NonInteractive and Secure Data Aggregation Scheme for Internet of Things
Abstract
:1. Introduction
 We design a noninteractive and secure data aggregation scheme that has low communication overheads, which is robust to the exiting users and supports mobile users offline. This scheme uses additive secret sharing to share the original data in two parts, and then masks two shared values with a random number. Finally, the ciphertext is sent to two noncolluding cloud servers separately. Compared with the previous aggregation ones, our scheme reduces the computation and communication costs of users.
 In most of the previous schemes, the server can obtain the final aggregation results, and it is possible for the cloud to misuse the aggregation results for malicious analysis and speculation. However, in our scheme, the two cloud servers perform data aggregation with the ciphertext of the aggregation result, and therefore the true aggregation result is wellprotected from the servers.
 This paper designs a set of algorithms so that the final aggregation result can be efficiently verified. Anyone can check the correctness of the aggregation results with a probability of 1, and it is impossible for an incorrect aggregation result to be successfully verified.
2. Related Work
3. Preliminaries
3.1. Secure MultiParty Computation
3.2. Additive Secret Sharing
3.3. PseudoRandom Generator
3.4. Bilinear Map
 Bilinearity: For any $a,b\in {Z}_{p}^{\ast}$ and $g\in {G}_{1},h\in {G}_{2},$ we have $e({g}^{a},{h}^{b})=e{(g,h)}^{ab}$.
 Computability: There is an efficient algorithm to compute $e(g,h)$ for $g\in {G}_{1},h\in {G}_{2}$.
 Nondegeneracy: There exists $g\in {G}_{1},h\in {G}_{2}$, such that $e(g,h)\ne 1$.
3.5. Verifiable Computation
 KeyGen $(f,\lambda )\to (pk,sk)$: The inputs to the key generation algorithm are the secure parameter $\lambda $ and function f, and then the outputs are $pk$ and $sk$.
 ProbGen $(sk,x)\to ({\sigma}_{x},{\tau}_{x})$: The inputs to the problem generation algorithm are $sk$ and x, and the outputs are ${\sigma}_{x},{\tau}_{x}$, where ${\sigma}_{x}$ is a public value and ${\tau}_{x}$ is a private value kept by the user.
 Compute $(pk,{\sigma}_{x})\to {\sigma}_{y}$: The algorithm takes $pk$ and ${\sigma}_{x}$ as inputs, and the cloud server computes the output value ${\sigma}_{y}$.
 Verify $(sk,{\tau}_{x},{\sigma}_{y})\to y\cup \perp $: The user uses $sk$ and ${\tau}_{x}$ to verify whether ${\sigma}_{y}$ is correct; if the verification passes, it will be accepted, otherwise, it will be rejected.
4. System Framework and NonInteractive and Secure Data Aggregation Scheme
4.1. System Framework
4.1.1. System Model
4.1.2. Threat Model
4.1.3. Design Goals
 Input privacy: The data collected by mobile users are sensitive data. These data should be masked before sending to the server; therefore, in this paper we should ensure that the data input is private.
 Output privacy: Since there are two noncolluding servers, they perform aggregation operations without obtaining the final aggregation result; therefore, in this paper we should ensure the output privacy.
 Verifiability: The verifier can utilize the verification algorithm to verify whether it is correct when all participants execute the protocol correctly.
 Noninteractivity: Our scheme guarantees noninteraction between users, which reduces the communication cost. Due to the noninteractivity between users, it will not affect the normal execution of the protocol even if someone drops out during the aggregation process.
 Efficiency: It is experimentally demonstrated that our aggregation scheme can obtain the aggregation result and verify its correctness with a low computation cost.
4.2. NonInteractive and Secure Data Aggregation Scheme
4.2.1. Key Generation
4.2.2. Masking of Private Data
Algorithm 1: NonInteractive and Secure Data Aggregation Scheme 

4.2.3. Data Aggregation
4.2.4. Verification of the Results
5. Analysis
5.1. Input and Output Privacy
5.2. Verification Algorithm Security
5.3. Robustness Analysis
5.4. Limitations
6. Performance Evaluation
6.1. Function Analysis
6.2. Experimental Results
7. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Symbols  Definition 

U  Mobile user dataset 
$<{x}_{i}{>}_{A},<{x}_{i}{>}_{B}$  The shares of ${x}_{i}$ 
${a}_{i}$  Random vector of the mask selected by user 
$<{c}_{i}{>}_{A}$, $<{c}_{i}{>}_{B}$  The ciphertexts of shared value $<{x}_{i}>$ 
m  Dimension of the private vector 
h  Verification vectors 
$PK$  The public key for verification 
$V{K}_{i}$  Authentication key for verification 
$sum$  Aggregation result 
$\sigma $  The proof of computation 
Schemes  Data Privacy  NonInteractity  Verification  Roustness  Result Privacy 

[12]  Yes  No  No  Yes  No 
[13]  Yes  No  Yes  Yes  No 
[16]  Yes  No  Yes  Yes  Yes 
[20]  Yes  No  Yes  No  No 
ours  Yes  Yes  Yes  Yes  Yes 
Computational Cost Comparison  Communication Cost Comparison  

Schemes  User  Server  Verifier  User–User Communication  User–Server Communication  User–Verifier Communication 
[12]  $O({n}^{2}+mn)$  $O\left(m{n}^{2}\right)$    $6(n1)m\leftp\right$  $7m\leftp\right$   
[13]  $O({n}^{2}+mn)$  $O\left(m{n}^{2}\right)$  $O\left(m\right)$  $6(n1)m\leftp\right$  $8m\leftp\right$   
[16]  $O(m+n)$  $O\left(mn\right)$  $O\left(mn\right)$  $m\leftp\right$  $3m\leftp\right$   
[20]  $O(m+n)$  $O\left(mn\right)$  $O\left(mn\right)$  $2(n1)m\leftp\right$  $2m\leftp\right$  $m\leftp\right$ 
ours  $O\left(m\right)$  $O\left(mn\right)$  $O\left(mn\right)$    $2m\leftp\right$  $m\leftp\right$ 
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Fu, Y.; Ren, Y.; Feng, G.; Zhang, X.; Qin, C. NonInteractive and Secure Data Aggregation Scheme for Internet of Things. Electronics 2021, 10, 2464. https://doi.org/10.3390/electronics10202464
Fu Y, Ren Y, Feng G, Zhang X, Qin C. NonInteractive and Secure Data Aggregation Scheme for Internet of Things. Electronics. 2021; 10(20):2464. https://doi.org/10.3390/electronics10202464
Chicago/Turabian StyleFu, Yanxia, Yanli Ren, Guorui Feng, Xinpeng Zhang, and Chuan Qin. 2021. "NonInteractive and Secure Data Aggregation Scheme for Internet of Things" Electronics 10, no. 20: 2464. https://doi.org/10.3390/electronics10202464