7,555 research outputs found
Quantum Collision-Resistance of Non-Uniformly Distributed Functions
We study the quantum query complexity of finding a collision for a function whose outputs are chosen according to a distribution with min-entropy . We prove that quantum queries are necessary to find a collision for function . This is needed in some security proofs in the quantum random oracle model (e.g. Fujisaki-Okamoto transform)
Quantum Collision-Resistance of Non-uniformly Distributed Functions: Upper and Lower Bounds
We study the quantum query complexity of finding a collision for a function whose outputs are chosen according to a non-uniform distribution . We derive some upper bounds and lower bounds depending on the min-entropy and the collision-entropy of . In particular, we improve the previous lower bound by Ebrahimi, Tabia, and Unruh from to where is the min-entropy of
Quantum-secure message authentication via blind-unforgeability
Formulating and designing unforgeable authentication of classical messages in
the presence of quantum adversaries has been a challenge, as the familiar
classical notions of unforgeability do not directly translate into meaningful
notions in the quantum setting. A particular difficulty is how to fairly
capture the notion of "predicting an unqueried value" when the adversary can
query in quantum superposition. In this work, we uncover serious shortcomings
in existing approaches, and propose a new definition. We then support its
viability by a number of constructions and characterizations. Specifically, we
demonstrate a function which is secure according to the existing definition by
Boneh and Zhandry, but is clearly vulnerable to a quantum forgery attack,
whereby a query supported only on inputs that start with 0 divulges the value
of the function on an input that starts with 1. We then propose a new
definition, which we call "blind-unforgeability" (or BU.) This notion matches
"intuitive unpredictability" in all examples studied thus far. It defines a
function to be predictable if there exists an adversary which can use
"partially blinded" oracle access to predict values in the blinded region. Our
definition (BU) coincides with standard unpredictability (EUF-CMA) in the
classical-query setting. We show that quantum-secure pseudorandom functions are
BU-secure MACs. In addition, we show that BU satisfies a composition property
(Hash-and-MAC) using "Bernoulli-preserving" hash functions, a new notion which
may be of independent interest. Finally, we show that BU is amenable to
security reductions by giving a precise bound on the extent to which quantum
algorithms can deviate from their usual behavior due to the blinding in the BU
security experiment.Comment: 23+9 pages, v3: published version, with one theorem statement in the
summary of results correcte
Making Existential-Unforgeable Signatures Strongly Unforgeable in the Quantum Random-Oracle Model
Strongly unforgeable signature schemes provide a more stringent security
guarantee than the standard existential unforgeability. It requires that not
only forging a signature on a new message is hard, it is infeasible as well to
produce a new signature on a message for which the adversary has seen valid
signatures before. Strongly unforgeable signatures are useful both in practice
and as a building block in many cryptographic constructions.
This work investigates a generic transformation that compiles any
existential-unforgeable scheme into a strongly unforgeable one, which was
proposed by Teranishi et al. and was proven in the classical random-oracle
model. Our main contribution is showing that the transformation also works
against quantum adversaries in the quantum random-oracle model. We develop
proof techniques such as adaptively programming a quantum random-oracle in a
new setting, which could be of independent interest. Applying the
transformation to an existential-unforgeable signature scheme due to Cash et
al., which can be shown to be quantum-secure assuming certain lattice problems
are hard for quantum computers, we get an efficient quantum-secure strongly
unforgeable signature scheme in the quantum random-oracle model.Comment: 15 pages, to appear in Proceedings TQC 201
Wave: A New Family of Trapdoor One-Way Preimage Sampleable Functions Based on Codes
We present here a new family of trapdoor one-way Preimage Sampleable
Functions (PSF) based on codes, the Wave-PSF family. The trapdoor function is
one-way under two computational assumptions: the hardness of generic decoding
for high weights and the indistinguishability of generalized -codes.
Our proof follows the GPV strategy [GPV08]. By including rejection sampling, we
ensure the proper distribution for the trapdoor inverse output. The domain
sampling property of our family is ensured by using and proving a variant of
the left-over hash lemma. We instantiate the new Wave-PSF family with ternary
generalized -codes to design a "hash-and-sign" signature scheme which
achieves existential unforgeability under adaptive chosen message attacks
(EUF-CMA) in the random oracle model. For 128 bits of classical security,
signature sizes are in the order of 15 thousand bits, the public key size in
the order of 4 megabytes, and the rejection rate is limited to one rejection
every 10 to 12 signatures.Comment: arXiv admin note: text overlap with arXiv:1706.0806
Quantum Lazy Sampling and Game-Playing Proofs for Quantum Indifferentiability
Game-playing proofs constitute a powerful framework for non-quantum
cryptographic security arguments, most notably applied in the context of
indifferentiability. An essential ingredient in such proofs is lazy sampling of
random primitives. We develop a quantum game-playing proof framework by
generalizing two recently developed proof techniques. First, we describe how
Zhandry's compressed quantum oracles~(Crypto'19) can be used to do quantum lazy
sampling of a class of non-uniform function distributions. Second, we observe
how Unruh's one-way-to-hiding lemma~(Eurocrypt'14) can also be applied to
compressed oracles, providing a quantum counterpart to the fundamental lemma of
game-playing. Subsequently, we use our game-playing framework to prove quantum
indifferentiability of the sponge construction, assuming a random internal
function
Random Oracles in a Quantum World
The interest in post-quantum cryptography - classical systems that remain
secure in the presence of a quantum adversary - has generated elegant proposals
for new cryptosystems. Some of these systems are set in the random oracle model
and are proven secure relative to adversaries that have classical access to the
random oracle. We argue that to prove post-quantum security one needs to prove
security in the quantum-accessible random oracle model where the adversary can
query the random oracle with quantum states.
We begin by separating the classical and quantum-accessible random oracle
models by presenting a scheme that is secure when the adversary is given
classical access to the random oracle, but is insecure when the adversary can
make quantum oracle queries. We then set out to develop generic conditions
under which a classical random oracle proof implies security in the
quantum-accessible random oracle model. We introduce the concept of a
history-free reduction which is a category of classical random oracle
reductions that basically determine oracle answers independently of the history
of previous queries, and we prove that such reductions imply security in the
quantum model. We then show that certain post-quantum proposals, including ones
based on lattices, can be proven secure using history-free reductions and are
therefore post-quantum secure. We conclude with a rich set of open problems in
this area.Comment: 38 pages, v2: many substantial changes and extensions, merged with a
related paper by Boneh and Zhandr
Transport Properties near the z=2 Insulator-Superconductor Transition
We consider here the fluctuation conductivity near the point of the
insulator-superconductor transition in a system of regular Josephson junction
arrays in the presence of particle-hole asymmetry or equivalently homogeneous
charge frustration. The transition is characterised by the dynamic critical
exponent , opening the possibility of the perturbative
renormalization-group (RG) treatment. The quartic interaction in the
Ginzburg-Landau action and the coupling to the Ohmic heat bath, giving the
finite quasiparticle life-time, lead to the non-monotonic behavior of the dc
conductivity as a function of temperature in the leading logarithmic
approximation.Comment: Revised version for publication. To appear in PR
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