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Simple and Generic Constructions of Succinct Functional Encryption

  • Fuyuki Kitagawa
  • Ryo Nishimaki
  • Keisuke Tanaka
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10770)

Abstract

We propose simple and generic constructions of succinct functional encryption. Our key tool is exponentially-efficient indistinguishability obfuscator (XIO), which is the same as indistinguishability 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 propose a significantly simple framework to construct succinct functional encryption via XIO and show that XIO is a powerful enough to achieve cutting-edge cryptography. In particular, we prove the followings:
  • Single-key weakly succinct secret-key functional encryption (SKFE) is constructed from XIO (even with a bad compression factor) and one-way function.

  • Single-key weakly succinct public-key functional encryption (PKFE) is constructed from XIO with a good compression factor and public-key encryption.

  • Single-key weakly succinct PKFE is constructed from XIO (even with a bad compression factor) and identity-based encryption.

Our new framework has side benefits. Our constructions do not rely on any number theoretic or lattice assumptions such as decisional Diffie-Hellman and learning with errors assumptions. 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.

Notes

Acknowledgement

The first and third authors are supported by NTT Secure Platform Laboratories, JST CREST JPMJCR14D6, JST OPERA, JSPS KAKENHI JP16H01705, JP16J10322, JP17H01695.

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Copyright information

© International Association for Cryptologic Research 2018

Authors and Affiliations

  1. 1.Tokyo Institute of TechnologyTokyoJapan
  2. 2.Secure Platform LaboratoriesNTT CorporationTokyoJapan

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