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Paper: Graded Encoding Schemes from Obfuscation

Authors:
Pooya Farshim
Julia Hesse
Dennis Hofheinz
Enrique Larraia
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DOI: 10.1007/978-3-319-76581-5_13
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Conference: PKC 2018
Abstract: We construct a graded encoding scheme (GES), an approximate form of graded multilinear maps. Our construction relies on indistinguishability obfuscation, and a pairing-friendly group in which (a suitable variant of) the strong Diffie–Hellman assumption holds. As a result of this abstract approach, our GES has a number of advantages over previous constructions. Most importantly: We can prove that the multilinear decisional Diffie–Hellman (MDDH) assumption holds in our setting, assuming the used ingredients are secure (in a well-defined and standard sense). Hence, our GES does not succumb to so-called “zeroizing” attacks if the underlying ingredients are secure.Encodings in our GES do not carry any noise. Thus, unlike previous GES constructions, there is no upper bound on the number of operations one can perform with our encodings. Hence, our GES essentially realizes what Garg et al. (EUROCRYPT 2013) call the “dream version” of a GES. Technically, our scheme extends a previous, non-graded approximate multilinear map scheme due to Albrecht et al. (TCC 2016-A). To introduce a graded structure, we develop a new view of encodings at different levels as polynomials of different degrees.
BibTeX
@inproceedings{pkc-2018-28895,
  title={Graded Encoding Schemes from Obfuscation},
  booktitle={Public-Key Cryptography – PKC 2018},
  series={Public-Key Cryptography – PKC 2018},
  publisher={Springer},
  volume={10770},
  pages={371-400},
  doi={10.1007/978-3-319-76581-5_13},
  author={Pooya Farshim and Julia Hesse and Dennis Hofheinz and Enrique Larraia},
  year=2018
}