109 research outputs found
Cryptography in the Bounded Quantum-Storage Model
We initiate the study of two-party cryptographic primitives with unconditional
security, assuming that the adversaryâs quantum memory is of bounded size. We show that oblivious
transfer and bit commitment can be implemented in this model using protocols where honest parties
need no quantum memory, whereas an adversarial player needs quantum memory of size at least n/2
in order to break the protocol, where n is the number of qubits transmitted. This is in sharp contrast
to the classical bounded-memory model, where we can only tolerate adversaries with memory of size
quadratic in honest playersâ memory size. Our protocols are efficient and noninteractive and can be
implemented using todayâs technology. On the technical side, a new entropic uncertainty relation
involving min-entropy is established
Cryptography in the Bounded-Quantum-Storage Model
This thesis initiates the study of cryptographic protocols in the
bounded-quantum-storage model. On the practical side, simple protocols for
Rabin Oblivious Transfer, 1-2 Oblivious Transfer and Bit Commitment are
presented. No quantum memory is required for honest players, whereas the
protocols can only be broken by an adversary controlling a large amount of
quantum memory. The protocols are efficient, non-interactive and can be
implemented with today's technology.
On the theoretical side, new entropic uncertainty relations involving
min-entropy are established and used to prove the security of protocols
according to new strong security definitions. For instance, in the realistic
setting of Quantum Key Distribution (QKD) against quantum-memory-bounded
eavesdroppers, the uncertainty relation allows to prove the security of QKD
protocols while tolerating considerably higher error rates compared to the
standard model with unbounded adversaries.Comment: PhD Thesis, BRICS, University of Aarhus, Denmark, 128 page
Robust Cryptography in the Noisy-Quantum-Storage Model
It was shown in [WST08] that cryptographic primitives can be implemented
based on the assumption that quantum storage of qubits is noisy. In this work
we analyze a protocol for the universal task of oblivious transfer that can be
implemented using quantum-key-distribution (QKD) hardware in the practical
setting where honest participants are unable to perform noise-free operations.
We derive trade-offs between the amount of storage noise, the amount of noise
in the operations performed by the honest participants and the security of
oblivious transfer which are greatly improved compared to the results in
[WST08]. As an example, we show that for the case of depolarizing noise in
storage we can obtain secure oblivious transfer as long as the quantum
bit-error rate of the channel does not exceed 11% and the noise on the channel
is strictly less than the quantum storage noise. This is optimal for the
protocol considered. Finally, we show that our analysis easily carries over to
quantum protocols for secure identification.Comment: 34 pages, 2 figures. v2: clarified novelty of results, improved
security analysis using fidelity-based smooth min-entropy, v3: typos and
additivity proof in appendix correcte
Practical Quantum Bit Commitment Protocol
A quantum protocol for bit commitment the security of which is based on
technological limitations on nondemolition measurements and long-term quantum
memory is presented.Comment: Quantum Inf. Process. (2011
Quantum computing on encrypted data
The ability to perform computations on encrypted data is a powerful tool for
protecting privacy. Recently, protocols to achieve this on classical computing
systems have been found. Here we present an efficient solution to the quantum
analogue of this problem that enables arbitrary quantum computations to be
carried out on encrypted quantum data. We prove that an untrusted server can
implement a universal set of quantum gates on encrypted quantum bits (qubits)
without learning any information about the inputs, while the client, knowing
the decryption key, can easily decrypt the results of the computation. We
experimentally demonstrate, using single photons and linear optics, the
encryption and decryption scheme on a set of gates sufficient for arbitrary
quantum computations. Because our protocol requires few extra resources
compared to other schemes it can be easily incorporated into the design of
future quantum servers. These results will play a key role in enabling the
development of secure distributed quantum systems
Conditional entropic uncertainty relations for Tsallis entropies
The entropic uncertainty relations are a very active field of scientific
inquiry. Their applications include quantum cryptography and studies of quantum
phenomena such as correlations and non-locality. In this work we find
entanglement-dependent entropic uncertainty relations in terms of the Tsallis
entropies for states with a fixed amount of entanglement. Our main result is
stated as Theorem~\ref{th:bound}. Taking the special case of von Neumann
entropy and utilizing the concavity of conditional von Neumann entropies, we
extend our result to mixed states. Finally we provide a lower bound on the
amount of extractable key in a quantum cryptographic scenario.Comment: 11 pages, 4 figure
A Tight High-Order Entropic Quantum Uncertainty Relation With Applications
We derive a new entropic quantum uncertainty relation involving min-entropy.
The relation is tight and can be applied in various quantum-cryptographic
settings.
Protocols for quantum 1-out-of-2 Oblivious Transfer and quantum Bit
Commitment are presented and the uncertainty relation is used to prove the
security of these protocols in the bounded quantum-storage model according to
new strong security definitions.
As another application, we consider the realistic setting of Quantum Key
Distribution (QKD) against quantum-memory-bounded eavesdroppers. The
uncertainty relation allows to prove the security of QKD protocols in this
setting while tolerating considerably higher error rates compared to the
standard model with unbounded adversaries. For instance, for the six-state
protocol with one-way communication, a bit-flip error rate of up to 17% can be
tolerated (compared to 13% in the standard model).
Our uncertainty relation also yields a lower bound on the min-entropy key
uncertainty against known-plaintext attacks when quantum ciphers are composed.
Previously, the key uncertainty of these ciphers was only known with respect to
Shannon entropy.Comment: 21 pages; editorial changes, additional applicatio
Quantum Cryptography Beyond Quantum Key Distribution
Quantum cryptography is the art and science of exploiting quantum mechanical
effects in order to perform cryptographic tasks. While the most well-known
example of this discipline is quantum key distribution (QKD), there exist many
other applications such as quantum money, randomness generation, secure two-
and multi-party computation and delegated quantum computation. Quantum
cryptography also studies the limitations and challenges resulting from quantum
adversaries---including the impossibility of quantum bit commitment, the
difficulty of quantum rewinding and the definition of quantum security models
for classical primitives. In this review article, aimed primarily at
cryptographers unfamiliar with the quantum world, we survey the area of
theoretical quantum cryptography, with an emphasis on the constructions and
limitations beyond the realm of QKD.Comment: 45 pages, over 245 reference
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