Cryptology ePrint Archive: Report 2017/275

Simple Generic Constructions of Succinct Functional Encryption

Fuyuki Kitagawa and Ryo Nishimaki and Keisuke Tanaka

Abstract: We propose simple generic constructions of succinct functional encryption. Our key tool is exponentially-efficient indistinguishability obfuscator (XIO), which is the same as indisitnguishability obfuscator (IO) except that the size of an obfuscated circuit (or the running-time of an obfuscator) is 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 XIO indicates how much XIO compresses the brute-force canonicalizer. In this study, we show that XIO is a powerful enough to achieve cutting-edge cryptography. In particular, we propose the following constructions:

- A single-key weakly succinct secret-key functional encryption (SKFE) scheme is constructed from XIO (even with a bad compression factor) and one-way function. - A single-key weakly succinct public-key functional encryption (PKFE) scheme is constructed from XIO with a good compression factor and public-key encryption scheme. -A single-key weakly succinct PKFE scheme is constructed from XIO (even with a bad compression factor) and identity-based encryption scheme.

Our schemes do not rely on any number theoretic or lattice assumptions such as decisional Diffie-Hellman and learning with errors assumpotions. Moreover, all security reductions incur only polynomial security loss. Known constructions of weakly succinct SKFE or PKFE from XIO with polynomial security loss rely on number theoretic or lattice assumptions.

It is known that sub-exponentially secure single-key weakly succinct PKFE scheme implies IO and that single-key weakly succinct (resp. multi-key non-succinct) SKFE implies XIO with a bad (resp. good) compression factor. Thus, we developed two new methods of constructing IO. One uses multi-key SKFE and plain public-key encryption schemes and the other uses single-key weakly succinct SKFE (or XIO) and identity-based encryption schemes.

Category / Keywords: foundations / Indistinguishability Obfuscation, Functional Encryption, Succinctness

Date: received 21 Mar 2017, last revised 24 May 2017

Contact author: ryo nishimaki at gmail com; kitagaw1-at-is titech ac jp

Available format(s): PDF | BibTeX Citation

Note: Revised the title and introduction. Only minor edits in the technical parts.

Version: 20170525:010721 (All versions of this report)

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