Aitken and Neville inverse interpolation methods for the Lucas logarithm problem

The Lucas function is a recently proposed one-way function used in public key cryptography. The security of cryptosystems based on the Lucas function relies on the difficulty of solving the Lucas logarithm problem. In this paper, the Lucas logarithm problem is studied using interpolation techniques. In particular, the inverse Aitken and the inverse Neville interpolation methods are applied to values of the Lucas sequence to obtain a polynomial that interpolates the Lucas logarithm. The results indicate that in all the considered instances of the problem a polynomial of low degree that interpolates the desired values exists.