370 research outputs found
Physical Randomness Extractors: Generating Random Numbers with Minimal Assumptions
How to generate provably true randomness with minimal assumptions? This
question is important not only for the efficiency and the security of
information processing, but also for understanding how extremely unpredictable
events are possible in Nature. All current solutions require special structures
in the initial source of randomness, or a certain independence relation among
two or more sources. Both types of assumptions are impossible to test and
difficult to guarantee in practice. Here we show how this fundamental limit can
be circumvented by extractors that base security on the validity of physical
laws and extract randomness from untrusted quantum devices. In conjunction with
the recent work of Miller and Shi (arXiv:1402:0489), our physical randomness
extractor uses just a single and general weak source, produces an arbitrarily
long and near-uniform output, with a close-to-optimal error, secure against
all-powerful quantum adversaries, and tolerating a constant level of
implementation imprecision. The source necessarily needs to be unpredictable to
the devices, but otherwise can even be known to the adversary.
Our central technical contribution, the Equivalence Lemma, provides a general
principle for proving composition security of untrusted-device protocols. It
implies that unbounded randomness expansion can be achieved simply by
cross-feeding any two expansion protocols. In particular, such an unbounded
expansion can be made robust, which is known for the first time. Another
significant implication is, it enables the secure randomness generation and key
distribution using public randomness, such as that broadcast by NIST's
Randomness Beacon. Our protocol also provides a method for refuting local
hidden variable theories under a weak assumption on the available randomness
for choosing the measurement settings.Comment: A substantial re-writing of V2, especially on model definitions. An
abstract model of robustness is added and the robustness claim in V2 is made
rigorous. Focuses on quantum-security. A future update is planned to address
non-signaling securit
Quantum to Classical Randomness Extractors
The goal of randomness extraction is to distill (almost) perfect randomness
from a weak source of randomness. When the source yields a classical string X,
many extractor constructions are known. Yet, when considering a physical
randomness source, X is itself ultimately the result of a measurement on an
underlying quantum system. When characterizing the power of a source to supply
randomness it is hence a natural question to ask, how much classical randomness
we can extract from a quantum system. To tackle this question we here take on
the study of quantum-to-classical randomness extractors (QC-extractors). We
provide constructions of QC-extractors based on measurements in a full set of
mutually unbiased bases (MUBs), and certain single qubit measurements. As the
first application, we show that any QC-extractor gives rise to entropic
uncertainty relations with respect to quantum side information. Such relations
were previously only known for two measurements. As the second application, we
resolve the central open question in the noisy-storage model [Wehner et al.,
PRL 100, 220502 (2008)] by linking security to the quantum capacity of the
adversary's storage device.Comment: 6+31 pages, 2 tables, 1 figure, v2: improved converse parameters,
typos corrected, new discussion, v3: new reference
Multiplexed Quantum Random Number Generation
Fast secure random number generation is essential for high-speed encrypted
communication, and is the backbone of information security. Generation of truly
random numbers depends on the intrinsic randomness of the process used and is
usually limited by electronic bandwidth and signal processing data rates. Here
we use a multiplexing scheme to create a fast quantum random number generator
structurally tailored to encryption for distributed computing, and high
bit-rate data transfer. We use vacuum fluctuations measured by seven homodyne
detectors as quantum randomness sources, multiplexed using a single integrated
optical device. We obtain a random number generation rate of 3.08 Gbit/s, from
only 27.5 MHz of sampled detector bandwidth. Furthermore, we take advantage of
the multiplexed nature of our system to demonstrate an unseeded strong
extractor with a generation rate of 26 Mbit/s.Comment: 10 pages, 3 figures and 1 tabl
Quantum-proof randomness extractors via operator space theory
Quantum-proof randomness extractors are an important building block for
classical and quantum cryptography as well as device independent randomness
amplification and expansion. Furthermore they are also a useful tool in quantum
Shannon theory. It is known that some extractor constructions are quantum-proof
whereas others are provably not [Gavinsky et al., STOC'07]. We argue that the
theory of operator spaces offers a natural framework for studying to what
extent extractors are secure against quantum adversaries: we first phrase the
definition of extractors as a bounded norm condition between normed spaces, and
then show that the presence of quantum adversaries corresponds to a completely
bounded norm condition between operator spaces. From this we show that very
high min-entropy extractors as well as extractors with small output are always
(approximately) quantum-proof. We also study a generalization of extractors
called randomness condensers. We phrase the definition of condensers as a
bounded norm condition and the definition of quantum-proof condensers as a
completely bounded norm condition. Seeing condensers as bipartite graphs, we
then find that the bounded norm condition corresponds to an instance of a well
studied combinatorial problem, called bipartite densest subgraph. Furthermore,
using the characterization in terms of operator spaces, we can associate to any
condenser a Bell inequality (two-player game) such that classical and quantum
strategies are in one-to-one correspondence with classical and quantum attacks
on the condenser. Hence, we get for every quantum-proof condenser (which
includes in particular quantum-proof extractors) a Bell inequality that can not
be violated by quantum mechanics.Comment: v3: 34 pages, published versio
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