A modular framework for randomness extraction based on Trevisan's construction

TL;DR

This paper presents a flexible, high-performance implementation of Trevisan's randomness extractor, analyzing its practical properties, improving theoretical proofs, and providing explicit non-asymptotic results, with applications in cryptography and quantum security.

Contribution

It introduces a modular, extensible implementation of Trevisan's extractor, enhancing theoretical analysis and providing practical, explicit non-asymptotic performance results.

Findings

Improved theoretical proofs of Trevisan's extractor.

Explicit non-asymptotic performance results.

Flexible implementation adaptable to various scenarios.

Abstract

Informally, an extractor delivers perfect randomness from a source that may be far away from the uniform distribution, yet contains some randomness. This task is a crucial ingredient of any attempt to produce perfectly random numbers---required, for instance, by cryptographic protocols, numerical simulations, or randomised computations. Trevisan's extractor raised considerable theoretical interest not only because of its data parsimony compared to other constructions, but particularly because it is secure against quantum adversaries, making it applicable to quantum key distribution. We discuss a modular, extensible and high-performance implementation of the construction based on various building blocks that can be flexibly combined to satisfy the requirements of a wide range of scenarios. Besides quantitatively analysing the properties of many combinations in practical settings, we improve previous theoretical proofs, and give explicit results for non-asymptotic cases. The self-contained description does not assume familiarity with extractors.