We may enforce an information flow policy by encrypting a protected resource and ensuring that only users authorized by the policy are able to decrypt the resource. In most schemes in the literature that use symmetric cryptographic primitives, each user is assigned a single secret and derives decryption keys using this secret and publicly available information. Recent work has challenged this approach by developing schemes, based on a chain partition of the information flow policy, that do not require public information for key derivation, the trade-off being that a user may need to be assigned more than one secret. In general, many different chain partitions exist for the same policy and, until now, it was not known how to compute an appropriate one. In this paper, we introduce the notion of a tree partition, of which chain partitions are a special case. We show how a tree partition may be used to define a cryptographic enforcement scheme and prove that such schemes can be instantiated in such a way as to preserve the strongest security properties known for cryptographic enforcement schemes. We establish a number of results linking the amount of secret material that needs to be distributed to users with a weighted acyclic graph derived from the tree partition. These results enable us to develop efficient algorithms for deriving tree and chain partitions that minimize the amount of secret material that needs to be distributed.
The significant open problem with prior work on chain-based schemes is the assumption that the chain partition is part of the input to the algorithm: there may be many such partitions and it is not immediately obvious how one should select a specific partition in order to optimize characteristics of the corresponding enforcement scheme (an example being to minimize the number of secrets issued). Hence, it seems very natural to ask how difficult it is to compute a good'' chain partition, given that Our recent work @cite_2 shows that it is possible to compute a minimal chain partition in polynomial time using a minimum cost network flow algorithm.
@cite_2
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The simple security property in an information flow policy can be enforced by encrypting data objects and distributing an appropriate secret to each user. A user derives a suitable decryption key from the secret and publicly available information. A chain-based enforcement scheme provides an alternative method of cryptographic enforcement that does not require any public information, the trade-off being that a user may require more than one secret. For a given information flow policy, there will be many different possible chain-based enforcement schemes. In this paper, we provide a polynomial-time algorithm for selecting a chain-based scheme which uses the minimum possible number of secrets. We also compute the number of secrets that will be required and establish an upper bound on the number of secrets required by any user. We present a model for video segmentation, applicable to RGB (and if available RGB-D) information that constructs multiple plausible partitions corresponding to the static and the moving objects in the scene: i) we generate multiple figure-ground segmentations, in each frame, parametrically, based on boundary and optical flow cues, then track, link and refine the salient segment chains corresponding to the different objects, over time, using long-range temporal constraints, ii) a video partition is obtained by composing segment chains into consistent tilings, where the different individual object chains explain the video and do not overlap. Saliency metrics based on figural and motion cues, as well as measures learned from human eye movements are exploited, with substantial gain, at the level of segment generation and chain construction, in order to produce compact sets of hypotheses which correctly reflect the qualities of the different configurations. The model makes it possible to compute multiple hypotheses over both individual object segmentations tracked over time, and for complete video partitions. We report quantitative, state of the art results in the SegTrack single object benchmark, and promising qualitative and quantitative results in clips filming multiple static and moving objects collected from Hollywood movies and from the MIT dataset. A joint degree matrix (JDM) specifies the number of connections between nodes of given degrees in a graph, for all degree pairs, and uniquely determines the degree sequence of the graph. We consider the space of all balanced realizations of an arbitrary JDM, realizations in which the links between any two fixed-degree groups of nodes are placed as uniformly as possible. We prove that a swap Markov chain Monte Carlo algorithm in the space of all balanced realizations of an arbitrary graphical JDM mixes rapidly, i.e., the relaxation time of the chain is bounded from above by a polynomial in the number of nodes @math . To prove fast mixing, we first prove a general factorization theorem similar to the Martin--Randall method for disjoint decompositions (partitions). This theorem can be used to bound from below the spectral gap with the help of fast mixing subchains within every partition and a bound on an auxiliary Markov chain between the partitions. Our proof of the general factorization theorem is direct and ... Parallel Matrix-Matrix Multiplication (MMM) is a fundamental part of the linear algebra libraries used by scientific applications on high performance computers. As heterogeneous systems have emerged as high performance computing platforms, the traditional homogeneous algorithms have been adapted to these heterogeneous environments. Although heterogeneous systems have been in use for some time, it remains an open problem of how to optimally partition data on heterogeneous processors to minimize computation, communication, and execution time. While the question of how to subdivide these MMM problems among heterogeneous processors has been studied, the underlying assumption of this prior study is that the data partition shape, the layout of the data within the matrix assigned to each processor, should be rectangular, i.e. that each processor should be assigned a rectangular portion of the matrix to compute. Our previous work in this area questioned the optimality of this traditional rectangular shape and studied this partition shape problem for two processors. In that work, we proposed a novel mathematical method for transforming partition shapes to decrease communication cost and an analytical technique for determining the optimal shape. In this work, we extend this technique to apply to three and more heterogeneous processors. While applying this method to two processors is relatively straightforward, the complexity grows immensely when considering three processors. With this complexity in mind, we propose a hybrid of experimental and analytical techniques. We postulate that a small number of partition shapes are potentially optimal, and perform extensive testing using a computer aided method to apply our previously developed analytical technique, without finding a counterexample. We identified six data partition shapes which are candidates to be the optimal three processor shape.