<p>The need for broadcast encryption arises when a sender wishes to securely distribute messages to varying subsets of receivers, using a broadcast channel, for instance in a pay-TV scenario. This is done by selecting subsets of users and giving all users in the same subset a common decryption key. The subsets will in general be overlapping so that each user belongs to many subsets and has several different decryption keys. When the sender wants to send a message to some users, the message is encrypted using keys that those users have. In this thesis we describe some broadcast encryption schemes that have been proposed in the literature. We focus on stateless schemes which do not require receivers to update their decryption keys after the initial keys have been received; particularly we concentrate on the Subset Difference (SD) scheme.</p><p>We consider the effects that the logical placement of the receivers in the tree structure used by the SD scheme has on the number of required transmissions for each message. Bounds for the number of required transmissions are derived based on the adjacency of receivers in the tree structure. The tree structure itself is also studied, also resulting in bounds on the number of required transmissions based on the placement of the users in the tree structure.</p><p>By allowing a slight discrepancy between the set of receivers that the sender intends to send to and the set of receivers that actually can decrypt the message, we can reduce the cost in number of transmissions per message. We use the concept of distortion to quantify the discrepancy and develop three simple algorithms to illustrate how the cost and distortion are related.</p> / Report code: LIU-Tek-Lic-2005:70.

The master thesis is based upon a new type of linear-phase Nyquist finitie impulse responseinterpolator and decimator implemented using a tree-structure. The tree-structure decreasesthe complexity, considerably, compared to the ordinary single-stage interpolator structure.The computational complexity is comparable to a multi-stage Nyquist interpolator structure,but the proposed tree-structure has slightly higher delay. The tree-structure should still beconsidered since it can interpolate with an arbitrary number and all subfilters operate at thebase rate which is not the case for multi-stage Nyquist interpolators.

In this paper, we propose a novel approach of vector quantization using a merge-based hierarchical neural network. Vector quantization¡]VQ¡^is known as a very useful technique for lossy data compression. Recently, Neural network¡]NN¡^algorithms have been used for VQ. Vlajic and Card proposed a modified adaptive resonance theory (modified ART2¡^[1] which is a constructing tree structure clustering method. However, modified ART2 has disadvantages of slow construction rate and constructing many redundant levels. Therefore, we propose a more efficient approach for constructing the tree in this paper. Our method establishes only those required levels without losing the fidelity of a compressed image.

This thesis proposes and tests a recursive, adpative, and computationally inexpensive method for partitioning real-number spaces. When tested for proof-of-concept on both one- and two- dimensional classification and control problems, the Fern algorithm was found to work well in one dimension, moderately well for two-dimensional classification, and not at all for two-dimensional control. Testing ferns as pure discretizers - which would involve a secondary discrete learner - has been left to future work. / text

In the future, more data intensive applications, such as P2P auction networks, P2P job--search networks, P2P multi--player games, will require the capability to respond to more complex queries such as the nearest neighbor queries involving numerous data types. For the problem of answering nearest neighbor queries (NN query) for spatial region data in the P2P environment, a quadtree-based structure probably is a good choice. However, the quadtree stores the data in the leaf nodes, resulting in the load unbalance and expensive cost of any query. The MX--CIF quadtree can solve this problem. The MX--CIF quadtree has three properties: controlling efficiently the height of the tree, reducing load unbalance, and reducing the NNquery scope with controlling the value of the radius. Although the P2P MX--CIF quadtree can do the NN query efficiently, it still has some problems as follows: low accuracy of the nearest neighbor query, the expensive cost of the tree construction, the high search cost of the NN query, and load unbalance. In fact, the index structures for the region data can also work for the point data which can be considered as the degenerated case of the region data. Therefore, the KDB--tree which is a well-known algorithm for the point data can be used to reduce load unbalance, but it has the same problem as the quadtree. The data is stored only in the leaf nodes of the KDB--tree. In this thesis, we propose an Adjustable KDB--tree (AKDB--tree) to improve this situation for the P2P system. The AKDB--tree has five properties: reducing load unbalance, low cost of the tree construction, storing the data in the internal nodes and leaf nodes, high accuracy and low search cost of the NN query. The Chord system is a well--known structured P2P system in which the data search is performed by a hash function, instead of flooding used in most of the unstructured P2P system. Since the Chord system is a hash approach, it is easy to deal with peers joining/exiting. Besides, in order to combine AKDB--tree with the Chord system, we design the IDs of the nodes in the AKDB--tree. Each node is hashed to the Chord system by the ID. The IDs can be used to differentiate the edge node in the AKDB-tree is a vertical edge or a horizontal edge and the relative position of two nodes in the 2D space. And, we can calculate the related edge of a region in the 2D space according to the ID of the region. As discussed above, we make use of the property of IDs to reduce the search cost of the NN query by a wide margin. In our simulation study, we compare our method with the P2P MX--CIF quadtree by considering five performance measures under four different situations of the P2P MX--CIF quadtree. From our simulation results, for the NN query, our AKDB-tree can provide the higher accuracy and lower search cost than the P2P MX--CIF quadtree. For the problem of load, our AKDB-tree is more balance than the P2P MX--CIF quadtree. For the time of the tree construction, our AKDB-tree needs shorter time than the P2P MX--CIF quadtree.

We propose a balanced tree structure overlay on a peer-to-peer network capable of supporting both exact queries and range queries efficiently. In spite of the tree structure causing distinctions to be made between nodes at different levels in the tree, we show that the load at each node is approximately equal. In spite of the tree structure providing precisely one path between any pair of nodes, we show that sideways routing tables maintained at each node provide sufficient fault tolerance to permit efficient repair. Specifically, in a network with N nodes, we guarantee that both exact queries and range queries can be answered in O(logN) steps and also that update operations (to both data and network) have an amortized cost of O(logN). An experimental assessment validates the practicality of our proposal. / Singapore-MIT Alliance (SMA)

Ett spels karta är begränsande i det att när man valt en viss storlek kan man inte gå utanför den ramen utan att göra relativt resurskrävande operationer. Denna undersökning genomfördes för att se om en trädstruktur kan användas som lösning att hantera en honeycomb-struktur på ett lämpligt sätt för att ständigt kunna utöka ett spels karta. Resultatet visar att det är möjligt att använda trädstrukturen relativt bra till växande kartor men att det inte är att rekommendera till spel, eftersom strukturen i sig är en omväg. I samband med denna karta skapades en slumpmässig path-generator som skulle kunna användas till att generellt skapa slumpmässiga kartor i spel. För att se vad försvårigheter man stöter på när man utvecklar en slumpad map-generator, vilket visade sig vara svårt i och med att man hittade många specialfall.

The need for broadcast encryption arises when a sender wishes to securely distribute messages to varying subsets of receivers, using a broadcast channel, for instance in a pay-TV scenario. This is done by selecting subsets of users and giving all users in the same subset a common decryption key. The subsets will in general be overlapping so that each user belongs to many subsets and has several different decryption keys. When the sender wants to send a message to some users, the message is encrypted using keys that those users have. In this thesis we describe some broadcast encryption schemes that have been proposed in the literature. We focus on stateless schemes which do not require receivers to update their decryption keys after the initial keys have been received; particularly we concentrate on the Subset Difference (SD) scheme. We consider the effects that the logical placement of the receivers in the tree structure used by the SD scheme has on the number of required transmissions for each message. Bounds for the number of required transmissions are derived based on the adjacency of receivers in the tree structure. The tree structure itself is also studied, also resulting in bounds on the number of required transmissions based on the placement of the users in the tree structure. By allowing a slight discrepancy between the set of receivers that the sender intends to send to and the set of receivers that actually can decrypt the message, we can reduce the cost in number of transmissions per message. We use the concept of distortion to quantify the discrepancy and develop three simple algorithms to illustrate how the cost and distortion are related. / <p>Report code: LIU-Tek-Lic-2005:70.</p>

<p>A wave digital filter is derived from an analog filter, which is realized as classical doubly resistively terminated reactancefilters. Perfectly designed wave digital filters express good dynamic signal range, low roundoff noise and excellent stabilitycharacteristics with respect to nonlinearity which are produced due to finite wordlength effects. Wave digital filters inheritthe sensitivity properties from analog filters, therefore, coefficients values can be selected to favorable values.Wave digital filters, derived from ladder filters, have low coefficient sensitivity in the passband and stopband. These WDFsare very complicated and are non-modular. The lattice wave digital filters are modular and are not complex. However, theyhave very high sensitivity in the stopband and thus require large coefficient wordlengths. The number of coefficients equalsthe filter order which have to be odd.This thesis discusses the wave digital filter structures that are modular because they are designed by cascading the first-orderand second-order sections. These WDFs can be pipelined. They also exhibit all the above mentioned favorable properties.Similar to lattice WDFs, these structures are restricted to symmetrical and antisymmetrical transfer functions. The synthesisof these structures is based on the factorization of the scattering matrix of lossless two-ports.In this thesis work, lowpass wave digital filters based on circulator-tree structure are designed with different orders startingfrom 3 and going upto 13. In parallel to these circulator-tree wave digital filters, the simple digital filters are also designedwith the same specification. The results of the two filters are compared with each other. It is observed that impulse responseand attenuation response of the two kind of filters perfectly match. Therefore, it is can be concluded that circulator-tree WDFupto Nth order can be synthesized. The implementation examples of two filter with order 3 and order 7 is presented in thisdocumentation for ready reference. It has also been shown that the order of sections does not affect the transfer function ofthe filter. Noise has been introduced and adaptor sections are penetrated. From the results it is concluded that the order of theadaptor sections does not matter and also that the noise does not affect the other adaptors sections, it only propagates throughother adaptors sections.</p>

A wave digital filter is derived from an analog filter, which is realized as classical doubly resistively terminated reactancefilters. Perfectly designed wave digital filters express good dynamic signal range, low roundoff noise and excellent stabilitycharacteristics with respect to nonlinearity which are produced due to finite wordlength effects. Wave digital filters inheritthe sensitivity properties from analog filters, therefore, coefficients values can be selected to favorable values.Wave digital filters, derived from ladder filters, have low coefficient sensitivity in the passband and stopband. These WDFsare very complicated and are non-modular. The lattice wave digital filters are modular and are not complex. However, theyhave very high sensitivity in the stopband and thus require large coefficient wordlengths. The number of coefficients equalsthe filter order which have to be odd.This thesis discusses the wave digital filter structures that are modular because they are designed by cascading the first-orderand second-order sections. These WDFs can be pipelined. They also exhibit all the above mentioned favorable properties.Similar to lattice WDFs, these structures are restricted to symmetrical and antisymmetrical transfer functions. The synthesisof these structures is based on the factorization of the scattering matrix of lossless two-ports.In this thesis work, lowpass wave digital filters based on circulator-tree structure are designed with different orders startingfrom 3 and going upto 13. In parallel to these circulator-tree wave digital filters, the simple digital filters are also designedwith the same specification. The results of the two filters are compared with each other. It is observed that impulse responseand attenuation response of the two kind of filters perfectly match. Therefore, it is can be concluded that circulator-tree WDFupto Nth order can be synthesized. The implementation examples of two filter with order 3 and order 7 is presented in thisdocumentation for ready reference. It has also been shown that the order of sections does not affect the transfer function ofthe filter. Noise has been introduced and adaptor sections are penetrated. From the results it is concluded that the order of theadaptor sections does not matter and also that the noise does not affect the other adaptors sections, it only propagates throughother adaptors sections.