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

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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Submitted on : Sunday, May 10, 2020 - 12:35:10 PM
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Thierry Mefenza, Damien Vergnaud. Polynomial interpolation of the generalized Diffie–Hellman and Naor–Reingold functions. Designs, Codes and Cryptography, Springer Verlag, 2019, 87 (1), pp.75-85. ⟨10.1007/s10623-018-0486-1⟩. ⟨hal-01990394⟩

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