221 research outputs found
Inside the Hypercube
Bernstein\u27s CubeHash is a hash function family that includes four functions submitted to the NIST Hash Competition. A CubeHash function is parametrized by a number of rounds r, a block byte size b, and a digest bit length h (the compression function makes r rounds, while the finalization function makes 10r rounds). The 1024-bit internal state of CubeHash is represented as a five-dimensional hypercube. The submissions to NIST recommends r=8, b=1, and h in {224,256,384,512}.
This paper presents the first external analysis of CubeHash, with: improved standard generic attacks for collisions and preimages; a multicollision attack that exploits fixed points; a study of the round function symmetries; a preimage attack that exploits these symmetries; a practical collision attack on a weakened version of CubeHash; a study of fixed points and an example of nontrivial fixed point; high-probability truncated differentials over 10 rounds.
Since the first publication of these results, several collision attacks for reduced versions of CubeHash were published by Dai, Peyrin, et al. Our results are more general, since they apply to any choice of the parameters, and show intrinsic properties of the CubeHash design, rather than attacks on specific versions
Portfolio selection using neural networks
In this paper we apply a heuristic method based on artificial neural networks
in order to trace out the efficient frontier associated to the portfolio
selection problem. We consider a generalization of the standard Markowitz
mean-variance model which includes cardinality and bounding constraints. These
constraints ensure the investment in a given number of different assets and
limit the amount of capital to be invested in each asset. We present some
experimental results obtained with the neural network heuristic and we compare
them to those obtained with three previous heuristic methods.Comment: 12 pages; submitted to "Computers & Operations Research
Multi-qubit stabilizer and cluster entanglement witnesses
One of the problems concerning entanglement witnesses (EWs) is the
construction of them by a given set of operators. Here several multi-qubit EWs
called stabilizer EWs are constructed by using the stabilizer operators of some
given multi-qubit states such as GHZ, cluster and exceptional states. The
general approach to manipulate the multi-qubit stabilizer EWs by
exact(approximate) linear programming (LP) method is described and it is shown
that the Clifford group play a crucial role in finding the hyper-planes
encircling the feasible region. The optimality, decomposability and
non-decomposability of constructed stabilizer EWs are discussed.Comment: 57 pages, 2 figure
The component structure of dense random subgraphs of the hypercube
Given , we let be the random subgraph of the
-dimensional hypercube where edges are present independently with
probability . It is well known that, as , if
then with high probability is connected; and if
then with high probability consists of one giant component together with
many smaller components which form the `fragment'. Here we fix , and investigate the fragment, and how it sits inside the
hypercube. In particular we give asymptotic estimates for the mean numbers of
components in the fragment of each size, and describe their asymptotic
distributions and indeed their joint distribution, much extending earlier work
of Weber
Bell-states diagonal entanglement witnesses for relativistic and non-relativistic multispinor systems in arbitrary dimensions
Two kinds of Bell-states diagonal (BSD) entanglement witnesses (EW) are
constructed by using the algebra of Dirac matrices in the space-time
of arbitrary dimension , where the first kind can detect some BSD
relativistic and non-relativistic -partite multispinor bound entangled
states in Hilbert space of dimension , including the
bipartite Bell-type and iso-concurrence type states in the four-dimensional
space-time (). By using the connection between Hilbert-Schmidt measure and
the optimal EWs associated with states, it is shown that as far as the spin
quantum correlations is concerned, the amount of entanglement is not a
relativistic scalar and has no invariant meaning. The introduced EWs are
manipulated via the linear programming (LP) which can be solved exactly by
using simplex method. The decomposability or non-decomposability of these EWs
is investigated, where the region of non-decomposable EWs of the first kind is
partially determined and it is shown that, all of the EWs of the second kind
are decomposable. These EWs have the preference that in the bipartite systems,
they can determine the region of separable states, i.e., bipartite
non-detectable density matrices of the same type as the EWs of the first kind
are necessarily separable. Also, multispinor EWs with non-polygon feasible
regions are provided, where the problem is solved by approximate LP, and in
contrary to the exactly manipulatable EWs, both the first and second kind of
the optimal approximate EWs can detect some bound entangled states.
Keywords: Relativistic entanglement, Entanglement Witness, Multispinor,
Linear Programming, Feasible Region. PACs Index: 03.65.UdComment: 62 page
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