Public key encryption with equality test (PKEET) is a cryptosystem that allows a tester who has trapdoors issued by one or more users U_i to perform equality tests on ciphertexts encrypted using public key(s) of U_i. Since this feature has a lot of practical applications including search on encrypted data, several PKEET schemes have been proposed so far. However, to the best of our knowledge, all the existing proposals are proven secure only under the hardness of number-theoretic problems and/or the random oracle heuristics.

In this paper, we show that this primitive can be achieved not only generically from well-established other primitives but also even without relying on the random oracle heuristics. More precisely, our generic construction for PKEET employs a two-level hierarchical identity-based encryption scheme, which is selectively secure against chosen plaintext attacks, a strongly unforgeable one-time signature scheme and a cryptographic hash function. Our generic approach toward PKEET has several advantages over all the previous works; it directly leads the first standard model construction and also directly implies the first lattice-based construction. Finally, we show how to extend our approach to the identity-based setting.

平等测试（PKEET）公共密钥加密密码系统，允许测试人员谁拥有由一个或多个用户发出的活板门ü_我对使用公共密钥（S）加密的密文进行平等的测试ü_我。由于此功能具有许多实际应用，包括搜索加密数据，因此迄今为止已提出了几种PKEET方案。然而，据我们所知，所有现有建议仅在数论问题和/或随机预言启发法的严格条件下被证明是安全的。

在本文中，我们证明了该原语不仅可以从完善的其他原语中普遍实现，甚至可以不依赖于随机Oracle启发式算法。更准确地说，我们针对PKEET的通用构造采用了两级基于身份的分层加密方案，该方案可选择性地防止选择的明文攻击，不可伪造的一次性签名方案和加密哈希函数。与以前的所有工作相比，我们对PKEET的通用方法具有多个优势；它直接引导第一个标准模型的构造，也直接暗示第一个基于格的构造。最后，我们展示了如何将我们的方法扩展到基于身份的设置。