Multi-sensor network tracking research utilizing searchable encryption algorithm in the cloud computing environment

Lightweight searchable encryption in edge computing

The Scheme implementation flow chart (Fig. 2) shows that each sensor conducts information detection in the multi-target detection environment and transmits target-related information to the cloud server for multi-level closed-loop information tracking. This scheme mainly targets two scenarios. The first one is to re-encrypt the initial public key encryption with keyword search (PEKS) ciphertext generated by the multi-sensor using the public-key searchable encryption technology for the number captured by the sensor. Finally, the generated PEKS ciphertext is stored in the cloud centre. The second scenario begins if a user or organisation wants access to the cloud centre’s valuable sensor storage data. The side server generates the PEKS search trap for the required data file. After receiving the trap, the cloud centre searches for the corresponding ciphertext and returns it to the user. The solution must meet this case’s data privacy and availability requirements. Therefore, this article designs the searchable encryption algorithm under the participants and process shown in Fig. 2 to realise the sharing of cloud data.

Initialization and key generation

To solve some technical defects of searchable encryption in the existing traditional cloud computing environment, such as the high time cost when only using terminal devices to generate PEKS ciphertext or trapdoors for search, it is difficult to ensure security when only using edge devices to generate PEKS ciphertext or trapdoors for search. The scheme research in this chapter will use edge servers for the auxiliary calculation to help terminal devices generate PEKS ciphertext and search trapdoors, improve the efficiency of ciphertext generation and retrieval without losing security, and reduce the energy consumption of terminal devices.

System Initialization Setup(1^k): Input the safety parameters given by the system k, generate public parameters $pp=\left(G,G_T,e\right)$, the algorithm is executed by KGC. Select generator g₀, g₁ ∈ G, 2D vector $x,y{\in }_R{Z}_p^2$ and hash functions $H_1:\left\{0,1\right\}\ast {\to }_R{Z}_p^{\ast }$; Then for each $at{t}_i\in U\left(i\in \left[1,n\right]\right)$ attribute, randomly selects a non-zero value $t_i{\in }_R{Z}_p^{\ast }$, Calculate $A_i=g_0^{t_i},B=g_0^x,Y=e{\left(g_0,g_1\right)}^v$; Finally, the KGC returns the public parameters and master key. ${\displaystyle PP=\left(pp,g_0,g_1,B,Y,H_1,A_i\right)}$ (1)${\displaystyle MSK=\left(x,y,t_i\right)}$ Key generation $\text{KeyGen}\left(PP,MSK,S\right)$: When an edge node joins the system, the KGC first select EN as the intermediary, then select $s{\in }_R{Z}_p^{\ast }$. To generate a public key $P{K}_{{}_{EN}}^{\ast }=P{K}_{{}_{EN}}^{-s}=e{\left(g_0,g_1\right)}^{-syr}$ and authorized user list (UL) to establish public key relationship $P{K}_{{}_{EN}}^{\ast }$ with shared data. When each DU of UL is added to the system.

The KGC first select for $a_j,b_j{\in }_R{Z}_p^2$, $at{t}_j^{\ast }\in S$ and $v,z{\in }_R{Z}_p^{\ast }$, and then it calculates $K_{j,1}=g_0^{b_j/t_{p1}\left(j\right)}$, $K_{j,2}=g_0^{\left(a_j-b_j\right)/t_{p1}\left(j\right)}$, $K_{j,3}=g_0^{xv/t_{p1}\left(j\right)}$, $K_0=g_0^{y+xv}$, $K_1=g_0^{to}{g}_1^2$, $K_2=g_1^2$, $K_3=g_0^{y-a}$, finally, the KGC will return $S{K}_{DU}=\left(K_0,u,K_{j,1}\right)$, SK_EN = {K₁, K₂, K₃, r, {K_j,2, K_j,3}} to DU and EN respectively.

Specific implementation

DO send Γ to an EN, and output the file symmetric key CT_τ through cooperation with the selected EN.

After obtaining Γ, for each node w in the tree T, select one of the specified EN d_w Degree polynomial q_w. set up $\mathrm{L}=\left\{l\right\}$ as the set of leaf nodes in T. Then EN calculates $C_1=g_0^{\theta },C_2=g_1^{\theta },C_l=g_0^{t_l{q}_l\left(0\right)}$. Finally, EN returns the CT_τ to DO, as shown in Formular Eq. (2): (2)${\displaystyle C{T}_{\tau }=\left(C_1,C_2,{C_l}_{l\in \mathrm{L}}\right)}$

Then DO select $h{\in }_R{Z}_p^{\ast }$, calculate $C{T}_{\tau }=C_1{g}_0^h$, $C_2^{{}^{\prime }}=C_2{g}_1^h$. Finally, DO sends the CT_τ and $C{T}_{\tau }^{\ast }$ return to CS through the selected EN, where $C{T}_{\tau }^{\ast }\left(CC{T}_{\tau },C^{{}^{\prime }},C_1,C_2,{\left\{C_l\right\}}_{l\in \mathrm{L}}\right)$.

Using DO to generate files uploaded by each sensor F_τ index of each attribute selected in $d_l{\in }_R{Z}_p^{\ast }$, calculate $l_0=Y^s,l_1=g_0^s,I_1=g_0^s,I_{l,1}=A_l^{d_1{H}_1\left(W\right)}$, W represents the subsequent data retrieval is realized through keywords F_τ. Finally, DO will use the above EN to set the final index set $I=\left\{I_{\tau }\right\}$ and tuples $\left(\left\{c_{\tau }\right\},C_{\tau }^{\ast }\right)$ to send to CS, where represented as I_τ = (I₀I₁(I_τ,1I_τ,2l∈L)).

For each attribute $at{t}_j^{\ast }\in S$, DU outputs $T_{j,1}^l=T_{j,1}^{\lambda /H_1\left(w^{{}^{\prime }}\right)}$, $T_{j,2}^l=K_{j,1}^{\lambda /H_1\left(w^{{}^{\prime }}\right)}$. Finally, the DU will return $T_{w^{{}^{\prime }},2}=\left(T_0,T_1^{{}^{\prime }},T_{j,1}^{{}^{\prime }},T_{j,2}\right)$to the selected EN. When receiving T_w′,2, EN calculates $T_0^{{}^{\prime }}=T_0\eta +r,T_{j,2}^{{}^{\prime }}=T_{j,2}^{\eta }$ for each attribute in S, and calculates $T_{DU}^{\ast }={\left(P{K}_{DU}^{\ast }\right)}^{\eta }$. Finally, EN will finally trap the door $T_{w^{{}^{\prime }}}=\left(T_0^{{}^{\prime }},T_1^{{}^{\prime }},T_{DU}^{{}^{\prime }}{T}_{j,1}^{{}^{\prime }},T_{j,2}^{{}^{\prime }}\right)$ and attribute S of DU are sent to CS.

Search function $Search\left(\left\{c_{\tau }\right\},C{T}_{\tau }^{\ast },I,S,T_{w^{\prime }},\Gamma \right)$: After obtaining trapdoors, CS first checks whether the data user has access rights according to the attributes of the DU and the established access structure to achieve secure access to data. When it has access rights, CS calculates $I_l^{\ast }=I_{l,1}\cdot A_l^{I_{l,2}}=A_l^{s/H\left(w\right)}$ and $e\left(I_l^{\ast },T_{j,1}^{{}^{\prime }}\right),e\left(I_l^{\ast },T_{j,2}^{{}^{\prime }}\right)$ for $at{t}_j^{\ast }\in S$. Then, CS checks legality of the trap door submitted T_w′, The corresponding search results containing the file ciphertext $\left(c_{\pi }^{{}^{\prime }}\right)$ and file key ciphertext $C{T}_{\pi }^{{}^{\prime }}$ are returned to EN.

Decryption function $Dec\left(c_{\pi }^{{}^{\prime }},C{T}_{\pi }^{{}^{\prime }},S{K}_{EN},S{K}_{DU},PP,T,\Gamma \right)$: To decrypt $c_{\pi }^{{}^{\prime }}$, the following recursive algorithm is adopted to obtain the embedded File key $C{T}_{\pi }^{{}^{\prime }}$ in $k_{\pi }^{{}^{\prime }}$. The specific decryption process involving EN and DU is as follows: First, EN calls the recursive algorithm by considering these two situations.

(1) When leaf node w satisfy $att\left(w\right)\in S$, EN calculates $att\left(w\right)\in S{\varphi }_w=e\left(K_{att\left(w\right),3},C_w\right)=e{\left(g_0,g_0\right)}^{xv{q}_w\left(0\right)}$;

(2) If the node w is a non leaf node, and EN is the node first calculate φ_w′ for Each child node of w, that is w′, EN calculate ${\phi }_w={\prod }_{w^{\prime }\in \varphi }{\phi }_{w^{\prime },S_w^{{}^{\prime }}\left(0\right)}=e{\left(g_0,g_1\right)}^{xv{q}_w\left(0\right)}$, where i = index(w′) = {index(w′) ∈ S_w}.

(3) If S matches the access structure Γ, EN obtained φ_v = e(g₀, g₁)^xvθ. After that, EN calculates M = e(g₀, g₀)^xv(θ+h) and $M^{\ast }=M/{\phi }_v=e{\left(g_0,g_0\right)}^{xvh}$, and then return $\left(c_{\pi }^{{}^{\prime }},C{C}_{\pi }^{{}^{\prime }},C^{{}^{\prime }},M^{\ast }\right)$to DU. Finally, DU calculates each file key decrypt ciphertext $k_{\pi }^{{}^{\prime }}$before each file satisfy $c_{\pi }^{{}^{\prime }}=E_{k_{\pi }^{{}^{\prime }}}\left(F_{\pi }^{{}^{\prime }}\right)$, where $C{C}_{\pi }^{{}^{\prime }}=C{C}_{p2\left(\pi \right)}$. (3)${\displaystyle k_{\pi }^{{}^{\prime }}=\frac{C{C}_{\pi }^{{}^{\prime }}{M}_{\ast }}{e\left(K_0,C^{{}^{\prime }}\right)}=\frac{k_{\pi }^{{}^{\prime }}\cdot e{\left(g_0,g_0\right)}^{yh}e{\left(g_0,g_0\right)}^{xvh}}{e\left(g_0^{y+xv},g_0^h\right)}}$

Efficiency analysis of each stage

The stored data generated after the execution of the two algorithms is shown in Table 2. It can be seen from Table 2 that the space occupied by the public parameters generated in this scheme is 50 times smaller than the space occupied by the algorithm in Yang et al. (2019). The space occupied by the encrypted index and PEKS ciphertext is also half of the space occupied by the algorithm in Yang et al. (2019). Because sensors and data users need to encrypt data transmission and ciphertext retrieval, the private key cost is relatively large. Still, the private key only needs to be saved and does not need secondary transmission on the communication channel. Therefore, compared with the algorithm in Yang et al. (2019), the space cost of this scheme is much lower. The simulation experiment in Table 3 takes 500 data as an example and compares the computational overhead obtained from the experiment with the encrypted index, generated PEKS ciphertext, and keyword search as variables. The overhead at each stage has been reduced, realising a dual reduction in space and computational overhead.

Comparative analysis of simulation experiments

Select multiple groups of data to perform the encryption index generation experiment on this scheme and the schemes in Lu et al. (2021), Zheng, Xu & Ateniese (2015) and Yang et al. (2019), and the results are obtained in Fig. 3. The algorithm for generating an encrypted index in the algorithm in Yang et al. (2019) is proportional to the polynomial degree, the number of keys. The number of keywords selected in the experiment in Fig. 3 is 100. The data in Fig. 3 shows that the encryption index generation in this scheme is faster than in the other three schemes.

Then, this article selects 250, 500 and 1,000 keywords for ciphertext generation experiments and obtains the data in Fig. 4. Whether in this scheme or the other three schemes, the running time is linear with the number of keywords. However, in this scheme’s PEKS ciphertext generation process, the part with significant computation is placed on the edge server with greater computing power, so the speed is much faster.

This article selects multiple groups of data items to conduct experiments on this scheme’s search encryption data algorithm and the three methods and obtains the data in Fig. 5. Figure 5 shows that the time for searching data increases linearly with the number of encrypted indexes, and the time cost of the three schemes is much higher than that of this scheme. With the increased number of encrypted indexes, the time cost gap is also larger. This is because the three schemes require polynomial operation for keyword matching. In contrast, this scheme only requires one power operation, so the time cost is much lower, which can meet the data retrieval efficiency in multi-sensor networking tracking in the cloud computing background.