# Information Security and Cryptography Research Group

## On the Randomness of Independent Experiments

### Thomas Holenstein and Renato Renner

Aug 2006, Available at http://arxiv.org/abs/cs.IT/0608007.

Given a probability distribution P, what is the minimum amount of bits needed to store a value x sampled according to P, such that x can later be recovered (except with some small probability)? Or, what is the maximum amount of uniform randomness that can be extracted from x? Answering these and similar information-theoretic questions typically boils down to computing so-called smooth entropies. In this paper, we derive explicit and almost tight bounds on the smooth entropies of n-fold product distributions.

## BibTeX Citation

@misc{HolRen06,
author       = {Thomas Holenstein and Renato Renner},
title        = {On the Randomness of Independent Experiments},
year         = 2006,
month        = 8,
note         = {Available at http://arxiv.org/abs/cs.IT/0608007},
}