Evaluating Entropy Sources for True Random Number Generators by Collision Counting

The general approach to evaluate the quality of entropy sources used in true random number generators is to estimate minentropy, which is based on estimating frequencies of all possible source outcomes. This method is space inefficient, for example for a source producing 30-bit outputs it needs 30Gb of storage to get an error smaller than one bit per sample. We show that for some popular designs estimating min-entropy can be replaced by much more efficient counting the number of collisions between consecutive samples. Namely, we propose an estimator for the collision entropy of a sequence of i.i.d samples X-1,..., X-n. The estimator utilizes a simple collision counting technique, and has the following features Is memory-efficient (reads samples in a forward-only mode, uses O(1) storage) Can be coupled with every min-entropy extractor, losing only extra log(1/is an element of) bits. We implemented our estimator with an iPhone accelerometer as the entropy source, and Toeplitz-matrix based universal hashing as an extractor. The quality of this TRNG was confirmed by applying the NIST tests suite.