimized cases can be comparable to even state-of-the-art direct lattice-based ZK proofs for Kyber. Our approach relies on a new result showing the uniqueness of Kyber and FrodoKEM secret keys, even if the requirement that all secret key components are small is partially relaxed, which may be of independent interest for improving efficiency of zero-knowledge proofs for other lattice-based statements.