Simple and Generic Constructions of Succinct Functional Encryption

We propose simple generic constructions of succinct functional encryption. Our key tool is strong exponentially efficient indistinguishability obfuscator (SXIO), which is the same as indistinguishability obfuscator (IO) except that the size of an obfuscated circuit and the running time of an obfuscator are slightly smaller than that of a brute-force canonicalizer that outputs the entire truth table of a circuit to be obfuscated. A “compression factor” of SXIO indicates how much SXIO compresses the brute-force canonicalizer. In this study, we propose a significantly simple framework to construct succinct functional encryption via SXIO and show that SXIO is powerful enough to achieve cutting-edge cryptography. In particular, we propose the following constructions: Single-key weakly succinct secret-key functional encryption (SKFE) is constructed from SXIO (even with a bad compression factor) and one-way functions. Single-key weakly succinct public-key functional encryption (PKFE) is constructed from SXIO with a good compression factor and public-key encryption. Single-key weakly succinct PKFE is constructed from SXIO (even with a bad compression factor) and identity-based encryption. Our new framework has side benefits. Our constructions do not rely on any number theoretic or lattice assumptions such as decisional Diffie–Hellman and learning with errors assumptions. Moreover, all security reductions incur only polynomial security loss. Known constructions of weakly succinct SKFE or PKFE from SXIO with polynomial security loss rely on number theoretic or lattice assumptions. As corollaries of our results, relationships among SXIO, a few variants of SKFE, and a variant of randomized encoding are discovered.