1. 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.
2. 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.
3. A single-key weakly succinct PKFE scheme is constructed from XIO (even with a bad compression factor) and identity-based encryption scheme.
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 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. It is not known whether single-key weakly succinct SKFE implies IO (if we use fully black-box reduction in a certain model, it is impossible), but our single-key weakly succinct SKFE scheme gives many interesting by-products.Category / Keywords: foundations / Indistinguishability Obfuscation, Functional Encryption, Succinctness Date: received 21 Mar 2017, last revised 5 Apr 2017 Contact author: ryo nishimaki at gmail com Available format(s): PDF | BibTeX Citation Note: Revise the security of secret-key encryption in Preliminaries and fix minor typos. Version: 20170405:112547 (All versions of this report) Short URL: ia.cr/2017/275 Discussion forum: Show discussion | Start new discussion