Polynomial interpolation of cryptographic functions related to Diffie–Hellman and discrete logarithm problem

Recently, the first author introduced some cryptographic functions closely related to the Diffie–Hellman problem called P-Diffie–Hellman functions. We show that the existence of a low-degree polynomial representing a P-Diffie–Hellman function on a large set would lead to an efficient algorithm for solving the Diffie–Hellman problem. Motivated by this result we prove lower bounds on the degree of such interpolation polynomials. Analogously, we introduce a class of functions related to the discrete logarithm and show similar reduction and interpolation results.