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

Thierry Mefenza , Damien Vergnaud (1, 2)

1 IUF - Institut universitaire de France
2 ALMASTY - ALgorithms for coMmunicAtion SecuriTY

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.

Mots clés: Naor–Reingold function; Generalized Diffie–Hellman function; Polynomial interpolation; finite fields

Domaines: Cryptographie et sécurité [cs.CR]

Thierry Mefenza, Damien Vergnaud. Polynomial interpolation of the generalized Diffie–Hellman and Naor–Reingold functions. Designs, Codes and Cryptography, 2019, 87 (1), pp.75-85. ⟨10.1007/s10623-018-0486-1⟩. ⟨hal-01990394⟩