Efficient and Verifiable Ciphertext Retrieval Scheme Based on Trusted Execution Environment
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摘要: 密文检索机制(Ciphertext Retrieval)支持密态数据下的安全检索，对称可搜索加密（SSE）是其核心研究分支。在实际应用中，云服务器为节约算力，可能返回错误或不完整的检索结果；同时攻击者可利用搜索与访问模式的泄露信息逆向推导关键字，引发严重的隐私泄露问题。因此，实现检索结果可验证性，并兼顾搜索与访问模式的隐私保护，具备重要的研究意义。现有支持模式隐私保护的可验证SSE方案，普遍依赖关键字遍历机制，验证效率较低，会显著增加用户的计算与通信开销，难以满足高效安全的密文检索需求。针对上述性能瓶颈，该文提出一种基于可信执行环境(TEE)的高效可验证密文检索方案。为提升密文检索等效率，该方案借助硬件级安全隔离与不经意数据重排的协同，实现关键字陷门尺寸独立于关键字字典的规模。同时，通过嵌入随机数以及盲化多项式常数项方式验证返回结果的正确性。得益于上述设计，该方案在效率层面取得了显著提升。具体而言，其一，该方案使得关键字陷门规模仅与查询关键字数量相关，而与全局字典规模无关，有效降低了计算和通信成本；其二，该方案仅需存储两个随机数即可实现可验证功能，大幅降低了用户本地存储开销。其三，数据用户与单服务器单轮交互中获取检索结果以及对称同态加密机制的应用等技术进一步提升了运行效率。此外，TEE中的密态计算弱化了对TEE的安全假设和信任程度。在通过模拟游戏方式完成对方案安全性的证明之后，该文对所提出的方案进行了综合的性能评估，评估结果证实了该方案在效率上显著优于其他具备相同功能的方案。Abstract: The ciphertext retrieval mechanism enables retrieval over encrypted data. Symmetric Searchable Encryption (SSE) is a critical branch of ciphertext retrieval. However, to save computing resources, cloud servers may return incorrect or incomplete results. Moreover, attackers may exploit information leaked from search and access patterns to reconstruct keyword details. Therefore, protecting the privacy of search and access patterns, while ensuring result verifiability, is necessary and meaningful. Nevertheless, existing verifiable SSE schemes that support search and access pattern privacy usually rely on keyword traversal mechanisms, and their verification mechanisms are inefficient. This results in high computational and communication overhead for users. To address these performance bottlenecks, an efficient and verifiable ciphertext retrieval scheme based on Trusted Execution Environment (TEE) is proposed. To improve ciphertext retrieval efficiency, the scheme uses the collaborative implementation of hardware-level security isolation and oblivious data rearrangement, so that the size of the keyword trapdoor is independent of the size of the keyword dictionary. Meanwhile, the correctness of the returned results is verified by embedding random numbers and blinding the constant terms of polynomials. Owing to these designs, significant efficiency improvements are achieved. Specifically, the scheme ensures that the size of keyword trapdoors depends only on the number of query keywords rather than on the global dictionary size, which effectively reduces communication and computational costs. The scheme also requires only two random numbers to achieve verifiability, which substantially reduces the user's local storage overhead. In addition, techniques such as single-server, single-round result retrieval and symmetric homomorphic encryption are adopted to further improve operational efficiency. Moreover, confidential computing within TEE weakens the security assumptions and trust requirements imposed on TEE. After the security of the proposed scheme is formally proved by simulation-based methods, a comprehensive performance evaluation is conducted. The results confirm that the proposed scheme is substantially more efficient than other schemes with the same functionality.
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1 加密数据的构建$ \text{DBBuild} $
输入：$ {\lambda } $和$ \text{DB} $ 输出：$ \text{EDBtree} $, $ \text{PM} $, $ \text{VK} $和$ \text{SK} $ $ {{\text{EDB}}}\leftarrow {\varnothing } $ 参数选择 设关键字字典$ {W} $的大小为$ {m} $ 选择一个随机数$ {\beta } $和一个随机数$ {\theta } $ 随机选择两个哈希函数$ {{H}\colon \{{0},{1}\}}^{{*}}\rightarrow {\mathbb{Z}}_{{p}} $ 随机抽样一个私钥为$ {k} $的伪随机函数$ {F} $ 初始化一个私钥为$ \text{sk} $的对称同态加密算法${ \text{ASHE}}=({{\text{Setup}}},{{\text{Enc}}},{{\text{Dec}}}) $ 具体步骤 1: $ {L}={\{|{{\text{DB}}}\left({{w}}_{{i}}\right)|\}}_{{\max}} $ 2: 对于每个关键字$ {{w}}_{{i}}\in {W} $，执行下面的算法： 3: $ {{k}}_{{{{w}}_{{i}}}}\leftarrow {F}\left({k},{{w}}_{{i}}\right) $ 4: $ {{P}}_{{{{w}}_{{i}}}}\left({x}\right)={{x}}^{{L}-\left| \text{{D}{B}}\left({{w}}_{{i}}\right)\right| }{({x}-{\beta })\prod }_{\text{{i}{d}}\in \text{{D}{B}}\left({{w}}_{{i}}\right)}({x}-(\text{{i}{d}}||{H}\left(\text{{i}{d}}\right)))=\displaystyle\sum\nolimits _{{j}=\mathbf{0}}^{{j}={L}+\mathbf{1}}{{{{\tau }}_{{i}{j}}}{x}}^{{j}} $ 5: $ {\text{EDB}}_{{{{w}}_{{i}}}}={\text{Enc}}_\text{{s}{k}}\left({{P}}_{{{{w}}_{{i}}}}\left({x}\right)-{H}({{w}}_{{i}}||{\theta })\right)={{\displaystyle\sum\nolimits _{{j}={0}}^{{L}+{1}}}{{\text{Enc}}}}_{{h}{p}{k}}\left({{\tau }}_{{i}{j}}\right){{x}}^{{j}} $ 6: $ {{\text{EDB}}}\leftarrow (({{k}}_{{{{w}}_{{1}}}},{\text{EDB}}_{{{{w}}_{{1}}}}),{{k}}_{{{{w}}_{{2}}}},{{{\text{EDB}}}}_{{{{w}}_{{2}}}}),\cdots ,({{k}}_{{{{w}}_{{m}}}},{{{\text{EDB}}}}_{{{{w}}_{{m}}}})) $和$ \text{{V}{K}}\leftarrow {\beta },{\theta } $ 7: 初始化Path ORAM二叉树结构EDBtree； 8: PM$ \leftarrow $随机将每个关键字映射到一条路径； 9: 对每个关键字对应的多项式执行： 10: 将多项式加密为数据块； 11: 将数据块插入到关键字映射路径上的对应桶中； 12: 使用虚拟块(dummy blocks)将每个桶填充至大小S； 13: 返回加密数据库$ {{\text{EDBtree}}} $，$ {{\text{PM}}} $，$ {{\text{VK}}} $和私钥$ {{\text{SK}}}=\left({k},\text{{s}{k}}\right) $； 14: 上传$ {{\text{EDBtree}}} $到云服务器的不可信环境； 15: 通过安全信道上传PM到云服务器的Enclave。 
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2 关键字陷门生成Trapdoor
输入：$ \text{sk} $和被询问的关键字集合$ {Q} $ 输出：关键字陷门$ \text{Token} $ 1: 对于$ {{w}}_{{i}}\in {Q} $，执行下面的循环： 2: $ {{k}}_{{{{w}}_{{i}}}\boldsymbol{'}}\leftarrow {F}\left({k},{{w}}_{{i}}\right) $。 3: 返回关键字陷门$ {{\text{Token}}}=\{{{k}}_{{{{w}}_{{1}}}{'}},{{k}}_{{{{w}}_{{2}}}{'}},\cdots ,{{k}}_{{{{w}}_{{n}}}{'}}\} $ 4: 通过与TEE建立的安全信道上传到Enclave中
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3 搜索过程Search
输入：$ \text{EDBtree} $和$ \text{Token} $ 输出：搜索结果$ {R} $ 云服务器 // Enclave 1:$ {R}\leftarrow \{\} $ 2: 解析$ {\text{Token}}=\{{{k}}_{{{{w}}_{{1}}}{'}}{{k}}_{{{{w}}_{{2}}}{'}},\cdots ,{{k}}_{{{{w}}_{{n}}}{'}}\} $ 3: 对于$ {{k}}_{{{{w}}_{{i}}}{'}} $执行： 4: 如果$ {{k}}_{{{{w}}_{{i}}}{'}} $对应的多项式数据块不在STASH中，执行： 5: 从PM中读取对应的路径PATH； 6: Enclave调用Path ORAM的Access (PATH, EDBtree)接口，从不可信环境中读取EDBtree中PATH路径上的密文数据块； 7: 解密数据块并得到$ {{k}}_{{{{w}}_{{i}}}{'}} $对应的加密多项式； 8: 计算$ {\text{Enc}}_\text{{s}{k}}(\mathbb{P}\left({x}\right){'})={\text{EDB}}_{{{{w}}_{{1}}}{'}} +{\text{EDB}}_{{{{w}}_{{2}}}{'}}$+···+$ {\text{EDB}}_{{{{w}}_{{i}}}{'}} $+···+$ {\text{EDB}}_{{{{w}}_{{n}}}{'}} $ $ \text{=}{\text{Enc}}_\text{{s}{k}}(\left({{P}}_{{{{w}}_{{1}}}{'}}\left({x}\right)-{H}({{w}}_{{1}}||{\theta })\right)+{H}({{w}}_{{2}}||{\theta })+\cdots +\left({{P}}_{{{{w}}_{{n}}}{'}}\left({x}\right)-{H}({{w}}_{{n}}||{\theta })\right)) $ 9:将搜索结果$ {\text{Enc}}_\text{{s}{k}}\left(\mathbb{P}\left({x}\right){'}\right) $返回给数据用户。 数据用户 10: 数据用户通过解密密钥$ {{\text{sk}}} $计算出明文$ \mathbb{P}{\left({x}\right)}^{{'}}={\text{Dec}}_\text{{s}{k}}\left({\text{Enc}}_\text{{s}{k}}\left(\mathbb{P}{\left({x}\right)}^{{'}}\right)\right)=\left({{P}}_{{{{w}}_{{1}}}{'}}\left({x}\right)-{H}({{w}}_{{1}}||{\theta })\right)+\cdots +$
$\left({{P}}_{{{{w}}_{{n}}}{'}}\left({x}\right)-{H}({{w}}_{{n}}||{\theta })\right) $11: 对于$ {{w}}_{{i}}\in {Q}=({{w}}_{{1}},{{w}}_{{2}},\cdots ,{{w}}_{{n}}) $，数据用户通过$ {{\text{VK}}} $获得$ \mathbb{P}\left({x}\right)=\mathbb{P}{\left({x}\right)}^{{'}}+{H}({{w}}_{{1}}||{\theta })+{H}({{w}}_{{2}}||{\theta })+\cdots +{H}({{w}}_{{n}}||{\theta }) $ 12:如果$ {\mathbb{P}}_{{\alpha }}\left({\beta }\right)\neq {0} $，数据用户拒绝搜索结果。如果验证通过，则数据用户计算出多项式$ \mathbb{P}\left({x}\right) $的根，然后从中找到符合格式$ \text{{i}{d}}||{H}\left(\text{{i}{d}}\right) $的有效根并将其添加到结果$ {R} $中。
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4 算法模拟
输入：$ {\mathcal{L}}_{{I}}{'}=({m},{L},{n}) $ 输出：$ \text{EDB} $和$ \text{Token} $ 加密数据$ \text{EDB} $的生成： 1 $ \text{EDB}\leftarrow {\varnothing } $ 2 对于$ {i}\in [{1},{m}] $，执行下面的算法: 3 选择随机数$ {{k}}_{{{{w}}_{{i}}}} $并记录元组$ ({i},{{k}}_{{{{w}}_{{i}}}}) $到表格$ {T} $中 4 选择$ {L} $+1个随机数$ {{\eta }}_{{j}} $得到$ {\text{EDB}}_{{{{w}}_{{i}}}}=\displaystyle\sum\nolimits_{{j}={1}}^{{L}+{1}}{{\eta }}_{{j}}{{x}}^{{j}} $ 5 生成$ \text{EDB}=(({{k}}_{{{{w}}_{{1}}}},{\text{EDB}}_{{1}}),{{k}}_{{{{w}}_{{2}}}},{\text{EDB}}_{{2}}),\cdots , $
$({{k}}_{{{{w}}_{{m}}}},{\text{EDB}}_{{m}})) $生成陷门$ {\text{Token}} $ 6 对于$ {i}\in [{1},{n}] $，执行下面的循环： 7 从$ {T} $中根据索引选出$ {{k}}_{{{{w}}_{{i}}}} $ 8 返回关键字陷门$ {\text{Token}}=\{{{k}}_{{{{w}}_{{1}}}},{{k}}_{{{{w}}_{{2}}}},\cdots ,{{k}}_{{{{w}}_{{n}}}}\} $
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表 1 搜索模式和访问模式隐藏的可验证多关键字可搜索加密机制比较
方案 计算代价 本地通信代价 本地存储代价 加法同态加密机制 初始化 陷门生成 搜索阶段 初始化 搜索 Wu方案[18] $ {O}({mL}) $ $ {O}({m}) $ $ {O}({mL}) $ $ {O}({mL}) $ $ {O}({mL}) $ $ {O}(1) $ 公钥加密 Ji方案[19] $ {O}({mL}) $ $ {O}({m}) $ $ {O}({mL}) $ $ {O}({mL}) $ $ {O}({mL}) $ $ {O}({m}) $ 对称机制 本文方案 $ {O}({mL}) $ $ {O}({n}) $ $ {n*O}(\mathrm{log}{N}) $ $ {O}({mL}) $ $ {O}(\mathrm{log}{L}) $ ${O}(1) $ 对称机制 注：$ {m} $是关键字字典集合的大小；$ {L} $是包含关键字文档标识集合大小的最大值；$ {n} $是要搜索关键字集合的大小；$ {N} $是Path ORAM桶的数量。
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