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Graded Encoding Schemes from Obfuscation

  • Pooya Farshim
  • Julia Hesse
  • Dennis HofheinzEmail author
  • Enrique Larraia
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10770)

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.

Keywords

Multilinear maps Graded encoding schemes Indistinguishability obfuscation 

Notes

Acknowledgments

We thank the anonymous reviewers for their helpful comments, and Kenny Paterson and Geoffroy Couteau for useful discussions. Pooya Farshim was supported in part by grant ANR-14-CE28-0003 (Project EnBid). Dennis Hofheinz was supported by ERC grant 724307, and by DFG grants HO 4534/2-2 and HO 4534/4-1. Enrique Larraia was supported by EPSRC grant EP/L018543/1.

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Copyright information

© International Association for Cryptologic Research 2018

Authors and Affiliations

  • Pooya Farshim
    • 1
    • 2
  • Julia Hesse
    • 1
    • 2
    • 3
  • Dennis Hofheinz
    • 3
    Email author
  • Enrique Larraia
    • 4
  1. 1.DIENS, École normale supérieure, CNRS, PSL Research UniversityParisFrance
  2. 2.InriaRocquencourtFrance
  3. 3.Karlsruhe Institute of TechnologyKarlsruheGermany
  4. 4.Royal Holloway, University of LondonLondonUK

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