This paper presents two functional encryption schemes for quadratic functions (or degree-2 polynomials) achieving simulation-based security in the semi-adaptive model with constant-size secret keys. Prior constructions in the standard model either achieve weaker security model [CRYPTO 17] or require linear-size secret keys (in the message length) [PKC 20]. One of our proposed schemes is comparable to existing schemes in the generic group model in terms of ciphertext size. Technically, we combine Wee’s compiler [TCC 17] with Gay’s paradigm [PKC 20]. However, we avoid (partially) function-hiding inner-product functional encryption used in Gay’s paradigm which makes our work conceptually simpler.

本文提出了二次函数（或 2 次多项式）的两种函数加密方案，在具有恒定大小密钥的半自适应模型中实现基于仿真的安全性。标准模型中的先前构造要么实现较弱的安全模型 [CRYPTO 17]，要么需要线性大小的密钥（在消息长度中）[PKC 20]。我们提出的方案之一在密文大小方面可与通用组模型中的现有方案相媲美。从技术上讲，我们将 Wee 的编译器 [TCC 17] 与 Gay 的范式 [PKC 20] 结合起来。然而，我们避免（部分）在 Gay 范式中使用隐藏函数的内积函数加密，这使我们的工作在概念上更简单。