### Abstract

We perform a direct analysis of the protocol of randomness amplification based on Bell inequality violations in terms of the convex combination of no-signaling boxes required to simulate quantum violation of the inequality. The probability distributions of bits generated by a Santha-Vazirani source are shown to be mixtures of permutations of Bernoulli distributions with parameter defined by the source. An intuitive proof is provided for the range of partial randomness from which perfect randomness can be extracted using quantum correlations violating the bipartite chain inequalities. Exact values are derived in the asymptotic limit of a large number of measurement settings.