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

@article{Mauerer2012AMF, title={A modular framework for randomness extraction based on Trevisan's construction}, author={Wolfgang Mauerer and Christopher Portmann and Volkher B. Scholz}, journal={ArXiv}, year={2012}, volume={abs/1212.0520} }

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…

## 29 Citations

### A Modular Framework for Quantum-Proof Randomness Extractors

- Mathematics, Computer ScienceInternational Journal of Theoretical Physics
- 2016

A modular framework is given to combine multi-bit output extractors (not only one-bit) with pseudorandom transform, and it is shown that it is sound in the presence of quantum side information and the security of two- bit output extractor is discussed by giving a tighter bound for it.

### A Modular Framework for Quantum-Proof Randomness Extractors

- Mathematics, Computer Science
- 2016

A modular framework is given to combine multi-bit output extractors (not only one-bit) with pseudorandom transform, and it is shown that it is sound in the presence of quantum side information and the security of two- bit output extractor is discussed by giving a tighter bound for it.

### Experimentally generated randomness certified by the impossibility of superluminal signals

- Computer ScienceNature
- 2018

1,024 random bits that are uniformly distributed to within 10−12 and unpredictable assuming the impossibility of superluminal communication are generated and certified using a loophole-free Bell test and a protocol is described that is optimized for devices that are characterized by a low per-trial violation of Bell inequalities.

### Quantum-proof multi-source randomness extractors in the Markov model

- Computer Science, MathematicsTQC
- 2016

It is proved that any multi-source extractor remains secure in the presence of quantum side information of this type (albeit with weaker parameters), which improves on previous results in which more restricted models were considered and the security of only some types of extractors was shown.

### An adaptive framework for quantum-secure device-independent randomness expansion

- Computer Science, Mathematics
- 2018

A protocol that robustly generates up to two bits of randomness per entangled qubit pair, which is twice that established in existing analyses of the spot-checking CHSH protocol in the low noise regime.

### Practical randomness and privacy amplification.

- Computer Science
- 2020

We present the first complete implementation of a randomness and privacy amplification protocol based on Bell tests. This allows the building of device-independent random number generators which…

### A Framework for Quantum-Secure Device-Independent Randomness Expansion

- Computer Science, MathematicsIEEE Transactions on Information Theory
- 2020

A protocol that robustly generates up to two bits of randomness per entangled qubit pair, which is twice that established in existing analyses of the spot-checking CHSH protocol in the low noise regime.

### Practical randomness amplification and privatisation with implementations on quantum computers

- Computer Science
- 2020

We present an end-to-end and practical randomness ampliﬁcation and privatisation protocol based on Bell tests. This allows the building of device-independent random number generators which output…

### Device-Independent Quantum Key Distribution

- PhysicsArXiv
- 2021

This paper presents a large-scale simulation of the response of the immune system to laser-spot assisted, 3D image analysis and shows the importance of knowing the number of cells in the nervous system and how they respond to laser treatment.

### Continuous Variable Optimisation of Quantum Randomness and Probabilistic Linear Amplification

- Computer Science
- 2018

This thesis presents the optimisation of experimental parameters for secure randomness generation and proposes a non-deterministic approach to enhance amplification of CV quantum state and concerns the improvement in the transmission of a quantum state.

## References

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Here, it is shown that the well-known construction paradigm for extractors proposed by Trevisan is sound in the presence of quantum side information and exploited the modularity of this paradigm to give several concrete extractor constructions.

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This work proposes a general “sample-then-extract” approach to constructing locally computable extractors: use essentially any randomness-efficient sampler to select bits from the input and then apply any extractor to the selected bits.

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It is shown that an encryption scheme with such nice properties can be derived immediately from any strong randomness extractor, a function which extracts randomness from a slightly random source, so that its output and its seed together are almost random.

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It is proved that certain extractors are suitable for key expansion in the bounded-storage model where the adversary has a limited amount of quantum memory.

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It is shown that, using the simpler Nisan--Wigderson generator and standard error-correcting codes, one can build even better extractors with the additional advantage that both the construction and the analysis are simple and admit a short self-contained description.

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