Robust Dynamic Searchable Symmetric Encryption with Collusion Resistant Feasible for Internet of Vehicles
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摘要: 随着车辆规模的持续扩大，车联网的应用日益广泛。车联网用户普遍将加密数据外包至云服务器，同时动态可搜索对称加密(Dynamic searchable symmetric encryption, DSSE)为解决加密数据动态更新与搜索提供了一种有效的手段。然而，传统的DSSE方案在实际应用中仍面临若干问题。一方面，DSSE无法同时支持多用户场景与搜索结果可验证。另一方面，DSSE还应实现前向与后向隐私从而保护敏感数据。此外，在设计方案时也需要考虑恶意用户与云服务器的合谋攻击风险与方案鲁棒性。因此，该文提出了适用于车联网的抗合谋攻击的鲁棒动态可搜索对称加密(Robust dynamic searchable symmetric encryption with collusion resistant feasible for Internet of Vehicles, RDSSE-CR)方案。该方案通过双位图索引与布尔电路，构建了同时满足前后向隐私与鲁棒性的DSSE框架。同时，该文采用基于身份的密钥封装机制以适用于可能存在恶意用户与不可信云服务器合谋的多用户场景，该机制显著降低数据拥有者端的存储开销。此外，云服务器返回搜索结果的同时须根据验证标签提供工作量证明，以实现搜索结果完整性和正确性的有效验证。安全性分析证明RDSSE-CR方案实现了自适应安全性。性能分析表明，与现有同类方案相比，本方案在存储开销方面具有显著优势，在实现更多功能的同时仍保持了较高的运行效率，因而更加适用于车联网应用场景。Abstract:
Objective With the continuous expansion of vehicle scale, the application of the Internet of Vehicles (IoV) is becoming increasingly widespread. Users commonly outsource encrypted data to cloud servers, and Dynamic Searchable Symmetric Encryption (DSSE) provides an effective solution for dynamically updating and searching encrypted data. However, traditional DSSE schemes still face several challenges in practical applications. On one hand, DSSE cannot simultaneously support multi-user scenarios and verifiable search results. Multi-user enhances the collaborative efficiency of the group and the verification of search results ensures the verifiability and reliability of the query results. On the other hand, DSSE must also achieve forward and backward privacy to protect sensitive data. Forward privacy ensures that the newly inserted vehicle data cannot be associated with historical query tokens. Backward privacy ensures that the deleted vehicle data will not be leaked in subsequent queries, and the cloud server cannot restore the removed data content using current or future query information. Furthermore, design considerations must account for the risk of collusive attacks by malicious users and cloud servers, as well as the robustness of the solution. Methods This scheme achieves forward privacy protection through a state chain mechanism generated by random numbers, ensuring that newly added data cannot be associated with historical query tokens. At the same time, the construction method based on bitmap indexing effectively guarantees backward privacy, preventing deleted data from revealing information in subsequent queries. Additionally, the scheme constructs a dual bitmap index structure consisting of keyword bitmap index and operation bitmap index, combined with Boolean circuit technology, and designs a DSSE framework that simultaneously meets the requirements of forward privacy, backward privacy, and robustness. This framework can maintain the stable operation of the system in the face of abnormal or unreasonable operation requests. On the other hand, this paper adopts the Identity-based Key Encapsulation Mechanism (ID-KEM) to be applicable to multi-user scenarios where corrupt users and untrusted cloud servers may collude. This mechanism enables data owners to avoid storing additional information for authorized users, thereby significantly reducing the storage overhead at the data owner's end. Moreover, the cloud server must provide proof of work based on the verification label when returning search results, to effectively verify the integrity and correctness of the search results. Results and Discussions This paper demonstrates the security of the RDSSE-CR scheme through a series of games between real game $ \text{REAL}_{\mathcal{A}}^{\prod }({1}^{\lambda }) $ and ideal game $ \mathrm{IDEAL}_{\mathcal{A}}^{\prod }({1}^{\lambda }) $. Firstly, by constructing games $ {G}_{0} $ to $ {G}_{7} $, the paper gradually eliminates the opponent's ability to distinguish, thereby under the assumptions of pseudo-random function security, hash function collusion resistant, and symmetric encryption security, it proves that the opponent's distinguishing advantage is negligible, and finally establishes that the scheme has $ \mathcal{L} $ - adaptive security. Secondly, since the search token is generated by a pseudo-random function bound to the user's identity, the tokens for the same keyword of different users are independent and uncorrelated, thus ensuring that even in the case of collusion attacks, it is impossible to derive the search tokens or privacy information of other authorized users. The experiment is divided into two parts: performance analysis and vehicle networking scenario simulation. The aim is to evaluate the efficiency of the scheme and its effectiveness in practical applications. In the performance test based on the Intel Core i7 environment, the RDSSE-CR scheme, compared with several existing schemes, has the lowest storage cost at the data owner's end and the user's end due to the fact that the data owner and the data user only need to maintain their own private keys ( Fig. 4 ). In terms of algorithm performance (Fig. 5 ), the RDSSE-CR scheme achieves the best verification efficiency by relying on efficient XOR operations, while maintaining a constant search token size. Although the update and search introduce a slight increase in cost due to the introduction of security mechanisms, it still has significant advantages in functionality and security. In the vehicle networking simulation based on SUMO and OMNeT++, this scheme successfully resisted attack interference, enabling the vehicle queue to maintain stable spacing and consistent speed when subjected to attacks (Fig. 6 ). This avoided the phenomenon of vehicle lag and queue collapse that occurred in the absence of the deployed scheme, fully demonstrating its practical application value in ensuring the safety and stability of vehicle networking in complex communication environments.Conclusions To meet the practical application requirements in the context of the Internet of Vehicles, this paper designs a verifiable multi-user dynamic searchable symmetric encryption that supports forward and backward privacy. In response to the security threat in a multi-user environment where untrusted cloud servers and corrupt users may collude, this scheme implements multi-user authorization based on the ID-KEM, effectively resisting collusion attacks. The proposed RDSSE-CR scheme ensures the robustness of the system when facing unreasonable operation requests by constructing a dual-bit map index structure and combining Boolean circuit design. During the search stage, the cloud server needs to generate a proof of work based on the verification label to allow users to verify the correctness and integrity of the search results. Future research will focus on the efficient revocation mechanism for violating users to further enhance the practicality and security of the scheme. -
表 1 具有鲁棒性的真值表
$ b{s}_{w}[i] $ $ (b{s}_{a}[i],b{s}_{b}[i]) $ (0,0) (0,1) (1,1) (1,0) 0 0 0 1 0 1 1 1 1 0 
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1 ID-KEM
$ \text{Setup}({1}^{\lambda }) $ 1: $ m\leftarrow Z_{p}^{\ast } $ 2: $ mpk\leftarrow {g}^{m} $ 3: $ par\leftarrow \{e,g,p,G,{G}_{1},N,h,H\} $ $ \text{KeyGen(}u,msk) $ 1: $ msk\leftarrow m $ 2: $ s{k}_{{{u}_{j}}}\leftarrow h{({{u}_{j}})}^{m} $ $ \text{Encap(}u,mpk) $ 1: $ n\leftarrow Z_{p}^{\ast } $ 2: $ {\mu }^{\prime}\leftarrow {g}^{n} $ 3: $ {\mu }_{j}\leftarrow ({\mu }^{\prime},j) $ 4: $ {r}_{j}\leftarrow H(e(h({u}_{j}),{({{g}^{m}})}^{n}),j) $ $ \text{Decap}(s{k}_{u},\mu ) $ 1: $ {r}_{j}\leftarrow H(e(h{({{u}_{j}})}^{m},{g}^{n}),j) $
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表 2 符号说明
符号 含义 $ par $ 系统公共参数 $ mpk $ 主公钥 $ msk $ 主私钥 $ s{k}_{{{u}_{j}}} $ 授权用户$ {u}_{j} $的密钥 $ {\mu }_{j} $ 封装密文 $ {r}_{j} $ 封装密钥 $ {K}_{w} $ 关键字状态密钥 $ {{{K}^{\prime}}}_{w} $ 计数器密钥 $ S{T}_{c} $ 关键字状态 $ U{T}_{c} $ 加密索引 $ (b{s}_{a},b{s}_{b}) $ 双位图索引 $ ({e}_{a},{e}_{b}) $ 加密双位图索引 $ {\mathrm{C}}_{S{{T}_{c}}} $ 加密状态 $ {m}_{j} $ 封装的内容 $ vt $ 工作量证明 $ token $ 搜索令牌 $ \Gamma $ 3.3节中的密钥封装方案 $ b{s}_{w} $ 聚合位图索引 $ {e}_{w} $ 加密聚合
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2 Setup
Input: $ \lambda ,{u}_{j} $ Output: $ k,\text{O,S,EDB},par,mpk,msk,s{k}_{{{u}_{j}}} $ DO: 1: $ k\leftarrow {\{0,1\}}^{\lambda } $ 2: $ \text{O,S,EDB}\leftarrow \mathrm{empty}\mathrm{map} $ 3: $ \text{Send (S,EDB) to CS} $ 4: $ \text{Store (}k,\text{O) in DO} $ PKG: 5: $ \mathrm{userList}\leftarrow \{{u}_{1},{u}_{2},\cdots,{u}_{m}\} $ 6: $ (par,msk,mpk)\leftarrow \Gamma .{\text{Setup(1}}^{\lambda }) $ 7: $ \text{for all}{u}_{j}\text{in}\mathrm{userList}\text{do} $ 8: $s{k}_{{{u}_{j}}}\leftarrow \Gamma .\mathrm{KeyGen}({u}_{j},msk) $ 9: end for 10: $\text{Send}s{k}_{{{u}_{j}}}\text{to DU}{u}_{j} $
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3 Update
Input: $ k,mpk,\text{userList},op,(w,ind),\mathrm{O} $ Output: $ {m}_{j},{\mu }_{j},({K}_{w},{{{K}^{\prime}}}_{w}),c,S{T}_{c},U{T}_{c},{C}_{S{{T}_{c}}},vt,({e}_{a},{e}_{b}) $ DO: 1: $ \mathrm{userList}\leftarrow \{{u}_{1},\cdots,{u}_{m}\} $ 2: $ \text{AccessList,CList}\leftarrow \mathrm{empty}\mathrm{map} $ 3: $ ({\mu }_{j},{r}_{j})\leftarrow \Gamma .\mathrm{Encap}({u}_{j},mpk) $ 4: $ \text{for all}w\text{in}W({u}_{j}\text{) do} $ 5: $ {K}_{w}||{{{K}^{\prime}}}_{w}\leftarrow F(k,w||{u}_{j}) $ 6: $ (S{T}_{c},c)\leftarrow \text{O}[w] $ 7: $ \text{if O}[w]=\bot \text{then} $ 8: $c\leftarrow -1,S{T}_{c}\leftarrow {\{0,1\}}^{\lambda } $ 9: $ \text{end if} $ 10: $ S{T}_{c}\leftarrow {\{0,1\}}^{\lambda },\text{where}c=c+1 $ 11: $ \text{O}[w]\leftarrow (S{T}_{c},c) $ 12: $ U{T}_{c}\leftarrow {H}_{1}({K}_{w},S{T}_{c}) $ 13: $ {\mathrm{C}}_{S{{T}_{c}}}\leftarrow {H}_{2}({K}_{w},S{T}_{c})\oplus S{T}_{c-1} $ 14: $ { Generate the bi-bitmap (}b{s}_{a},\mathrm{b}{s}_{b}) $ based on 2.1
technology15: $ {e}_{a}\leftarrow {H}_{3}({{{K}^{\prime}}}_{w},c)\oplus b{s}_{a} $ 16: $ {e}_{b}\leftarrow {H}_{4}({{{K}^{\prime}}}_{w},c)\oplus b{s}_{b} $ 17: $ vt\leftarrow {F}_{1}(w,c-1)\oplus {F}_{1}(w,c)\oplus {F}_{1}(w,ind)$ 18: $ \text{ AccessList}[{u}_{j}]\leftarrow (w,{K}_{w},{{{K}^{\prime}}}_{w},S{T}_{c},c)$ 19: end for 20: $ {m}_{j}\leftarrow \text{SE.Enc}({r}_{j},\text{AccessList}[{u}_{j}])$ 21:$ \text{CList}[{u}_{j}]\leftarrow ({\mu }_{j},{m}_{j}) $ 22:$\mathrm{Send}(U{T}_{c},({e}_{a},{e}_{b},{\mathrm{C}}_{S{{T}_{c}}},vt))\text{and CList}[{u}_{j}]\mathrm{to}\text{CS} $ CS: 23:$ \text{EDB[}U{T}_{c}]\leftarrow ({e}_{a},{e}_{b},{\mathrm{C}}_{S{{T}_{c}}},vt) $
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4 Search
Input: $ s{k}_{{{u}_{j}}},\text{CList}[{u}_{j}],\text{EDB,S,AccessList}[{u}_{j}] $ Output: $ \text{E},{e}_{w},\text{EDB,S,}proof,ind\text{s} $ DU: 1: $ \text{Receive}({\mu }_{j},{m}_{j})\text{from CS} $ 2: $ {r}_{j}\leftarrow \Gamma .\text{Decap}(s{k}_{{{u}_{j}}},{\mu }_{j}) $ 3: $ \text{AccessList}[{u}_{j}]\leftarrow \text{SE.Dec}({r}_{j},{m}_{j}) $ 4: $ (w,{K}_{w},{{{K}^{\prime}}}_{w},S{T}_{c},c)\leftarrow \text{AccessList}[{u}_{j}] $ 5: $ \mathrm{if}(S{T}_{c},c)=\bot \text{then} $ 6: $ \text{return}\varnothing $ 7: end if 8: $ token\leftarrow ({K}_{w},S{T}_{c},c) $ 9: $ \mathrm{Send}\;token\;\mathrm{to}\;\text{CS} $ CS: 10: $ \text{1if S}[{K}_{w}] =\mathrm{Null}\text{then} $ 11: $ {e}_{w}\leftarrow {0}^{n} $ 12: else 13: ${e}_{w}\leftarrow \text{S}[{K}_{w}] $ 14: end if 15: $ \text{E}\leftarrow \text{empty map} $ 16: $ \text{for}i=c\text{to}0\text{do}$ 17: $ U{T}_{i}\leftarrow {H}_{1}({K}_{w},S{T}_{i})$ 18: $ ({e}_{a},{e}_{b},{\mathrm{C}}_{S{{T}_{i-1}}},vt)\leftarrow \text{EDB[}U{T}_{i}] $ 19: $ \text{E}[i-{c}_{0}]\leftarrow ({e}_{a},{e}_{b}) $ 20: $ proof\leftarrow proof\oplus vt $ 21: $\text{ Remove EDB[}U{T}_{i}] $ 22: $ \mathrm{if}{\mathrm{C}}_{S{{T}_{i-1}}}=\bot \text{then} $ 23: Break 24: end if 25: $ S{T}_{i-1}\leftarrow {H}_{2}({K}_{w},S{T}_{i})\oplus {\mathrm{C}}_{S{{T}_{i-1}}}$ 26: end for 27: $ \text{EDB[}U{T}_{c}]\leftarrow ({e}_{a},{e}_{b},{\mathrm{C}}_{S{{T}_{c-1}}},vt) $ 28: $ \mathrm{Send}({e}_{w},\text{E,}proof)\mathrm{to}\text{DU}$ DU: 29: $ b{s}_{w}\leftarrow {0}^{n}\$ 30: $ \text{if}{e}_{w}\neq {0}^{n}\text{then} $ 31: $ b{s}_{w}\leftarrow {H}_{5}({{{K}^{\prime}}}_{w},c)\oplus {e}_{w} $ 32: end if 33: $ \text{for}\;i =0\;\text{to}\;c\;\text{do} $ 34: $ ({e}_{a},{e}_{b})\leftarrow \text{E}[i]$ 35: $ b{s}_{a}\leftarrow {e}_{a}\oplus {H}_{3}({{{K}^{\prime}}}_{w},i) $ 36: $ b{s}_{b}\leftarrow {e}_{b}\oplus {H}_{4}({{{K}^{\prime}}}_{w},i)$ 37: $ b{s}_{w}\leftarrow (\overline{b{s}_{a}}\wedge b{s}_{w})\oplus (b{s}_{a}\wedge b{s}_{b}) $ 38: end for 39: $ {e}_{w}\leftarrow b{s}_{w}\oplus {H}_{5}({{{K}^{\prime}}}_{w},c+1) $ 40: $ \text{Send}\;{e}_{w}\text{to CS} $ 41: $ \mathrm{Parse}\;b{s}_{w}\;\text{into file identifiers}ind\text{s} $ 42: $ \mathrm{Return}\;ind\text{s} $ CS: 43: $ \text{S}[{K}_{w}]\leftarrow {e}_{w} $
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5 Verify
Input: $ w,ind\text{s},\text{AccessList}[{u}_{j}],proof $ Output: $ accept/reject $ DU: 1: $ (w,{K}_{w},{{{K}^{\prime}}}_{w},S{T}_{c},c)\leftarrow \text{AccessList}[{u}_{j}] $ 2: $ proof'\leftarrow {F}_{1}(w,0)\oplus {F}_{1}(w,c) $ 3: $ \text{for each}ind\text{in}inds\text{do} $ 4: $ proof'\leftarrow proof'\oplus {F}_{1}(w,ind) $ 5: end for 6: $ \text{if}\;proof =proof'\text{then} $ 7: $ \text{return}\;accept $ 8: else 9: $ \text{return}\;reject$ 10: end if
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6 Simulator
Setup DO: 1: $ \text{O,S,EDB}\leftarrow \mathrm{empty}\mathrm{map} $ 2: $ \text{Send (S,EDB) to CS and keep others locally} $ 3: $ \mathrm{userList}\leftarrow \{{u}_{1},{u}_{2},\cdots,{u}_{m}\} $ 4: $ (par,msk,mpk)\leftarrow \Gamma .{\text{Setup(1}}^{\lambda }) $ 5: $ \text{for all}{u}_{j}\text{in}\mathrm{userList}\text{do} $ 6:$ s{k}_{{{u}_{j}}}\leftarrow \Gamma .\mathrm{KeyGen}({u}_{j},msk) $ 7:$ \text{end for} $ 8:$ \text{Send}s{k}_{{{u}_{j}}}\text{to DU}{u}_{j} $ Update DO: 1: $ ts\leftarrow ts+1 $ 2: $ S{T}_{c}\leftarrow {\{0,1\}}^{\lambda } $ 3: $ {\text{T}}_{1}[ts]\leftarrow {\{0,1\}}^{\lambda } $ 4: $ {\text{T}}_{2}[ts]\leftarrow {\{0,1\}}^{\lambda } $ 5: $ \text{Generate the bi-bitmap (}b{s}_{a},b{s}_{b}) $ 6: $ {\text{T}}_{3}[ts]\leftarrow {\{0,1\}}^{\lambda } $ Search DU: 1: $ ts\leftarrow ts+1 $ 2: $ \tilde{w}\leftarrow \min \text{sp(}w) $ 3: $ \text{Parse Ti(}w\text{) as}(t{s}_{0},\cdots,t{s}_{c}) $ 4: $ {K}_{\tilde{w}}||{{{K}^{\prime}}}_{\tilde{w}}\leftarrow {\text{T}}_{F}(\tilde{w}) $ 5: $ \text{for}i=c\text{to 0 do}$ 6: $ S{T}_{i-1}\leftarrow \{0,1\}^{\lambda }$ 7: $\text{ Program}{H}_{1}({K}_{\tilde{w}},S{T}_{i})\leftarrow {\text{T}}_{1}[t{s}_{i}]$ 8: $ \text{Program}{H}_{2}({K}_{\tilde{w}},S{T}_{i})\leftarrow {\text{T}}_{2}[ts]\oplus S{T}_{i-1} $ 9: $ \text{Program}{H}_{3}({{{K}^{\prime}}}_{\tilde{w}},i)\leftarrow {\text{T}}_{3}[ts] $ 10: $ \text{Program}{H}_{4}({{{K}^{\prime}}}_{\tilde{w}},i)\leftarrow {\text{T}}_{4}[ts] $ 11: $ proof \leftarrow proof \oplus {\text{VT}}[ts] $ 12: end for 13: $ \text{Program}{H}_{5}({{{K}^{\prime}}}_{\tilde{w}},i+1)\leftarrow {\text{T}}_{5}[ts] $ 14: $ \mathrm{Send}({K}_{\tilde{w}},S{T}_{c},c)\mathrm{to}\text{CS} $ 15: $ \text{Return rp(}w) $ Verify DU: 1: $ proo{f}^{\prime}\leftarrow {\text{T}}_{{{F}_{1}}}[0]\oplus {\text{T}}_{{{F}_{1}}}[c] $ 2: $ \text{for each}ind\text{in rp}[w]\text{do} $ 3: $ proo{f}^{\prime}\leftarrow proo{f}^{\prime}\oplus {\text{T}}_{{{F}_{1}}}[ind]$ 4: end for 5: $ \mathrm{if}\;proof=proo{f}^{\prime}\;\text{then} $ 6: $ \text{return}accept $ 7: else 8: $ \text{return}\;reject $ 9: end if
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表 3 功能性与复杂度对比
方案 多用户 结果可验证 前向隐私 后向隐私 抗合谋 鲁棒性 更新复杂度 搜索复杂度 验证复杂度 $ \text{Q-}\mu \text{SE} $(2020)[31] Π × Π Type-II Π × $ O(|\text{DB}|)\cdot F $ $ O({R}_{w})\cdot F $ - NIMS(2023)[10] Π × Π Type-III × × $ O(|\mathrm{DB}|+|W|)\cdot F $ $ O({a}_{w}+|W|) $ - FBVDSSE(2025)[21] × Π Π Type-II × × $ O(|\mathrm{DB}|)\cdot (F+Exp) $ $ O({R}_{w})\cdot (F+Exp) $ $ O({R}_{w})\cdot Exp $ RDSSE-CR Π Π Π Type-$ {\text{I}}^{-} $ Π Π $ O(|\mathrm{DB}|)\cdot (F+Hash) $ $ O({R}_{w})\cdot (F+Hash) $ $ O({R}_{w})\cdot F $ $ F $和$ Hash $分别表示伪随机函数和哈希函数。$ {R}_{w} $表示对应关键字w的搜索结果的大小，$ {a}_{w} $和$ {R}_{w} $分别表示关键字w的更新总数和对应关键字w的搜索结果的大小。|W|和|DB|分别表示关键字的总数和关键字/文档对的数量。$ Exp $表示幂运算。
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表 4 参数配置
参数 值 队列规模 6 速度 24 m/s 默认间距 20 m 车道数量 4 高速公路长度 18 km 模拟时间 100 s 网络协议 LTE-V2X 消息大小 256 bytes
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