387 research outputs found
Robust Randomness Amplifiers: Upper and Lower Bounds
A recent sequence of works, initially motivated by the study of the nonlocal
properties of entanglement, demonstrate that a source of
information-theoretically certified randomness can be constructed based only on
two simple assumptions: the prior existence of a short random seed and the
ability to ensure that two black-box devices do not communicate (i.e. are
non-signaling). We call protocols achieving such certified amplification of a
short random seed randomness amplifiers.
We introduce a simple framework in which we initiate the systematic study of
the possibilities and limitations of randomness amplifiers. Our main results
include a new, improved analysis of a robust randomness amplifier with
exponential expansion, as well as the first upper bounds on the maximum
expansion achievable by a broad class of randomness amplifiers. In particular,
we show that non-adaptive randomness amplifiers that are robust to noise cannot
achieve more than doubly exponential expansion. Finally, we show that a wide
class of protocols based on the use of the CHSH game can only lead to (singly)
exponential expansion if adversarial devices are allowed the full power of
non-signaling strategies. Our upper bound results apply to all known
non-adaptive randomness amplifier constructions to date.Comment: 28 pages. Comments welcom
Simple extractors via constructions of cryptographic pseudo-random generators
Trevisan has shown that constructions of pseudo-random generators from hard
functions (the Nisan-Wigderson approach) also produce extractors. We show that
constructions of pseudo-random generators from one-way permutations (the
Blum-Micali-Yao approach) can be used for building extractors as well. Using
this new technique we build extractors that do not use designs and
polynomial-based error-correcting codes and that are very simple and efficient.
For example, one extractor produces each output bit separately in
time. These extractors work for weak sources with min entropy , for
arbitrary constant , have seed length , and their
output length is .Comment: 21 pages, an extended abstract will appear in Proc. ICALP 2005; small
corrections, some comments and references adde
Secure self-calibrating quantum random bit generator
Random bit generators (RBGs) are key components of a variety of information
processing applications ranging from simulations to cryptography. In
particular, cryptographic systems require "strong" RBGs that produce
high-entropy bit sequences, but traditional software pseudo-RBGs have very low
entropy content and therefore are relatively weak for cryptography. Hardware
RBGs yield entropy from chaotic or quantum physical systems and therefore are
expected to exhibit high entropy, but in current implementations their exact
entropy content is unknown. Here we report a quantum random bit generator
(QRBG) that harvests entropy by measuring single-photon and entangled
two-photon polarization states. We introduce and implement a quantum
tomographic method to measure a lower bound on the "min-entropy" of the system,
and we employ this value to distill a truly random bit sequence. This approach
is secure: even if an attacker takes control of the source of optical states, a
secure random sequence can be distilled.Comment: 5 pages, 2 figure
A PCP Characterization of AM
We introduce a 2-round stochastic constraint-satisfaction problem, and show
that its approximation version is complete for (the promise version of) the
complexity class AM. This gives a `PCP characterization' of AM analogous to the
PCP Theorem for NP. Similar characterizations have been given for higher levels
of the Polynomial Hierarchy, and for PSPACE; however, we suggest that the
result for AM might be of particular significance for attempts to derandomize
this class.
To test this notion, we pose some `Randomized Optimization Hypotheses'
related to our stochastic CSPs that (in light of our result) would imply
collapse results for AM. Unfortunately, the hypotheses appear over-strong, and
we present evidence against them. In the process we show that, if some language
in NP is hard-on-average against circuits of size 2^{Omega(n)}, then there
exist hard-on-average optimization problems of a particularly elegant form.
All our proofs use a powerful form of PCPs known as Probabilistically
Checkable Proofs of Proximity, and demonstrate their versatility. We also use
known results on randomness-efficient soundness- and hardness-amplification. In
particular, we make essential use of the Impagliazzo-Wigderson generator; our
analysis relies on a recent Chernoff-type theorem for expander walks.Comment: 18 page
Security of practical private randomness generation
Measurements on entangled quantum systems necessarily yield outcomes that are
intrinsically unpredictable if they violate a Bell inequality. This property
can be used to generate certified randomness in a device-independent way, i.e.,
without making detailed assumptions about the internal working of the quantum
devices used to generate the random numbers. Furthermore these numbers are also
private, i.e., they appear random not only to the user, but also to any
adversary that might possess a perfect description of the devices. Since this
process requires a small initial random seed, one usually speaks of
device-independent randomness expansion.
The purpose of this paper is twofold. First, we point 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. Furthermore, the initial
random seed does not need to be private with respect to the adversary, provided
that it is generated in a way that is independent from the measured systems.
The devices, though, will generate cryptographically-secure randomness that
cannot be predicted by the adversary and thus one can, given access to free
public randomness, talk about private randomness generation.
The theoretical tools to quantify the generated randomness according to these
criteria were already introduced in [S. Pironio et al, Nature 464, 1021
(2010)], but the final results were improperly formulated. The second aim of
this paper is to correct this inaccurate formulation and therefore lay out a
precise theoretical framework for practical device-independent randomness
expansion.Comment: 18 pages. v3: important changes: the present version focuses on
security against classical side-information and a discussion about the
significance of these results has been added. v4: minor changes. v5: small
typos correcte
Перспективи розвитку експортоорієнтованої стратегії підприємств
Рассмотрен вопрос стратегического развития экспортноориентрованной политики предприятий. Раскрыты перспективы развития международных торговых отношений Украины.Розглянуто питання стратегічного розвитку експортноорієнтовної політики підприємств. Розкрито перспективи розвитку міжнародних торгівельних відносин України
From Low-Distortion Norm Embeddings to Explicit Uncertainty Relations and Efficient Information Locking
The existence of quantum uncertainty relations is the essential reason that
some classically impossible cryptographic primitives become possible when
quantum communication is allowed. One direct operational manifestation of these
uncertainty relations is a purely quantum effect referred to as information
locking. A locking scheme can be viewed as a cryptographic protocol in which a
uniformly random n-bit message is encoded in a quantum system using a classical
key of size much smaller than n. Without the key, no measurement of this
quantum state can extract more than a negligible amount of information about
the message, in which case the message is said to be "locked". Furthermore,
knowing the key, it is possible to recover, that is "unlock", the message. In
this paper, we make the following contributions by exploiting a connection
between uncertainty relations and low-distortion embeddings of L2 into L1. We
introduce the notion of metric uncertainty relations and connect it to
low-distortion embeddings of L2 into L1. A metric uncertainty relation also
implies an entropic uncertainty relation. We prove that random bases satisfy
uncertainty relations with a stronger definition and better parameters than
previously known. Our proof is also considerably simpler than earlier proofs.
We apply this result to show the existence of locking schemes with key size
independent of the message length. We give efficient constructions of metric
uncertainty relations. The bases defining these metric uncertainty relations
are computable by quantum circuits of almost linear size. This leads to the
first explicit construction of a strong information locking scheme. Moreover,
we present a locking scheme that is close to being implementable with current
technology. We apply our metric uncertainty relations to exhibit communication
protocols that perform quantum equality testing.Comment: 60 pages, 5 figures. v4: published versio
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