Adaptively Secure and Succinct Functional Encryption: Improving Security and Efficiency, Simultaneously

Functional encryption (FE) is advanced encryption that enables us to issue functional decryption keys where functions are hardwired. When we decrypt a ciphertext of a message $m$ by a functional decryption key where a function $f$ is hardwired, we can obtain $f(m)$ and nothing else. We say FE is selectively or adaptively secure when target messages are chosen at the beginning or after function queries are sent, respectively. In the weakly-selective setting, function queries are also chosen at the beginning. We say FE is single-key/collusion-resistant when it is secure against adversaries that are given only-one/polynomially-many functional decryption keys, respectively. We say FE is sublinearly-succinct/succinct when the running time of an encryption algorithm is sublinear/poly-logarithmic in the function description size, respectively. In this study, we propose a generic transformation from weakly-selectively secure, single-key, and sublinearly-succinct (we call ``building block\u27\u27) PKFE for circuits into adaptively secure, collusion-resistant, and succinct (we call ``fully-equipped\u27\u27) one for circuits. We assume only the existence of the building block PKFE for circuits. That is, our transformation relies on neither concrete assumptions such as learning with errors nor indistinguishability obfuscation (IO). This is the first generic construction of fully-equipped PKFE that does not rely on IO. As side-benefits of our results, we obtain the following primitives from the building block PKFE for circuits: (1) laconic oblivious transfer (2) succinct garbling scheme for Turing machines (3) selectively secure, collusion-resistant, and succinct PKFE for Turing machines (4) low-overhead adaptively secure traitor tracing (5) key-dependent-message secure and leakage-resilient public-key encryption. We also obtain a generic transformation from simulation-based adaptively secure garbling schemes that satisfy a natural decomposability property into adaptively indistinguishable garbling schemes whose online complexity does not depend on the output length