84 research outputs found
Leftover Hashing Against Quantum Side Information
The Leftover Hash Lemma states that the output of a two-universal hash
function applied to an input with sufficiently high entropy is almost uniformly
random. In its standard formulation, the lemma refers to a notion of randomness
that is (usually implicitly) defined with respect to classical side
information. Here, we prove a (strictly) more general version of the Leftover
Hash Lemma that is valid even if side information is represented by the state
of a quantum system. Furthermore, our result applies to arbitrary delta-almost
two-universal families of hash functions. The generalized Leftover Hash Lemma
has applications in cryptography, e.g., for key agreement in the presence of an
adversary who is not restricted to classical information processing
Non-Asymptotic Analysis of Privacy Amplification via Renyi Entropy and Inf-Spectral Entropy
This paper investigates the privacy amplification problem, and compares the
existing two bounds: the exponential bound derived by one of the authors and
the min-entropy bound derived by Renner. It turns out that the exponential
bound is better than the min-entropy bound when a security parameter is rather
small for a block length, and that the min-entropy bound is better than the
exponential bound when a security parameter is rather large for a block length.
Furthermore, we present another bound that interpolates the exponential bound
and the min-entropy bound by a hybrid use of the Renyi entropy and the
inf-spectral entropy.Comment: 6 pages, 4 figure
Variations on Classical and Quantum Extractors
Many constructions of randomness extractors are known to work in the presence
of quantum side information, but there also exist extractors which do not
[Gavinsky {\it et al.}, STOC'07]. Here we find that spectral extractors
with a bound on the second largest eigenvalue
are quantum-proof. We then discuss fully
quantum extractors and call constructions that also work in the presence of
quantum correlations decoupling. As in the classical case we show that spectral
extractors are decoupling. The drawback of classical and quantum spectral
extractors is that they always have a long seed, whereas there exist classical
extractors with exponentially smaller seed size. For the quantum case, we show
that there exists an extractor with extremely short seed size
, where denotes the quality of the
randomness. In contrast to the classical case this is independent of the input
size and min-entropy and matches the simple lower bound
.Comment: 7 pages, slightly enhanced IEEE ISIT submission including all the
proof
Source-device-independent heterodyne-based quantum random number generator at 17 Gbps
For many applications, quantum random number generation should be fast and independent from assumptions on the apparatus. Here, the authors devise and implement an approach which assumes a trusted detector but not a trusted source, and allows random bit generations at ~17 Gbps using off-the-shelf components
Insider-proof encryption with applications for quantum key distribution
It has been pointed out that current protocols for device independent quantum
key distribution can leak key to the adversary when devices are used repeatedly
and that this issue has not been addressed. We introduce the notion of an
insider-proof channel. This allows us to propose a means by which devices with
memories could be reused from one run of a device independent quantum key
distribution protocol to the next while bounding the leakage to Eve, under the
assumption that one run of the protocol could be completed securely using
devices with memories.Comment: 20 pages, version 2: new presentation introducing the insider-proof
channel as a cryptographic elemen
Source-independent quantum random number generation
Quantum random number generators can provide genuine randomness by appealing
to the fundamental principles of quantum mechanics. In general, a physical
generator contains two parts---a randomness source and its readout. The source
is essential to the quality of the resulting random numbers; hence, it needs to
be carefully calibrated and modeled to achieve information-theoretical provable
randomness. However, in practice, the source is a complicated physical system,
such as a light source or an atomic ensemble, and any deviations in the
real-life implementation from the theoretical model may affect the randomness
of the output. To close this gap, we propose a source-independent scheme for
quantum random number generation in which output randomness can be certified,
even when the source is uncharacterized and untrusted. In our randomness
analysis, we make no assumptions about the dimension of the source. For
instance, multiphoton emissions are allowed in optical implementations. Our
analysis takes into account the finite-key effect with the composable security
definition. In the limit of large data size, the length of the input random
seed is exponentially small compared to that of the output random bit. In
addition, by modifying a quantum key distribution system, we experimentally
demonstrate our scheme and achieve a randomness generation rate of over
bit/s.Comment: 11 pages, 7 figure
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