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Data processing scheme based on blockchain
EURASIP Journal on Wireless Communications and Networking volume 2020, Article number: 239 (2020)
Abstract
In the white paper written on Bitcoin, a chain of blocks was proposed by Satoshi Nakamoto. Since then, blockchain has been rapidly developed. Blockchain is not only limited to the field of cryptocurrency but also has been extensively applied to the Internet of Things, supply chain finance, electronic evidence storage, data sharing, and egovernment fields. Both the public chain and the alliance chain have been extensively developed. In the data processing field, blockchain has a particularly good application potential. The Square Kilometre Array (SKA) is a proposal consisting of a joint venture of more than ten countries, resulting in the world’s largest synthetic aperture radio telescope. In the SKA, the processing scale of the data is large, and it consists of several data processing nodes. The data will be processed in the cloud computing mode. Taking the SKA under consideration, this report proposes a data processing scheme based on blockchain for the anticounterfeiting, antitampering and traceability of data. Furthermore, the authenticity and integrity of the data are assured. The primary aspects include data distribution, data operation and data sharing, which correspond to the data reception, data algorithm processing and result sharing of data operation in the SKA. With this process, the integrity, reliability and authenticity of the data are guaranteed. Additionally, smart contracts, homomorphic hashing, secure containers, aggregate signatures and oneway encrypted channels are implemented to ensure the intelligence, security and high performance of the process.
Introduction
Blockchain is a distributed ledger technology [1]. Initially, blockchain was used primarily in the field of cryptocurrency, with Bitcoin being the most common. Litecoin [2], Monroe [3] and Zcash [4] are accepted as well. With the introduction of Ethereum in 2013, the applications of blockchain have expanded, in which the combination of smart contracts and blockchains plays an important role. However, the target of Ethereum is primarily the public blockchain. Due to the low transaction rate of Ethereum and insufficient privacy protection, successful application cases currently include issuing TOKEN and simple games, such as CryptoKitties. In Bitcoin, only seven transactions per second can be handled. Although the performance of Ethereum is better than that of Bitcoin, it can only handle 15–20 transactions per second; thus, it is unable to meet practical demand. Additionally, certain practical applications have higher requirements for privacy protection, which Ethereum cannot currently meet. In 2015, the Hyperledger project was launched, in which the IBMbacked Fabric framework was the most recognized. Fabric is aimed at the alliance blockchain, which essentially meets the needs of practical applications in terms of performance, privacy protection and usability.
With the development of the public and alliance chains, the blockchain application field has rapidly developed. Blockchain has been extensively applied to the Internet of Things [5], supply chain finance, digital data storage certificate, data processing and egovernment [6] fields. In the field of data processing, blockchain guarantees the authenticity, security and reliability of data [7]. Various studies have introduced the use of blockchain for medical data sharing [8], personal data protection [9] and data distribution [10].
Astronomical data have certain characteristics, such as large amounts of data, realtime requirements [11], complicated calculation processes [12], heterogeneous calculation nodes [13], diverse storage models, various data access patterns [14], high expansibility, etc. Highperformance computing, distributed computing, parallel computing, uniform resource management, container technology and telescope observation control system technology are needed [15]. Currentrelated technologies, such as Apache Hadoop, OpenMP, MPI, etc., all face various problems in processing astronomical data [16]. In the SKA data process, it is necessary to use cloud computing [17]. In distributed data processing, attention should be given to data protection [18]. Therefore, the security of the datadistributed storage [19] and the integrity of the data [20] are particularly important. During data processing, there are extremely high requirements for the synchronization of time [21] and the optimization of algorithm in data merging [22]. Blockchain can play a positive role in ensuring the integrity, security and availability of the data.
In the remainder of this report, Sect. 2 primarily introduces the data distribution scheme based on blockchain, which reflects the generation and collection of data in the SKA. Section 3 introduces the method of data operation, which reflects the combination of collected data and related algorithms. Section 3.3 introduces the process of sharing data, which reflects the sharing problem of the result after the original data is processed by the related algorithms. Section 4 summarizes the conclusions of this report.
Preliminaries
In this section, we first define certain notations used in this report. If S is a set, then S denotes the number of elements in this set. If b is a real number, then \(a \leftarrow b\) indicates that a = b. If C is a node and c is an element, then \(C \Leftarrow c\) denotes sending c to C. If a and b are two real numbers, then \(ab\) indicates the cascading of a and b.
Bilinear mapping
\({\mathbb{G}}_{1}\) and \({\mathbb{G}}_{2}\) are two multiplicative cyclic groups of prime order p, where g_{1} is a generator of \({\mathbb{G}}_{1}\) and g_{2} is a generator of \({\mathbb{G}}_{2}\). ψ is a computable isomorphism from \({\mathbb{G}}_{2}\) to \({\mathbb{G}}_{1}\), with ψ(g_{2}) = g_{1}. A bilinear pairing can be defined as \({\mathcal{G}} = (n,{\mathbb{G}}_{1} ,{\mathbb{G}}_{2} ,{\mathbb{G}}_{T} ,e,g_{1} ,g_{2} )\) where \({\mathbb{G}}_{1} = \left\langle {g_{1} } \right\rangle ,\;{\mathbb{G}}_{2} = \left\langle {g_{2} } \right\rangle\) and \({\mathbb{G}}_{T}\) are multiplicative groups of order n. Let \(e:{\mathbb{G}}_{1} \times {\mathbb{G}}_{2} \to {\mathbb{G}}_{T}\) be defined as a map with the following properties:

Bilinear: \(\forall u \in {\mathbb{G}}_{1} ,v \in {\mathbb{G}}_{2}\) and \(a,b \in {\mathbb{Z}}_{n} :e\left( {u^{a} ,v^{b} } \right) = e\left( {u,v} \right)^{ab}\).

Nondegenerate: There exists u ∈ \({\mathbb{G}}_{1}\), v ∈ \({\mathbb{G}}_{2}\) such that \(e(u,v) \ne {\mathcal{O}}\), where \({\mathcal{O}}\) denotes the identity of \({\mathbb{G}}_{T}\).

Computability: There is an efficient algorithm to compute e(u,v) for all u ∈ \({\mathbb{G}}_{1}\), v ∈ \({\mathbb{G}}_{2}\).
Then, e is considered bilinear mapping.
Aggregate signature
An aggregate signature is a variant signature scheme used to aggregate any number of signatures into one signature. For example, suppose there are n users in the system {u_{1},u_{2},…,u_{n}}, n public keys {pk_{1}, pk_{2},…,pk_{n}}, n messages {m_{1}, m_{2},…,m_{n}} and n signatures {σ_{1}, σ_{2},…,σ_{n}} for these messages. The generator of the aggregate signature (here the generator can be arbitrary and does not need to be in {u_{1},u_{2},…,u_{n}}) can aggregate {σ_{1}, σ_{2},…, σ_{n}} to a short signature σ. Importantly, the aggregate signature is verifiable, i.e., given a set of public keys {pk_{1}, pk_{2},…,pk_{n}} and its signatures of the original message set {m_{1},m_{2},…,m_{n}}, it can be verified that the user u_{i} has created a signature of message m_{i}. The execution of the aggregate signature is described in detail below.
AS = (Gen, Sign, Verify, AggS, AggV) is a quintuple of the polynomial time algorithm, and the details can be noted as follows:
DS = (Gen, Sign, Verify) is a common signature scheme, which is also known as the benchmark for the aggregate signature.
Aggregation signatures generation (AggS). Based on Gen and Sign, the common signature function and the aggregation of {m_{1}, m_{2},…, m_{n}}, {u_{1}, u_{2},…, u_{n}} and {σ_{1}, σ_{2},…, σ_{n}} can be realized, thus aggregating a new signature σ_{n}.
Aggregation signature verification (AggV) Suppose that each u_{i} corresponds to a public–private key pair {pk_{i}, sk_{i}}. If AggV(pk_{1},…,pk_{n}, m_{1},…,m_{n}, AggS(pk_{1},…, pk_{n}, m_{1},…,m_{n}, Sign(sk_{1},m_{1}),…,Sign(sk_{n},m_{n}))) = 1, then the output is 1; otherwise, the output is 0.
Furthermore, the aggregate signature can support incremental aggregation; thus, if σ_{1} and σ_{2} can be aggregated to σ_{12}, then σ_{12} and σ_{3} can be aggregated to σ_{123}.
Homomorphic hash
Homomorphism is the mapping of two algebraic structures in abstract algebra that remain structurally constant. There are two groups, \({\mathbb{G}}_{1}\) and \({\mathbb{G}}_{2}\), and f is the mapping from \({\mathbb{G}}_{2}\) to \({\mathbb{G}}_{1}\). If \(\forall a,b \in {\mathbb{G}}_{1}\), \(f(ab) = f(a)f(b)\), then f is called a homomorphism from \({\mathbb{G}}_{2}\) to \({\mathbb{G}}_{1}\).
The homomorphic hash has long been used in peertopeer networks [23], which use correction and network codes together against attack events. In a peertopeer network, each peer will obtain the original data block directly from the other peers; thus, hash functions such as SHA1 can be used to directly verify the correctness of the received data block by comparing the hash value of the received data block with the original hash value.
Using the homomorphic hash function mentioned in earlier studies [24], i.e., \(h_{{\mathbb{G}}} \left( \cdot \right)\), a set of hash parameters can be obtained as \(h_{{\mathbb{G}}} \left( \cdot \right)\), \({\mathbb{G}} = \left( {p,q,g} \right)\). The parameter description is shown in Table 1. Each of these elements in g can be represented as \(x^{{\left( {p  1} \right)/q}} \bmod p\), where \(x \in {\mathbb{Z}}_{p}\) and \(x \ne 1\).
where \(rand\left( \cdot \right)\) is a pseudorandom function, which can be used as a pseudorandom number generator to initialize the homomorphism hash function parameters in the generating process, generate random numbers in the tag generate process, and determine the random data block in the challenge process, thus creating challenges that can cover the entire data range.
For a block b_{i}, the hash value can be calculated as follows:
The hash values of the original block \(\left( {b_{1} ,b_{2} , \ldots ,b_{n} } \right)\) are \(h\left( {b_{1} } \right),h\left( {b_{2} } \right), \ldots ,h\left( {b_{n} } \right)\).
Given a coding block e_{j} and a coefficient vector \((c_{j,1} ,c_{j,2} , \ldots ,c_{j,n} )\), the homomorphic hash function \(h_{{\mathbb{G}}} \left( \cdot \right)\) can satisfy the equation as follows:
This feature can be used to verify the integrity of a code block. First, the publisher needs to calculate the homomorphic hash values of each data block in advance. The download downloads these homomorphic hash values. Once the verification block is received, its hash value can be calculated using Eq. (3). Then, Eq. (4) can be used to verify the correctness of the verification block [25].
Results and discussion
Blockchainbased data distribution scheme
Here, we simplify the process of receiving astronomical data in the SKA. The SOURCE represents the original astronomical data, and the Data Receiving Station (DRS) represents the real astronomical data receiving device. The DRS setting is distributed. Different DRSs are responsible for receiving data within their own respective areas. Considering the limitation of the hardware functions, the DRS is only responsible for data reception, temporary storage and data forwarding; it does not participate in data calculation. All data calculation is completed by the Data Processing Node (DPN), which is connected to the blockchain. The concrete architecture is shown in Fig. 1.
The method of processing data from the SOURCE to the DRS is relatively simple. It involves processing the data format and setting the storage mode, which is not the focus of this study. Here, the execution process of the DRS to the DPN is introduced.
Furthermore, we use the idea of distributed storage in an IPFS, as shown in Fig. 2.
Each block contains a list of trading objects, a link to the previous block, and a hash value for the state tree/database.
Additionally, we introduce the method used to import data into a blockchain. Let q be a large prime number. Then, select \(P \in {\mathbb{G}}_{1} ,Q \in {\mathbb{G}}_{2}\) to define an additive group \({\mathbb{G}}_{1}\) and a multiplicative group \({\mathbb{G}}_{2}\) with order q. Thus, a bilinear mapping \(e:{\mathbb{G}}_{1} \times {\mathbb{G}}_{2} \to {\mathbb{G}}_{T}\) and hash functions \(H:\left\{ {0,1} \right\}^{*} \to \left\{ {0,1} \right\}^{*}\), \(H_{0} :\left\{ {0,1} \right\}^{ * } \to {\mathbb{Z}}_{q}^{ * }\), \(H_{1} :\left\{ {0,1} \right\}^{ * } \times {\mathbb{G}}_{1} \to {\mathbb{G}}_{{2}}\), \(H_{2} :\left\{ {0,1} \right\}^{ * } \to {\mathbb{G}}_{1}\), \(H_{DV} :\left\{ {0,1} \right\}^{ * } \to {\mathbb{G}}_{1}\) can be obtained. The number of data receiving stations is m, the number of data processing nodes responsible for the ith data receiving station is \(m_{i}\), and the current view is v.

1
Using the current view, calculate \(P_{v} = v \cdot P\). Combined with the existing parameters, the system parameters can be obtained as follows: \(Params = \left\{ {G_{1} ,G_{2} ,e,q,P,Q,P_{v} ,H_{0} ,H_{1} ,H_{2} ,H_{DV} } \right\}\).

2
The user \(u_{i}\) selects a random value \(x_{i} \in {\mathbb{Z}}_{q}^{ * }\) as its secret value and calculates \(P_{i} = x_{i} \cdot P\), \(Q_{i} = H_{1} \left( {ID_{i} P_{i} } \right)\), and \(D_{i} = v \cdot Q_{i}\) to generate the user's private key \(S_{i} = \left( {D_{i} ,x_{i} } \right)\).
It can be assumed that the public key of the \(jth\:(j = 1,2, \ldots m_{i} )\) Data Processing Node \(\left( {DPN_{i}^{j} } \right)\) of the \(ith\:(j = 1,2, \ldots m_{i} )\) Data Receiving Station \(\left( {DRS_{i} } \right)\) in the rth round is \(\left\{ {pk_{i}^{1} ,pk_{i}^{2} , \ldots ,pk_{i}^{{m_{i} }} } \right\}\). The data produced by the SOURCE is \(D_{i}^{r}\). Each DRS consensus for the resulting data can be reached using a static aggregate Practical Byzantine Fault Tolerance (PBFT) [26, 27]. The specific process is shown in Algorithm 1.
To verify the validity of the aggregate signature σ, Algorithm 1 can be implemented. Using the system parameter Params, user's corresponding identity list \(ID = \left\{ {ID_{1} , \ldots ,ID_{n} } \right\}\), public keys list \(P = \left\{ {P_{1} , \ldots ,P_{n} } \right\}\), messages list \(M = \left\{ {m_{1} , \ldots ,m_{n} } \right\}\), signature list \(\sigma = \left\{ {\sigma_{1} , \ldots ,\sigma_{n} } \right\}\), computer \(Q_{i} = H_{1} \left( {ID_{i} P_{i} } \right)\) and \(T = H_{2} \left( {P_{v} } \right)\), the equation can be verified as follows:
If the equation holds true, then the validation passes; otherwise, the validation fails.
The correctness of this basic framework is given below. Theorems 1 and 2 provide the correctness of the verification process of a single signature and the correctness of the verification process of an aggregate signature, respectively.
Theorem 1
The verification process of a single signature is correct.
Proof: The verification process of the signature \(\sigma_{i} = \left( {V_{i} ,R_{i} } \right)\) that \(DRS_{i}\) performs for \(D_{i}^{r}\) can be given as follows:
Theorem 2
The verification process of an aggregation signature is correct.
Proof:
Blockchainbased data operation scheme
The Science Data Processor (SDP) [28] is the SKA Data processing module. The main data are taken from the Central Signal Processor (CSP) module [29], the metadata are taken from the Telescope Manager (TM) module, and the Signal and Data Transport (SaDT) module is responsible for the data transmission. Multiple regional data processing centres will be built. The primary functions of the SDP can be given as follows:

Extract data from the CSP and TM modules

Treat source data as data products that can be used for scientific research

Archive and store data products

Provide access to data products

Control and feedback information to the TM module for a timely challenge observation
In the SKA SDP, the two most important computational tasks are FFT [30] and gridding [31]. These two algorithms account for an important part of the total computation, and their efficient implementation provides considerable assistance in the design of the SKA SDP.
As depicted in Fig. 3, in the data calculation scheme based on the blockchain, the Data Supply Node (DSN) and the Algorithm Supply Node (ASN) are separated, and all of the data and algorithms enter the Secure Container [32] through a oneway encrypted channel under the control of the Smart Contract (SM) to perform calculations. Providers and the provided time of the data and algorithms are recorded on the blockchain through the SM. It can be assumed that there are w Data Supply Nodes and one Algorithm Supply Node. Before entering the Secure Container, all of the data \(D_{i} \;(i = 1,2, \ldots ,w)\) and algorithms A are signed by the private key(sk_{i}) of the DSN_{i} and the private key(sk_{a}) of the ASN. Furthermore, the data and algorithms are first encrypted by the public key SC_{pk} of the Secure Container and then decrypted and verified after entering the Secure Container by the public key (pk_{i}) of the DSN_{i}, the public key(pk_{a}) of the ASN and the private key of the Secure Container. This specific process is shown in Algorithm 2 and Algorithm 3.
As described in Algorithm 2, each DSN signs the data with its own private key and then encrypts the data with the public key of the security container. The processed data are sent to the security container. Then, the subblock \(H\left( {D_{i} } \right)time_{i}\) is calculated. Then, the ASN signs the algorithm with its own private key and encrypts the data with the private key of the security container. The processed data are sent to the security container. The subblock \(H\left( A \right)time_{a}\) is then calculated. At last, the final block \(b_{1} b_{2}  \cdots b_{w} b_{a}\) is calculated.
As described in Algorithm 3, the security container verifies each \(D_{i}^{^{\prime}}\) with its private key and the public key of each DSN. The processed data are then sent to the security container. Next, the subblock \(H\left( {D_{i}^{^{\prime}} } \right)time_{i}\) is calculated. Then, \(A^{^{\prime}}\) is verified with its private key and the public key of the ASN. The processed data are sent to the security container. The subblock \(H\left( {A^{^{\prime}} } \right)time_{a}\) is calculated. At last, the final block \(b_{1}^{\prime } b_{2}^{\prime }  \cdots b_{w}^{\prime } b_{a}^{\prime }\) is calculated.
Blockchainbased data sharing scheme
The Data Requirement Nodes, which are represented by the public keys \(\left\{ {pk_{1} ,pk_{2} , \ldots ,pk_{r} } \right\}\) of the calculation result, are determined in advance through the smart contract. Under intrusive surveillance, the calculated result Re is shared to the nodes represented by these public keys. The shared results, targets and shared time are recorded on the blockchain through the smart contracts. The concrete architecture is shown in Fig. 4.
As shown in Fig. 4, the allocation of data is allocated by the data container to each data consumer. In order to ensure the security of data, data allocation adopts the way of single channel. The data allocation rules are determined by the smart contract of the system.
Before recording on the blockchain, it is necessary to verify the target, and the target verifies the calculated results. If the verification passes, then it is signed. If more than 2/3 of the target's signature is obtained, then the block formed will be recorded on the blockchain. The simple architecture is shown in Fig. 5.
It is assumed that there are r Data Requirement Nodes (DRNs). The calculated results Re are encrypted by the public key \(pk_{i}\) of \(DRN_{i} \;\left( {i = 1,2, \ldots ,r} \right)\) and signed by the private key \(SC_{sk}\) of the SC to obtain \({\text{Re}}_{i}\). The cascading of the hash value of \({\text{Re}}_{i}\) and the time forms the block \(b_{i}\). The homomorphic hash \(h\) is used by \(pk_{i}\). Then, \(b_{i} \;\left( {i = 1,2, \ldots ,r} \right)\) forms the final block b. At last, the homomorphic hash is verified. If the verification passes, then the calculation results \({\text{Re}}_{i}\) will be sent to the \(DRN_{i}\), which will be decrypted by the private key \(sk_{i}\) of the \(DRN_{i}\) and the public key \(SC_{pk}\) of the secure container. This specific process is shown in Algorithm 4.
As described in Algorithm 4, each calculated result is encrypted by the private key of the security container and the public key of each target to obtain \({\text{Re}}_{i}\). Then, cascading the hash value of \({\text{Re}}_{i}\) and the time forms the subblock \(b_{i}\). \(h_{i}\) is obtained by \(pk_{i}\) using the homomorphic hash \(h\). Then, \(b \leftarrow b_{1} b_{2}  \cdots b_{r}\) and \(h \leftarrow \prod\nolimits_{i = 1}^{r} {h\left( {pk_{i} } \right)}\) are computed.
Conclusion
This study discusses the data storage, data operation and data sharing methods for large amounts of data processing. Using the blockchain data structure combined with intelligent contracts, homomorphic hashes, secure containers, aggregate signatures and oneway encrypted channels, the authenticity, integrity and reliability of data for the collection, calculation and results sharing of astronomical data is ensured. Combined with the SKA project, this scheme can be applied to astronomical data processing. This method provides innovative ideas for the application of blockchain in the fields of large data volume, rapid data generation, high complexity data processing and high value data processing results.
Availability of data and materials
Not applicable.
Abbreviations
 IoT:

Internet of Things
 SKA:

Square Kilometre Array
 DRS:

Data Receiving Station
 DPN:

Data Processing Node
 PBFT:

Practical Byzantine Fault Tolerance
 SDP:

Science Data Processor
 CSP:

Central Signal Processor
 TM:

Telescope Manager
 SaDT:

Signal and Data Transport
 DSN:

Data Supply Node
 ASN:

Algorithm Supply Node
 SM:

Smart Contract
 DRNs:

Data Requirement Nodes
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Acknowledgements
We gratefully acknowledge the anonymous reviewers for taking the time to review our manuscript.
Funding
This research is supported by the Innovative Research Groups of the National Natural Science Foundation of China (Grant No. 61521003), Intergovernmental Special Programme of the National Key Research and Development Programme (2016YFE0100300, 2016YFE0100600), National Scientific Fund Programme for Young Scholar (61672470) and Science and Technology Project of Henan Province (182102210617, 202102210351).
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Fu, J., Xu, M., Huang, Y. et al. Data processing scheme based on blockchain. J Wireless Com Network 2020, 239 (2020). https://doi.org/10.1186/s13638020018556
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 Keywords
 Blockchain
 Data sharing
 SKA
 Cloud computing
 Privacy protection