Speaker recognition systems classify a test signal as a speaker or an imposter by evaluating a matching score between input and reference signals. We propose a new information theoretic approach for computation of the matching score using the Rényi entropy. The proposed entropic distance, the Kernelized Rényi distance (KRD), is formulated in a non-parametric way and the resulting measure is efficiently evaluated in a parallelized fashion on a graphical processor. The distance is then adapted as a scoring function and its performance compared with other popular scoring approaches in a speaker identification and speaker verification framework.