70 research outputs found
Quantum Circuit Implementation and Resource Analysis of LBlock and LiCi
Due to Grover's algorithm, any exhaustive search attack of block ciphers can
achieve a quadratic speed-up. To implement Grover,s exhaustive search and
accurately estimate the required resources, one needs to implement the target
ciphers as quantum circuits. Recently, there has been increasing interest in
quantum circuits implementing lightweight ciphers. In this paper we present the
quantum implementations and resource estimates of the lightweight ciphers
LBlock and LiCi. We optimize the quantum circuit implementations in the number
of gates, required qubits and the circuit depth, and simulate the quantum
circuits on ProjectQ. Furthermore, based on the quantum implementations, we
analyze the resources required for exhaustive key search attacks of LBlock and
LiCi with Grover's algorithm. Finally, we compare the resources for
implementing LBlock and LiCi with those of other lightweight ciphers.Comment: 29 pages,21 figure
Quantum Simulation Logic, Oracles, and the Quantum Advantage
Query complexity is a common tool for comparing quantum and classical
computation, and it has produced many examples of how quantum algorithms differ
from classical ones. Here we investigate in detail the role that oracles play
for the advantage of quantum algorithms. We do so by using a simulation
framework, Quantum Simulation Logic (QSL), to construct oracles and algorithms
that solve some problems with the same success probability and number of
queries as the quantum algorithms. The framework can be simulated using only
classical resources at a constant overhead as compared to the quantum resources
used in quantum computation. Our results clarify the assumptions made and the
conditions needed when using quantum oracles. Using the same assumptions on
oracles within the simulation framework we show that for some specific
algorithms, like the Deutsch-Jozsa and Simon's algorithms, there simply is no
advantage in terms of query complexity. This does not detract from the fact
that quantum query complexity provides examples of how a quantum computer can
be expected to behave, which in turn has proved useful for finding new quantum
algorithms outside of the oracle paradigm, where the most prominent example is
Shor's algorithm for integer factorization.Comment: 48 pages, 46 figure
Quantum linearization attacks
Recent works have shown that quantum period-finding can be used to break many popular constructions (some block ciphers such as Even-Mansour, multiple MACs and AEs...) in the superposition query model. So far, all the constructions broken exhibited a strong algebraic structure, which enables to craft a periodic function of a single input block. Recoverin
Quantum forgery attacks on COPA,AES-COPA and marble authenticated encryption algorithms
The classic forgery attacks on COPA, AES-COPA and Marble authenticated
encryption algorithms need to query about 2^(n/2) times, and their success
probability is not high. To solve this problem, the corresponding quantum
forgery attacks on COPA, AES-COPA and Marble authenticated encryption
algorithms are presented. In the quantum forgery attacks on COPA and AES-COPA,
we use Simon's algorithm to find the period of the tag generation function in
COPA and AES-COPA by querying in superposition, and then generate a forged tag
for a new message. In the quantum forgery attack on Marble, Simon's algorithm
is used to recover the secret parameter L, and the forged tag can be computed
with L. Compared with classic forgery attacks on COPA, AES-COPA and Marble, our
attack can reduce the number of queries from O(2^(n/2)) to O(n) and improve
success probability close to 100%.Comment: 21 pages, 11 figure
Homomorphic Encryption of the k=2 Bernstein-Vazirani Algorithm
The nonrecursive Bernstein-Vazirani algorithm was the first quantum algorithm
to show a superpolynomial improvement over the corresponding best classical
algorithm. Here we define a class of circuits that solve a particular case of
this problem for second-level recursion. This class of circuits simplifies the
number of gates required to construct the oracle by making it grow linearly
with the number of qubits in the problem. We find an application of this scheme
to quantum homomorphic encryption (QHE) which is an important cryptographic
technology useful for delegated quantum computation. It allows a remote server
to perform quantum computations on encrypted quantum data, so that the server
cannot know anything about the client's data. Liang developed QHE schemes with
perfect security, -homomorphism, no interaction between server and
client, and quasi-compactness bounded by where M is the number of gates
in the circuit. Precisely these schemes are suitable for circuits with a
polynomial number of gates . Following these schemes, the
simplified circuits we have constructed can be evaluated homomorphically in an
efficient way.Comment: Revtex file, color figure
Cryptography from tensor problems
We describe a new proposal for a trap-door one-way function. The new proposal belongs to the "multivariate quadratic" family but the trap-door is different from existing methods, and is simpler
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