From Weakly Selective to Selective Security in Compact Functional Encryption

We provide a generic transformation from weakly selective secure FE to selective secure FE through an approach called hybrid functional key generation. Furthermore, our transformation preserves the compactness of the FE scheme. Additionally, we note that this transformation is much simpler than the prior work [GS16]. We consider the simplicity of the construction in this work as a positive feature and the hybrid functional key generation approach as a new method that can be applied in functional encryption schemes. Furthermore, we try to weaken the input FE scheme of our transformation to be a non-compact one instead of a fully-compact one, by additionally assuming the hardness of LWE (or Ring-LWE) assumption. We achieve this result by utilizing the FE scheme for bounded collusions with decomposable and succinct ciphertext property, which can be solely based on the LWE (or Ring-LWE) assumption. Finally we present the implications of our result, which improves previous results, in building general-purpose indistinguishability obfuscator from (well-expressed) functional encryption.