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Paper 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.

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

Metadata
Available format(s)
PDF
Category
Foundations
Publication info
Preprint. MINOR revision.
Keywords
Indistinguishability ObfuscationFunctional EncryptionSuccinctness
Contact author(s)
ryo nishimaki @ gmail com; kitagaw1-at-is titech ac jp
History
2018-02-16: last of 8 revisions
2017-03-25: received
See all versions
Short URL
https://ia.cr/2017/275
License
Creative Commons Attribution
CC BY
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