76 research outputs found
Quantum Coins
One of the earliest cryptographic applications of quantum information was to
create quantum digital cash that could not be counterfeited. In this paper, we
describe a new type of quantum money: quantum coins, where all coins of the
same denomination are represented by identical quantum states. We state
desirable security properties such as anonymity and unforgeability and propose
two candidate quantum coin schemes: one using black box operations, and another
using blind quantum computation.Comment: 12 pages, 4 figure
Quantum Tokens for Digital Signatures
The fisherman caught a quantum fish. "Fisherman, please let me go", begged
the fish, "and I will grant you three wishes". The fisherman agreed. The fish
gave the fisherman a quantum computer, three quantum signing tokens and his
classical public key. The fish explained: "to sign your three wishes, use the
tokenized signature scheme on this quantum computer, then show your valid
signature to the king, who owes me a favor".
The fisherman used one of the signing tokens to sign the document "give me a
castle!" and rushed to the palace. The king executed the classical verification
algorithm using the fish's public key, and since it was valid, the king
complied.
The fisherman's wife wanted to sign ten wishes using their two remaining
signing tokens. The fisherman did not want to cheat, and secretly sailed to
meet the fish. "Fish, my wife wants to sign ten more wishes". But the fish was
not worried: "I have learned quantum cryptography following the previous story
(The Fisherman and His Wife by the brothers Grimm). The quantum tokens are
consumed during the signing. Your polynomial wife cannot even sign four wishes
using the three signing tokens I gave you".
"How does it work?" wondered the fisherman. "Have you heard of quantum money?
These are quantum states which can be easily verified but are hard to copy.
This tokenized quantum signature scheme extends Aaronson and Christiano's
quantum money scheme, which is why the signing tokens cannot be copied".
"Does your scheme have additional fancy properties?" the fisherman asked.
"Yes, the scheme has other security guarantees: revocability, testability and
everlasting security. Furthermore, if you're at sea and your quantum phone has
only classical reception, you can use this scheme to transfer the value of the
quantum money to shore", said the fish, and swam away.Comment: Added illustration of the abstract to the ancillary file
Quantum Cryptography II: How to re-use a one-time pad safely even if P=NP
When elementary quantum systems, such as polarized photons, are used to
transmit digital information, the uncertainty principle gives rise to novel
cryptographic phenomena unachievable with traditional transmission media, e.g.
a communications channel on which it is impossible in principle to eavesdrop
without a high probability of being detected. With such a channel, a one-time
pad can safely be reused many times as long as no eavesdrop is detected, and,
planning ahead, part of the capacity of these uncompromised transmissions can
be used to send fresh random bits with which to replace the one-time pad when
an eavesdrop finally is detected. Unlike other schemes for stretching a
one-time pad, this scheme does not depend on complexity-theoretic assumptions
such as the difficulty of factoring.Comment: Original 1982 submission to ACM Symposium on Theory of Computing with
spelling and typographical corrections, and comments by the authors 32 years
later. Submitted to Natural Computin
A formal definition and a new security mechanism of physical unclonable functions
The characteristic novelty of what is generally meant by a "physical
unclonable function" (PUF) is precisely defined, in order to supply a firm
basis for security evaluations and the proposal of new security mechanisms. A
PUF is defined as a hardware device which implements a physical function with
an output value that changes with its argument. A PUF can be clonable, but a
secure PUF must be unclonable. This proposed meaning of a PUF is cleanly
delineated from the closely related concepts of "conventional unclonable
function", "physically obfuscated key", "random-number generator", "controlled
PUF" and "strong PUF". The structure of a systematic security evaluation of a
PUF enabled by the proposed formal definition is outlined. Practically all
current and novel physical (but not conventional) unclonable physical functions
are PUFs by our definition. Thereby the proposed definition captures the
existing intuition about what is a PUF and remains flexible enough to encompass
further research. In a second part we quantitatively characterize two classes
of PUF security mechanisms, the standard one, based on a minimum secret
read-out time, and a novel one, based on challenge-dependent erasure of stored
information. The new mechanism is shown to allow in principle the construction
of a "quantum-PUF", that is absolutely secure while not requiring the storage
of an exponentially large secret. The construction of a PUF that is
mathematically and physically unclonable in principle does not contradict the
laws of physics.Comment: 13 pages, 1 figure, Conference Proceedings MMB & DFT 2012,
Kaiserslautern, German
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
Quantum Copy-Protection and Quantum Money
Forty years ago, Wiesner proposed using quantum states to create money that
is physically impossible to counterfeit, something that cannot be done in the
classical world. However, Wiesner's scheme required a central bank to verify
the money, and the question of whether there can be unclonable quantum money
that anyone can verify has remained open since. One can also ask a related
question, which seems to be new: can quantum states be used as copy-protected
programs, which let the user evaluate some function f, but not create more
programs for f? This paper tackles both questions using the arsenal of modern
computational complexity. Our main result is that there exist quantum oracles
relative to which publicly-verifiable quantum money is possible, and any family
of functions that cannot be efficiently learned from its input-output behavior
can be quantumly copy-protected. This provides the first formal evidence that
these tasks are achievable. The technical core of our result is a
"Complexity-Theoretic No-Cloning Theorem," which generalizes both the standard
No-Cloning Theorem and the optimality of Grover search, and might be of
independent interest. Our security argument also requires explicit
constructions of quantum t-designs. Moving beyond the oracle world, we also
present an explicit candidate scheme for publicly-verifiable quantum money,
based on random stabilizer states; as well as two explicit schemes for
copy-protecting the family of point functions. We do not know how to base the
security of these schemes on any existing cryptographic assumption. (Note that
without an oracle, we can only hope for security under some computational
assumption.)Comment: 14-page conference abstract; full version hasn't appeared and will
never appear. Being posted to arXiv mostly for archaeological purposes.
Explicit money scheme has since been broken by Lutomirski et al
(arXiv:0912.3825). Other quantum money material has been superseded by
results of Aaronson and Christiano (coming soon). Quantum copy-protection
ideas will hopefully be developed in separate wor
Current and voltage based bit errors and their combined mitigation for the Kirchhoff-law-Johnson-noise secure key exchange
We classify and analyze bit errors in the current measurement mode of the
Kirchhoff-law-Johnson-noise (KLJN) key distribution. The error probability
decays exponentially with increasing bit exchange period and fixed bandwidth,
which is similar to the error probability decay in the voltage measurement
mode. We also analyze the combination of voltage and current modes for error
removal. In this combination method, the error probability is still an
exponential function that decays with the duration of the bit exchange period,
but it has superior fidelity to the former schemes.Comment: 9 pages, accepted for publication in Journal of Computational
Electronic
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