Functional encryption (FE) and predicate encryption (PE) can be utilized in deploying and executing machine learning (ML) algorithms to improve efficiency. However, most of existing FE and PE algorithms only consider generic functions. Actually, quadratic-functions-based FE and PE can be used to further reduce the computation costs significantly. In this paper, we present a functional encryption scheme for quadratic functions from those for generic functions. In our constructions, ciphertexts are associated with a pair of vectors \((\mathsf {x},\mathsf {y})\in \mathbb {Z}^{n}_{q}\times \mathbb {Z}^{m}_{q}\), private keys are associated with a quadratic function, and the decryption of ciphertexts CT_(x,y) with a private key sk_F, where F is a n × m-dimensional matrix, recovers \((\mathsf {x})^{\top }\mathsf {F}\mathsf {y}\in \mathbb {Z}_{q}\). Compared with Baltico et al.’s FEs for quadratic functions (at Crypto 2017), our schemes could obtain almost the same ciphertexts size of \(O((n+m)\log q)\) as their schemes (in contrast to O(n) in Baltico et al.’s schemes), and the computation for quadratic functions in our scheme does not rely on bilinear maps, while their schemes must rely on this assumption. In particular, our schemes under the standard assumptions achieve adaptive security, while Baltico et al.’s scheme only obtains selective security. Moreover, beyond the MDDH and GGM assumptions, our schemes allow for instantiations under standard assumptions such as LWE, LPN, and etc.

功能加密（FE）和谓词加密（PE）可用于部署和执行机器学习（ML）算法，以提高效率。但是，大多数现有的FE和PE算法仅考虑通用功能。实际上，基于二次函数的FE和PE可用于进一步显着降低计算成本。在本文中，我们提出了针对二次函数的泛型函数加密方案。在我们的构造中，密文与一对向量\（（\ mathsf {x}，\ mathsf {y}）\ in \ mathbb {Z} ^ {n} _ {q} \ times \ mathbb {Z} ^ {m} _ {q} \），私钥与二次函数和密文C T _（x，y）的解密相关联使用私钥s k _F，其中F是n × m维矩阵，恢复\（（\ mathsf {x}）^ {\ top} \ mathsf {F} \ mathsf {y} \ in \ mathbb {Z } _ {q} \）。与Baltico等人的关于二次函数的FE相比（在Crypto 2017），我们的方案可以获得与他们的方案几乎相同的密文大小\（O（（n + m）\ log q）\）（与Ø（ñ）（在Baltico等人的方案中），并且我们方案中二次函数的计算不依赖于双线性映射，而他们的方案必须依赖此假设。特别是，在标准假设下，我们的方案实现了自适应安全性，而Baltico等人的方案仅获得了选择性安全性。此外，除了MDDH和GGM假设之外，我们的方案还允许在标准假设（例如LWE，LPN等）下进行实例化。