Distribution and Polynomial Interpolation of the Dodis-Yampolskiy Pseudo-Random Function

Thierry Mefenza (1, 2) , Damien Vergnaud (1, 2)

1 CASCADE - Construction and Analysis of Systems for Confidentiality and Authenticity of Data and Entities
2 DI-ENS - Département d'informatique - ENS Paris

We give some theoretical support to the security of the cryptographic pseudo-random function proposed by Dodis and Yampolskiy in 2005. We study the distribution of the function values over general finite fields and over elliptic curves defined over prime finite fields. We also prove lower bounds on the degree of polynomials interpolating the values of these functions in these two settings.

Keywords: Dodis-Yampolskiy pseudo-random function; discrepancy; polynomial interpolation; finite fields; elliptic curves

Domains: Cryptography and Security [cs.CR]

Thierry Mefenza, Damien Vergnaud. Distribution and Polynomial Interpolation of the Dodis-Yampolskiy Pseudo-Random Function. Arithmetic of Finite Fields - 6th International Workshop, WAIFI 2016, Jul 2016, Ghent, Belgium. pp.125-140, ⟨10.1007/978-3-319-55227-9_10⟩. ⟨hal-02571888⟩