# Universal Security for Randomness Expansion from the Spot-Checking Protocol

@article{Miller2017UniversalSF, title={Universal Security for Randomness Expansion from the Spot-Checking Protocol}, author={Carl A. Miller and Yaoyun Shi}, journal={SIAM J. Comput.}, year={2017}, volume={46}, pages={1304-1335} }

Colbeck [Ph.D. thesis, 2006] proposed using Bell inequality violations to generate certified random numbers. While full quantum-security proofs have been given, it remains a major open problem to identify the broadest class of Bell inequalities and lowest performance requirements to achieve such security. In this paper, working within the broad class of spot-checking protocols, we prove exactly which Bell inequality violations can be used to achieve full security. Our result greatly improves…

## 69 Citations

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The minimum von Neumann entropies for a given CHSH score are found and the gain that can be made by using the two-sided randomness and by using a protocol without spot-checking where the input randomness is recycled.

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The minimum von Neumann entropies for a given CHSH score are found and the gain that can be made by using the two-sided randomness and by using a protocol without spot-checking where the input randomness is recycled.

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## References

SHOWING 1-10 OF 29 REFERENCES

Robust protocols for securely expanding randomness and distributing keys using untrusted quantum devices

- Computer Science, MathematicsSTOC
- 2014

This work shows how to expand a random seed at an exponential rate without trusting the underlying quantum devices, and has the following new features: tolerating a constant level of implementation imprecision, requiring only a unit size quantum memory per device component for the honest implementation, and allowing a large natural class of constructions.

Security and Composability of Randomness Expansion from Bell Inequalities

- Computer ScienceArXiv
- 2011

A meaningful lower bound on the min-entropy of the data produced by an untrusted device based on the observed nonlocal behavior of the device is obtained and confirms the essence of the (improperly formulated) claims of Pironio et al. and puts them on solid ground.

Physical Randomness Extractors: Generating Random Numbers with Minimal Assumptions

- Computer Science, Mathematics
- 2014

The Equivalence Lemma, a general principle for proving composition security of untrusted-device protocols, implies that unbounded randomness expansion can be achieved simply by cross-feeding any two expansion protocols, and can be made robust, which is known for the first time.

Security of practical private randomness generation

- Computer Science
- 2013

It is pointed out that in most real, practical situations, where the concept of device independence is used as a protection against unintentional flaws or failures of the quantum apparatuses, it is sufficient to show that the generated string is random with respect to an adversary that holds only classical side information; i.e., proving randomness against quantum side information is not necessary.

Bounding the seed length of Miller and Shi's unbounded randomness expansion protocol

- Computer Science, Mathematics
- 2014

An analysis of the required seed size is presented, giving explicit upper bounds for the number of initial random bits needed to jump-start the protocol.

Contextuality offers device-independent security

- Computer Science
- 2010

This work shows that if two persons share systems which locally exhibit the Kochen-Specker paradox, then they can extract secure key, even if they do not trust the quantum devices, which is the first operational protocol that directly implements the fundamental feature of Nature: the information gain vs. disturbance trade-off.

Certifiable quantum dice: or, true random number generation secure against quantum adversaries

- Computer ScienceSTOC '12
- 2012

A modified protocol uses a seed of O(log3 n) uniformly random bits to generate n bits that are poly-1(n)-indistinguishable from uniform even from the point of view of a quantum adversary who may have had prior access to the devices, and may be entangled with them.

Quantum-Proof Randomness Extractors via Operator Space Theory

- MathematicsIEEE Transactions on Information Theory
- 2017

It is argued that the theory of operator spaces offers a natural framework for studying to what extent extractors are secure against quantum adversaries: it is shown that very high min-entropy extractors as well as extractors with small output are always (approximately) quantum-proof.

Multi-Source Randomness Extractors Against Quantum Side Information, and their Applications

- Computer ScienceElectron. Colloquium Comput. Complex.
- 2014

A new model called General Entangled (GE) Adversary Model, which allows arbitrary entanglement in the side information and subsumes both the IA model and the BS model is proposed, and equivalence between strong OA-security and strong GE-security is established.

Optimal robust quantum self-testing by binary nonlocal XOR games

- Mathematics
- 2012

Self-testing a quantum device means verifying the existence of a certain quantum state as well as the effect of the associated measurements based only on the statistics of the measurement outcomes.…