Online test based on mutual information for true random number generators

Abstract

Shannon entropy is one of the widely used randomness mea- sures especially for cryptographic applications. However, the conventional entropy tests are less sensitive to the inter-bit dependency in random sam- ples. In this paper, we propose new online randomness test schemes for true random number generators (TRNGs) based on the mutual infor- mation between consecutive k-bit output blocks for testing of inter-bit dependency in random samples. By estimating the block entropies of distinct lengths at the same time, it is possible to measure the mutual information, which is closely related to the amount of the statistical de- pendency between two consecutive data blocks. In addition, we propose a new estimation method for entropies, which accumulates intermediate values of the number of frequencies. The proposed method can estimate entropy with less samples than Maurer-Coron type entropy test can. By numerical simulations, it is shown that the new proposed scheme can be used as a reliable online entropy estimator for TRNGs used by crypto- graphic modules. © 2013 The Korean Mathematical Society.