A punctured programming approach to adaptively secure functional encryption

Abstract

We propose the first construction for achieving adaptively secure functional encryption (FE) for poly-sized circuits (without complexity leveraging) from indistinguishability obfuscation (iO). Our reduction has polynomial loss to the underlying primitives. We develop a “punctured programming” approach to constructing and proving systems where outside of obfuscation we rely only on primitives realizable from pseudo random generators. Our work consists of two constructions. Our first FE construction is provably secure against any attacker that is limited to making all of its private key queries after it sees the challenge ciphertext. (This notion implies selective security.) Our construction makes use of an we introduce called puncturable deterministic encryption (PDE) which may be of independent interest. With this primitive in place we show a simple FE construction. We then provide a second construction that achieves adaptive security from indistinguishability obfuscation. Our central idea is to achieve an adaptively secure functional encryption by bootstrapping from a one bounded FE scheme that is adaptively secure. By using bootstrapping we can use “selective-ish” techniques at the outer level obfuscation level and push down the challenge of dealing with adaptive security to the one bounded FE scheme, where it has been already been solved. We combine our bootstrapping framework with a new “key signaling” technique to achieve our construction and proof. Altogether, we achieve the first construction and proof for adaptive security for functional encryption.