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

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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.

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Notes

  1. Actually, the security of Joux’s key exchange relies on the stronger decision bilinear Diffie–Hellman assumption in groups equipped with a bilinear map. This assumption implies the tripartite decision Diffie–Hellman assumption in the so-called target group of the bilinear map.

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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. École normale supérieure, CNRS, PSL Research University, Paris, France

    Thierry Mefenza

  2. Sorbonne Universités, UPMC, CNRS, Institut Universitaire de France, Paris, France

    Damien Vergnaud

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  1. Thierry Mefenza
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  2. Damien Vergnaud
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Correspondence to Damien Vergnaud.

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Communicated by A. Winterhof.

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Mefenza, T., Vergnaud, D. Polynomial interpolation of the generalized Diffie–Hellman and Naor–Reingold functions. Des. Codes Cryptogr. 87, 75–85 (2019). https://doi.org/10.1007/s10623-018-0486-1

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  • DOI: https://doi.org/10.1007/s10623-018-0486-1

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