Hierarchical Functional Encryption for Quadratic Transformation

In this paper, we study the notion of hierarchical functional encryption (HFE) which allows the secret key holder to delegate a portion of its decryption ability to others and the delegation can be done in a hierarchical structure. We present the first concrete HFE scheme for quadratic transformations (QT) that enjoys public key, ciphertext, and secret key of linear size in the message size. The scheme achieves semi-adaptive simulation-based security under bilateral k-Lin assumption and k-Lin assumption in the standard model. Besides, we give concrete HFE scheme for linear transformations (LT) based on k-Lin assumption with semi-adaptive simulation-based security; the unique prior construction [ACISP 17] just achieves indistinguishability-based (IND) security. Technically, for constructing HFE-QT scheme, we follow Wee’s concrete functional encryption for quadratic functions (QFE) scheme [TCC 20] where they use inner-product functional encryption (IPFE) as an underlying building block to construct the QFE scheme. In order to achieve our goal, we replace the IPFE with HFE for linear transformations (LT) so that the scheme possesses the property of quadratic transformations and key delegation.