From Single-Key to Collusion-Resistant Secret-Key Functional Encryption by Leveraging Succinctness

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Presented at TokyoCryptoDay 2017 by

Fuyuki Kitagawa

We show how to construct a secret-key functional encryption (SKFE) scheme that supports unbounded polynomially many functional decryption keys solely from an SKFE scheme that supports only one functional decryption key. The underlying single-key SKFE scheme needs to be weakly succinct, that is, the size of its encryption circuit is sub-linear in the size of functions. In our construction, if the underlying single-key SKFE scheme is sub-exponentially secure, then so does the resulting scheme. By combining this result and the result by Bitansky, Nishimaki, Passel`egue, and Wichs (TCC 2016 B), we can obtain an indistinguishability obfuscation from a sub-exponentially secure weakly succinct SKFE scheme that supports only a single functional decryption key if we additionally assume a sub-exponentially secure plain public key encryption scheme.