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
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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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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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