A proposal for founding mistrustful quantum cryptography on coin tossing

A significant branch of classical cryptography deals with the problems which arise when mistrustful parties need to generate, process or exchange information. As Kilian showed a while ago, mistrustful classical cryptography can be founded on a single protocol, oblivious transfer, from which general secure multi-party computations can be built. The scope of mistrustful quantum cryptography is limited by no-go theorems, which rule out, inter alia, unconditionally secure quantum protocols for oblivious transfer or general secure two-party computations. These theorems apply even to protocols which take relativistic signalling constraints into account. The best that can be hoped for, in general, are quantum protocols computationally secure against quantum attack. I describe here a method for building a classically certified bit commitment, and hence every other mistrustful cryptographic task, from a secure coin tossing protocol. No security proof is attempted, but I sketch reasons why these protocols might resist quantum computational attack.Comment: Title altered in deference to Physical Review's fear of question marks. Published version; references update

Insecurity of position-based quantum cryptography protocols against entanglement attacks

Recently, position-based quantum cryptography has been claimed to be unconditionally secure. In contrary, here we show that the existing proposals for position-based quantum cryptography are, in fact, insecure if entanglement is shared among two adversaries. Specifically, we demonstrate how the adversaries can incorporate ideas of quantum teleportation and quantum secret sharing to compromise the security with certainty. The common flaw to all current protocols is that the Pauli operators always map a codeword to a codeword (up to an irrelevant overall phase). We propose a modified scheme lacking this property in which the same cheating strategy used to undermine the previous protocols can succeed with a rate at most 85%. We conjecture that the modified protocol is unconditionally secure and prove this to be true when the shared quantum resource between the adversaries is a two- or three- level system

A Fourier approach to cloud motion estimation

A Fourier technique is described for estimating cloud motion from pairs of pictures using the phase of the cross spectral density. The method allows motion estimates to be made for individual spatial frequencies, which are related to cloud pattern dimensions. Results obtained are presented and compared with the results of a Fourier domain cross correlation scheme. Using both artificial and real cloud data show that the technique is relatively sensitive to the presence of mixtures of motions, changes in cloud shape, and edge effects

On the communication cost of entanglement transformations

We study the amount of communication needed for two parties to transform some given joint pure state into another one, either exactly or with some fidelity. Specifically, we present a method to lower bound this communication cost even when the amount of entanglement does not increase. Moreover, the bound applies even if the initial state is supplemented with unlimited entanglement in the form of EPR pairs, and the communication is allowed to be quantum mechanical. We then apply the method to the determination of the communication cost of asymptotic entanglement concentration and dilution. While concentration is known to require no communication whatsoever, the best known protocol for dilution, discovered by Lo and Popescu [Phys. Rev. Lett. 83(7):1459--1462, 1999], requires a number of bits to be exchanged which is of the order of the square root of the number of EPR pairs. Here we prove a matching lower bound of the same asymptotic order, demonstrating the optimality of the Lo-Popescu protocol up to a constant factor and establishing the existence of a fundamental asymmetry between the concentration and dilution tasks. We also discuss states for which the minimal communication cost is proportional to their entanglement, such as the states recently introduced in the context of ``embezzling entanglement'' [W. van Dam and P. Hayden, quant-ph/0201041].Comment: 9 pages, 1 figure. Added a reference and some further explanations. In v3 some arguments are given in more detai

Coin Tossing is Strictly Weaker Than Bit Commitment

We define cryptographic assumptions applicable to two mistrustful parties who each control two or more separate secure sites between which special relativity guarantees a time lapse in communication. We show that, under these assumptions, unconditionally secure coin tossing can be carried out by exchanges of classical information. We show also, following Mayers, Lo and Chau, that unconditionally secure bit commitment cannot be carried out by finitely many exchanges of classical or quantum information. Finally we show that, under standard cryptographic assumptions, coin tossing is strictly weaker than bit commitment. That is, no secure classical or quantum bit commitment protocol can be built from a finite number of invocations of a secure coin tossing black box together with finitely many additional information exchanges.Comment: Final version; to appear in Phys. Rev. Let

A decoy-state protocol for quantum cryptography with 4 intensities of coherent states

In order to beat any type of photon-number-splitting attack, we propose a protocol for quantum key distributoin (QKD) using 4 different intensities of pulses. They are vacuum and coherent states with mean photon number $\mu,\mu'$ and $\mu_s$. $\mu_s$ is around 0.55 and this class of pulses are used as the main signal states. The other two classes of coherent states ($\mu,\mu'$) are also used signal states but their counting rates should be studied jointly with the vacuum. We have shown that, given the typical set-up in practice, the key rate from the main signal pulses is quite close to the theoretically allowed maximal rate in the case given the small overall transmittance of $10^{-4}$

Field-induced structure transformation in electrorheological solids

We have computed the local electric field in a body-centered tetragonal (BCT) lattice of point dipoles via the Ewald-Kornfeld formulation, in an attempt to examine the effects of a structure transformation on the local field strength. For the ground state of an electrorheological solid of hard spheres, we identified a novel structure transformation from the BCT to the face-centered cubic (FCC) lattices by changing the uniaxial lattice constant c under the hard sphere constraint. In contrast to the previous results, the local field exhibits a non-monotonic transition from BCT to FCC. As c increases from the BCT ground state, the local field initially decreases rapidly towards the isotropic value at the body-centered cubic lattice, decreases further, reaching a minimum value and increases, passing through the isotropic value again at an intermediate lattice, reaches a maximum value and finally decreases to the FCC value. An experimental realization of the structure transformation is suggested. Moreover, the change in the local field can lead to a generalized Clausius-Mossotti equation for the BCT lattices.Comment: Submitted to Phys. Rev.