Functional encryption with application to machine learning: simple conversions from generic functions to quadratic functions

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 ( x , y ) ∈ ℤ q n × ℤ q m $(\mathsf {x},\mathsf {y})\in \mathbb {Z}^{n}_{q}\times \mathbb {Z}^{m}_{q}$ , private keys are associated with a quadratic function, and the decryption of ciphertexts C T ( x , y ) with a private key s k F , where F is a n × m -dimensional matrix, recovers ( x ) ⊤ F y ∈ ℤ q $(\mathsf {x})^{\top }\mathsf {F}\mathsf {y}\in \mathbb {Z}_{q}$ . 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 ) $O((n+m)\log q)$ 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.