947 research outputs found
Grover's Quantum Search Algorithm for an Arbitrary Initial Mixed State
The Grover quantum search algorithm is generalized to deal with an arbitrary
mixed initial state. The probability to measure a marked state as a function of
time is calculated, and found to depend strongly on the specific initial state.
The form of the function, though, remains as it is in the case of initial pure
state. We study the role of the von Neumann entropy of the initial state, and
show that the entropy cannot be a measure for the usefulness of the algorithm.
We give few examples and show that for some extremely mixed initial states
carrying high entropy, the generalized Grover algorithm is considerably faster
than any classical algorithm.Comment: 4 pages. See http://www.cs.technion.ac.il/~danken/MSc-thesis.pdf for
extended discussio
Algebraic analysis of quantum search with pure and mixed states
An algebraic analysis of Grover's quantum search algorithm is presented for
the case in which the initial state is an arbitrary pure quantum state of n
qubits. This approach reveals the geometrical structure of the quantum search
process, which turns out to be confined to a four-dimensional subspace of the
Hilbert space. This work unifies and generalizes earlier results on the time
evolution of the amplitudes during the quantum search, the optimal number of
iterations and the success probability. Furthermore, it enables a direct
generalization to the case in which the initial state is a mixed state,
providing an exact formula for the success probability.Comment: 13 page
A simple proof of the unconditional security of quantum key distribution
Quantum key distribution is the most well-known application of quantum
cryptography. Previous proposed proofs of security of quantum key distribution
contain various technical subtleties. Here, a conceptually simpler proof of
security of quantum key distribution is presented. The new insight is the
invariance of the error rate of a teleportation channel: We show that the error
rate of a teleportation channel is independent of the signals being
transmitted. This is because the non-trivial error patterns are permuted under
teleportation. This new insight is combined with the recently proposed quantum
to classical reduction theorem. Our result shows that assuming that Alice and
Bob have fault-tolerant quantum computers, quantum key distribution can be made
unconditionally secure over arbitrarily long distances even against the most
general type of eavesdropping attacks and in the presence of all types of
noises.Comment: 13 pages, extended abstract. Comments will be appreciate
Modified Bennett-Brassard 1984 Quantum Key Distribution With Two-way Classical Communications
The quantum key distribution protocol without public announcement of bases is
equipped with a two-way classical communication symmetric entanglement
purification protocol. This modified key distribution protocol is
unconditionally secure and has a higher tolerable error rate of 20%, which is
higher than previous scheme without public announcement of bases.Comment: 5 pages. To appear in Physical Review
On differential uniformity of maps that may hide an algebraic trapdoor
We investigate some differential properties for permutations in the affine
group, of a vector space V over the binary field, with respect to a new group
operation , inducing an alternative vector space structure on .Comment: arXiv admin note: text overlap with arXiv:1411.768
Quantum Key Distribution with Classical Bob
Secure key distribution among two remote parties is impossible when both are
classical, unless some unproven (and arguably unrealistic)
computation-complexity assumptions are made, such as the difficulty of
factorizing large numbers. On the other hand, a secure key distribution is
possible when both parties are quantum.
What is possible when only one party (Alice) is quantum, yet the other (Bob)
has only classical capabilities? We present a protocol with this constraint,
and prove its robustness against attacks: we prove that any attempt of an
adversary to obtain information (and even a tiny amount of information)
necessarily induces some errors that the legitimate users could notice.Comment: 4 and a bit pages, 1 figure, RevTe
Boomerang Connectivity Table:A New Cryptanalysis Tool
A boomerang attack is a cryptanalysis framework that regards a block cipher as the composition of two sub-ciphers and builds a particular characteristic for with probability by combining differential characteristics for and with probability and , respectively.
Crucially the validity of this figure is under the assumption that the characteristics for and can be chosen independently. Indeed, Murphy has shown that independently chosen characteristics may turn out to be incompatible. On the other hand, several researchers observed that the probability can be improved to or around the boundary between and by considering a positive dependency of the two characteristics, e.g.~the ladder switch and S-box switch by Biryukov and Khovratovich.
This phenomenon was later formalised by Dunkelman et al.~as a sandwich attack that regards as , where satisfies some differential propagation among four texts with probability , and the entire probability is .
In this paper, we revisit the issue of dependency of two characteristics in , and propose a new tool called Boomerang Connectivity Table (BCT), which evaluates in a systematic and easy-to-understand way when is composed of a single S-box layer. With the BCT, previous observations on the S-box including the incompatibility, the ladder switch and the S-box switch are represented in a unified manner. Moreover, the BCT can detect a new switching effect, which shows that the probability around the boundary may be even higher than or .
To illustrate the power of the BCT-based analysis, we improve boomerang attacks against Deoxys-BC, and disclose the mechanism behind an unsolved probability amplification for generating a quartet in SKINNY. Lastly, we discuss the issue of searching for S-boxes having good BCT and extending the analysis to modular addition
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