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Designs, Codes and Cryptography

, Volume 87, Issue 1, pp 75–85 | Cite as

Polynomial interpolation of the generalized Diffie–Hellman and Naor–Reingold functions

  • Thierry Mefenza
  • Damien VergnaudEmail author
Article
  • 72 Downloads

Abstract

In cryptography, for breaking the security of the Generalized Diffie–Hellman and Naor–Reingold functions, it would be sufficient to have polynomials with small weight and degree which interpolate these functions. We prove lower bounds on the degree and weight of polynomials interpolating these functions for many keys in several fixed points over a finite field.

Keywords

Naor–Reingold function Generalized Diffie–Hellman function Polynomial interpolation Finite fields 

Mathematics Subject Classification

11T71 94A60 

Notes

Acknowledgements

The authors are supported in part by the French ANR JCJC ROMAnTIC project (ANR-12-JS02-0004) and by the Simons foundation Pole PRMAIS.

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Authors and Affiliations

  1. 1.École normale supérieure, CNRS, PSL Research UniversityParisFrance
  2. 2.Sorbonne Universités, UPMC, CNRS, Institut Universitaire de FranceParisFrance

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