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Verifiable Private Polynomial Evaluation

  • Xavier Bultel
  • Manik Lal Das
  • Hardik Gajera
  • David Gérault
  • Matthieu Giraud
  • Pascal Lafourcade
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10592)

Abstract

Delegating the computation of a polynomial to a server in a verifiable way is challenging. An even more challenging problem is ensuring that this polynomial remains hidden to clients who are able to query such a server. In this paper, we formally define the notion of Private Polynomial Evaluation (PPE). Our main contribution is to design a rigorous security model along with relations between the different security properties. We define polynomial protection (\(\textsf {PP}\)), proof unforgeability (\(\textsf {UNF}\)), and indistinguishability against chosen function attack (\(\textsf {IND}\text {-}\textsf {CFA}\)), which formalizes the resistance of a PPE against attackers trying to guess which polynomial is used among two polynomials of their choice. As a second contribution, we give a cryptanalysis of two PPE schemes of the literature. Finally, we design a PPE scheme called \(\mathsf {PIPE}\) and we prove that it is \(\textsf {PP}\)-, \(\textsf {UNF}\)- and \(\textsf {IND}\text {-}\textsf {CFA}\)-secure under the decisional Diffie-Hellman assumption in the random oracle model.

Notes

Acknowledgements

This research was conducted with the support of the FEDER program of 2014–2020, the region council of Auvergne-Rhône-Alpes, the support of the “Digital Trust” Chair from the University of Auvergne Foundation, the Indo-French Centre for the Promotion of Advanced Research (IFCPAR) and the Center Franco-Indien Pour La Promotion De La Recherche Avancée (CEFIPRA) through the project DST/CNRS 2015-03 under DST-INRIA-CNRS Targeted Programme.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Xavier Bultel
    • 1
  • Manik Lal Das
    • 2
  • Hardik Gajera
    • 2
  • David Gérault
    • 1
  • Matthieu Giraud
    • 1
  • Pascal Lafourcade
    • 1
  1. 1.Université Clermont Auvergne, CNRS, LIMOSClermont-FerrandFrance
  2. 2.DA-IICTGandhinagarIndia

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