Deterministic Chaos in Digital Cryptography

This thesis studies the application of deterministic chaos to digital cryptography. Cryptographic systems such as pseudo-random generators (PRNG), block ciphers and hash functions are regarded as a dynamic system (X, j), where X is a state space (Le. message space) and f : X -+ X is an iterated function. In both chaos theory and cryptography, the object of study is a dynamic system that performs an iterative nonlinear transformation of information in an apparently unpredictable but deterministic manner. In terms of chaos theory, the sensitivity to the initial conditions together with the mixing property ensures cryptographic confusion (statistical independence) and diffusion (uniform propagation of plaintext and key randomness into cihertext). This synergetic relationship between the properties of chaotic and cryptographic systems is considered at both the theoretical and practical levels: The theoretical background upon which this relationship is based, includes discussions on chaos, ergodicity, complexity, randomness, unpredictability and entropy. Two approaches to the finite-state implementation of chaotic systems (Le. pseudo-chaos) are considered: (i) floating-point approximation of continuous-state chaos; (ii) binary pseudo-chaos. An overview is given of chaotic systems underpinning cryptographic algorithms along with their strengths and weaknesses. Though all conventional cryposystems are considered binary pseudo-chaos, neither chaos, nor pseudo-chaos are sufficient to guarantee cryptographic strength and security. A dynamic system is said to have an analytical solution Xn = (xo) if any trajectory point Xn can be computed directly from the initial conditions Xo, without performing n iterations. A chaotic system with an analytical solution may have a unpredictable multi-valued map Xn+l = f(xn). Their floating-point approximation is studied in the context of pseudo-random generators. A cryptographic software system E-Larm ™ implementing a multistream pseudo-chaotic generator is described. Several pseudo-chaotic systems including the logistic map, sine map, tangent- and logarithm feedback maps, sawteeth and tent maps are evaluated by means of floating point computations. Two types of partitioning are used to extract pseudo-random from the floating-point state variable: (i) combining the last significant bits of the floating-point number (for nonlinear maps); and (ii) threshold partitioning (for piecewise linear maps). Multi-round iterations are produced to decrease the bit dependence and increase non-linearity. Relationships between pseudo-chaotic systems are introduced to avoid short cycles (each system influences periodically the states of other systems used in the encryption session). An evaluation of cryptographic properties of E-Larm is given using graphical plots such as state distributions, phase-space portraits, spectral density Fourier transform, approximated entropy (APEN), cycle length histogram, as well as a variety of statistical tests from the National Institute of Standards and Technology (NIST) suite. Though E-Larm passes all tests recommended by NIST, an approach based on the floating-point approximation of chaos is inefficient in terms of the quality/performance ratio (compared with existing PRNG algorithms). Also no solution is known to control short cycles. In conclusion, the role of chaos theory in cryptography is identified; disadvantages of floating-point pseudo-chaos are emphasized although binary pseudo-chaos is considered useful for cryptographic applications.Durand Technology Limite

Transform Based And Search Aware Text Compression Schemes And Compressed Domain Text Retrieval

In recent times, we have witnessed an unprecedented growth of textual information via the Internet, digital libraries and archival text in many applications. While a good fraction of this information is of transient interest, useful information of archival value will continue to accumulate. We need ways to manage, organize and transport this data from one point to the other on data communications links with limited bandwidth. We must also have means to speedily find the information we need from this huge mass of data. Sometimes, a single site may also contain large collections of data such as a library database, thereby requiring an efficient search mechanism even to search within the local data. To facilitate the information retrieval, an emerging ad hoc standard for uncompressed text is XML which preprocesses the text by putting additional user defined metadata such as DTD or hyperlinks to enable searching with better efficiency and effectiveness. This increases the file size considerably, underscoring the importance of applying text compression. On account of efficiency (in terms of both space and time), there is a need to keep the data in compressed form for as much as possible. Text compression is concerned with techniques for representing the digital text data in alternate representations that takes less space. Not only does it help conserve the storage space for archival and online data, it also helps system performance by requiring less number of secondary storage (disk or CD Rom) accesses and improves the network transmission bandwidth utilization by reducing the transmission time. Unlike static images or video, there is no international standard for text compression, although compressed formats like .zip, .gz, .Z files are increasingly being used. In general, data compression methods are classified as lossless or lossy. Lossless compression allows the original data to be recovered exactly. Although used primarily for text data, lossless compression algorithms are useful in special classes of images such as medical imaging, finger print data, astronomical images and data bases containing mostly vital numerical data, tables and text information. Many lossy algorithms use lossless methods at the final stage of the encoding stage underscoring the importance of lossless methods for both lossy and lossless compression applications. In order to be able to effectively utilize the full potential of compression techniques for the future retrieval systems, we need efficient information retrieval in the compressed domain. This means that techniques must be developed to search the compressed text without decompression or only with partial decompression independent of whether the search is done on the text or on some inversion table corresponding to a set of key words for the text. In this dissertation, we make the following contributions: (1) Star family compression algorithms: We have proposed an approach to develop a reversible transformation that can be applied to a source text that improves existing algorithm\u27s ability to compress. We use a static dictionary to convert the English words into predefined symbol sequences. These transformed sequences create additional context information that is superior to the original text. Thus we achieve some compression at the preprocessing stage. We have a series of transforms which improve the performance. Star transform requires a static dictionary for a certain size. To avoid the considerable complexity of conversion, we employ the ternary tree data structure that efficiently converts the words in the text to the words in the star dictionary in linear time. (2) Exact and approximate pattern matching in Burrows-Wheeler transformed (BWT) files: We proposed a method to extract the useful context information in linear time from the BWT transformed text. The auxiliary arrays obtained from BWT inverse transform brings logarithm search time. Meanwhile, approximate pattern matching can be performed based on the results of exact pattern matching to extract the possible candidate for the approximate pattern matching. Then fast verifying algorithm can be applied to those candidates which could be just small parts of the original text. We present algorithms for both k-mismatch and k-approximate pattern matching in BWT compressed text. A typical compression system based on BWT has Move-to-Front and Huffman coding stages after the transformation. We propose a novel approach to replace the Move-to-Front stage in order to extend compressed domain search capability all the way to the entropy coding stage. A modification to the Move-to-Front makes it possible to randomly access any part of the compressed text without referring to the part before the access point. (3) Modified LZW algorithm that allows random access and partial decoding for the compressed text retrieval: Although many compression algorithms provide good compression ratio and/or time complexity, LZW is the first one studied for the compressed pattern matching because of its simplicity and efficiency. Modifications on LZW algorithm provide the extra advantage for fast random access and partial decoding ability that is especially useful for text retrieval systems. Based on this algorithm, we can provide a dynamic hierarchical semantic structure for the text, so that the text search can be performed on the expected level of granularity. For example, user can choose to retrieve a single line, a paragraph, or a file, etc. that contains the keywords. More importantly, we will show that parallel encoding and decoding algorithm is trivial with the modified LZW. Both encoding and decoding can be performed with multiple processors easily and encoding and decoding process are independent with respect to the number of processors

Advanced Data Mining Techniques for Compound Objects

Knowledge Discovery in Databases (KDD) is the non-trivial process of identifying valid, novel, potentially useful, and ultimately understandable patterns in large data collections. The most important step within the process of KDD is data mining which is concerned with the extraction of the valid patterns. KDD is necessary to analyze the steady growing amount of data caused by the enhanced performance of modern computer systems. However, with the growing amount of data the complexity of data objects increases as well. Modern methods of KDD should therefore examine more complex objects than simple feature vectors to solve real-world KDD applications adequately. Multi-instance and multi-represented objects are two important types of object representations for complex objects. Multi-instance objects consist of a set of object representations that all belong to the same feature space. Multi-represented objects are constructed as a tuple of feature representations where each feature representation belongs to a different feature space. The contribution of this thesis is the development of new KDD methods for the classification and clustering of complex objects. Therefore, the thesis introduces solutions for real-world applications that are based on multi-instance and multi-represented object representations. On the basis of these solutions, it is shown that a more general object representation often provides better results for many relevant KDD applications. The first part of the thesis is concerned with two KDD problems for which employing multi-instance objects provides efficient and effective solutions. The first is the data mining in CAD parts, e.g. the use of hierarchic clustering for the automatic construction of product hierarchies. The introduced solution decomposes a single part into a set of feature vectors and compares them by using a metric on multi-instance objects. Furthermore, multi-step query processing using a novel filter step is employed, enabling the user to efficiently process similarity queries. On the basis of this similarity search system, it is possible to perform several distance based data mining algorithms like the hierarchical clustering algorithm OPTICS to derive product hierarchies. The second important application is the classification and search for complete websites in the world wide web (WWW). A website is a set of HTML-documents that is published by the same person, group or organization and usually serves a common purpose. To perform data mining for websites, the thesis presents several methods to classify websites. After introducing naive methods modelling websites as webpages, two more sophisticated approaches to website classification are introduced. The first approach uses a preprocessing that maps single HTML-documents within each website to so-called page classes. The second approach directly compares websites as sets of word vectors and uses nearest neighbor classification. To search the WWW for new, relevant websites, a focused crawler is introduced that efficiently retrieves relevant websites. This crawler minimizes the number of HTML-documents and increases the accuracy of website retrieval. The second part of the thesis is concerned with the data mining in multi-represented objects. An important example application for this kind of complex objects are proteins that can be represented as a tuple of a protein sequence and a text annotation. To analyze multi-represented objects, a clustering method for multi-represented objects is introduced that is based on the density based clustering algorithm DBSCAN. This method uses all representations that are provided to find a global clustering of the given data objects. However, in many applications there already exists a sophisticated class ontology for the given data objects, e.g. proteins. To map new objects into an ontology a new method for the hierarchical classification of multi-represented objects is described. The system employs the hierarchical structure of the ontology to efficiently classify new proteins, using support vector machines

Information Theoretic-Based Privacy Protection on Data Publishing and Biometric Authentication

Ph.DDOCTOR OF PHILOSOPH

Random hypergraphs for hashing-based data structures

This thesis concerns dictionaries and related data structures that rely on providing several random possibilities for storing each key. Imagine information on a set S of m = |S| keys should be stored in n memory locations, indexed by [n] = {1,…,n}. Each object x [ELEMENT OF] S is assigned a small set e(x) [SUBSET OF OR EQUAL TO] [n] of locations by a random hash function, independent of other objects. Information on x must then be stored in the locations from e(x) only. It is possible that too many objects compete for the same locations, in particular if the load c = m/n is high. Successfully storing all information may then be impossible. For most distributions of e(x), however, success or failure can be predicted very reliably, since the success probability is close to 1 for loads c less than a certain load threshold c^* and close to 0 for loads greater than this load threshold. We mainly consider two types of data structures: • A cuckoo hash table is a dictionary data structure where each key x [ELEMENT OF] S is stored together with an associated value f(x) in one of the memory locations with an index from e(x). The distribution of e(x) is controlled by the hashing scheme. We analyse three known hashing schemes, and determine their exact load thresholds. The schemes are unaligned blocks, double hashing and a scheme for dynamically growing key sets. • A retrieval data structure also stores a value f(x) for each x [ELEMENT OF] S. This time, the values stored in the memory locations from e(x) must satisfy a linear equation that characterises the value f(x). The resulting data structure is extremely compact, but unusual. It cannot answer questions of the form “is y [ELEMENT OF] S?”. Given a key y it returns a value z. If y [ELEMENT OF] S, then z = f(y) is guaranteed, otherwise z may be an arbitrary value. We consider two new hashing schemes, where the elements of e(x) are contained in one or two contiguous blocks. This yields good access times on a word RAM and high cache efficiency. An important question is whether these types of data structures can be constructed in linear time. The success probability of a natural linear time greedy algorithm exhibits, once again, threshold behaviour with respect to the load c. We identify a hashing scheme that leads to a particularly high threshold value in this regard. In the mathematical model, the memory locations [n] correspond to vertices, and the sets e(x) for x [ELEMENT OF] S correspond to hyperedges. Three properties of the resulting hypergraphs turn out to be important: peelability, solvability and orientability. Therefore, large parts of this thesis examine how hyperedge distribution and load affects the probabilities with which these properties hold and derive corresponding thresholds. Translated back into the world of data structures, we achieve low access times, high memory efficiency and low construction times. We complement and support the theoretical results by experiments.Diese Arbeit behandelt Wörterbücher und verwandte Datenstrukturen, die darauf aufbauen, mehrere zufällige Möglichkeiten zur Speicherung jedes Schlüssels vorzusehen. Man stelle sich vor, Information über eine Menge S von m = |S| Schlüsseln soll in n Speicherplätzen abgelegt werden, die durch [n] = {1,…,n} indiziert sind. Jeder Schlüssel x [ELEMENT OF] S bekommt eine kleine Menge e(x) [SUBSET OF OR EQUAL TO] [n] von Speicherplätzen durch eine zufällige Hashfunktion unabhängig von anderen Schlüsseln zugewiesen. Die Information über x darf nun ausschließlich in den Plätzen aus e(x) untergebracht werden. Es kann hierbei passieren, dass zu viele Schlüssel um dieselben Speicherplätze konkurrieren, insbesondere bei hoher Auslastung c = m/n. Eine erfolgreiche Speicherung der Gesamtinformation ist dann eventuell unmöglich. Für die meisten Verteilungen von e(x) lässt sich Erfolg oder Misserfolg allerdings sehr zuverlässig vorhersagen, da für Auslastung c unterhalb eines gewissen Auslastungsschwellwertes c* die Erfolgswahrscheinlichkeit nahezu 1 ist und für c jenseits dieses Auslastungsschwellwertes nahezu 0 ist. Hauptsächlich werden wir zwei Arten von Datenstrukturen betrachten: • Eine Kuckucks-Hashtabelle ist eine Wörterbuchdatenstruktur, bei der jeder Schlüssel x [ELEMENT OF] S zusammen mit einem assoziierten Wert f(x) in einem der Speicherplätze mit Index aus e(x) gespeichert wird. Die Verteilung von e(x) wird hierbei vom Hashing-Schema festgelegt. Wir analysieren drei bekannte Hashing-Schemata und bestimmen erstmals deren exakte Auslastungsschwellwerte im obigen Sinne. Die Schemata sind unausgerichtete Blöcke, Doppel-Hashing sowie ein Schema für dynamisch wachsenden Schlüsselmengen. • Auch eine Retrieval-Datenstruktur speichert einen Wert f(x) für alle x [ELEMENT OF] S. Diesmal sollen die Werte in den Speicherplätzen aus e(x) eine lineare Gleichung erfüllen, die den Wert f(x) charakterisiert. Die entstehende Datenstruktur ist extrem platzsparend, aber ungewöhnlich: Sie ist ungeeignet um Fragen der Form „ist y [ELEMENT OF] S?“ zu beantworten. Bei Anfrage eines Schlüssels y wird ein Ergebnis z zurückgegeben. Falls y [ELEMENT OF] S ist, so ist z = f(y) garantiert, andernfalls darf z ein beliebiger Wert sein. Wir betrachten zwei neue Hashing-Schemata, bei denen die Elemente von e(x) in einem oder in zwei zusammenhängenden Blöcken liegen. So werden gute Zugriffszeiten auf Word-RAMs und eine hohe Cache-Effizienz erzielt. Eine wichtige Frage ist, ob Datenstrukturen obiger Art in Linearzeit konstruiert werden können. Die Erfolgswahrscheinlichkeit eines naheliegenden Greedy-Algorithmus weist abermals ein Schwellwertverhalten in Bezug auf die Auslastung c auf. Wir identifizieren ein Hashing-Schema, das diesbezüglich einen besonders hohen Schwellwert mit sich bringt. In der mathematischen Modellierung werden die Speicherpositionen [n] als Knoten und die Mengen e(x) für x [ELEMENT OF] S als Hyperkanten aufgefasst. Drei Eigenschaften der entstehenden Hypergraphen stellen sich dann als zentral heraus: Schälbarkeit, Lösbarkeit und Orientierbarkeit. Weite Teile dieser Arbeit beschäftigen sich daher mit den Wahrscheinlichkeiten für das Vorliegen dieser Eigenschaften abhängig von Hashing Schema und Auslastung, sowie mit entsprechenden Schwellwerten. Eine Rückübersetzung der Ergebnisse liefert dann Datenstrukturen mit geringen Anfragezeiten, hoher Speichereffizienz und geringen Konstruktionszeiten. Die theoretischen Überlegungen werden dabei durch experimentelle Ergebnisse ergänzt und gestützt

A comparison of statistical machine learning methods in heartbeat detection and classification

In health care, patients with heart problems require quick responsiveness in a clinical setting or in the operating theatre. Towards that end, automated classification of heartbeats is vital as some heartbeat irregularities are time consuming to detect. Therefore, analysis of electro-cardiogram (ECG) signals is an active area of research. The methods proposed in the literature depend on the structure of a heartbeat cycle. In this paper, we use interval and amplitude based features together with a few samples from the ECG signal as a feature vector. We studied a variety of classification algorithms focused especially on a type of arrhythmia known as the ventricular ectopic fibrillation (VEB). We compare the performance of the classifiers against algorithms proposed in the literature and make recommendations regarding features, sampling rate, and choice of the classifier to apply in a real-time clinical setting. The extensive study is based on the MIT-BIH arrhythmia database. Our main contribution is the evaluation of existing classifiers over a range sampling rates, recommendation of a detection methodology to employ in a practical setting, and extend the notion of a mixture of experts to a larger class of algorithms

Coping With New Challengens for Density-Based Clustering

Knowledge Discovery in Databases (KDD) is the non-trivial process of identifying valid, novel, potentially useful, and ultimately understandable patterns in data. The core step of the KDD process is the application of a Data Mining algorithm in order to produce a particular enumeration of patterns and relationships in large databases. Clustering is one of the major data mining tasks and aims at grouping the data objects into meaningful classes (clusters) such that the similarity of objects within clusters is maximized, and the similarity of objects from different clusters is minimized. Beside many others, the density-based clustering notion underlying the algorithm DBSCAN and its hierarchical extension OPTICS has been proposed recently, being one of the most successful approaches to clustering. In this thesis, our aim is to advance the state-of-the-art clustering, especially density-based clustering by identifying novel challenges for density-based clustering and proposing innovative and solid solutions for these challenges. We describe the development of the industrial prototype BOSS (Browsing OPTICS plots for Similarity Search) which is a first step towards developing a comprehensive, scalable and distributed computing solution designed to make the efficiency and analytical capabilities of OPTICS available to a broader audience. For the development of BOSS, several key enhancements of OPTICS are required which are addressed in this thesis. We develop incremental algorithms of OPTICS to efficiently reconstruct the hierarchical clustering structure in frequently updated databases, in particular, when a set of objects is inserted in or deleted from the database. We empirically show that these incremental algorithms yield significant speed-up factors over the original OPTICS algorithm. Furthermore, we propose a novel algorithm for automatic extraction of clusters from hierarchical clustering representations that outperforms comparative methods, and introduce two novel approaches for selecting meaningful representatives, using the density-based concepts of OPTICS and producing better results than the related medoid approach. Another major challenge for density-based clustering is to cope with high dimensional data. Many today's real-world data sets contain a large number of measurements (or features) for a single data object. Usually, global feature reduction techniques cannot be applied to these data sets. Thus, the task of feature selection must be combined with and incooperated into the clustering process. In this thesis, we present original extensions and enhancements of the density-based clustering notion to cope with high dimensional data. In particular, we propose an algorithm called SUBCLU (density based SUBspace CLUstering) that extends DBSCAN to the problem of subspace clustering. SUBCLU efficiently computes all clusters that would have been found if DBSCAN is applied to all possible subspaces of the feature space. An experimental evaluation on real-world data sets illustrates that SUBCLU is more effective than existing subspace clustering algorithms because it is able to find clusters of arbitrary size and shape, and produces determine results. A semi-hierarchical extension of SUBCLU called RIS (Ranking Interesting Subspaces) is proposed that does not compute the subspace clusters directly, but generates a list of subspaces ranked by their clustering characteristics. A hierarchical clustering algorithm can be applied to these interesting subspaces in order to compute a hierarchical (subspace) clustering. A comparative evaluation of RIS and SUBCLU shows that RIS in combination with OPTICS can achieve an information gain over SUBCLU. In addition, we propose the algorithm 4C (Computing Correlation Connected Clusters) that extends the concepts of DBSCAN to compute density-based correlation clusters. 4C benefits from an innovative, well-defined and effective clustering model, outperforming related approaches in terms of clustering quality on real-world data sets.Knowledge Discovery in Databases (KDD) ist der Prozess der (semi-)automatischen Extraktion von Wissen aus Datenbanken, das gültig, bisher unbekannt und potentiell nützlich für eine gegebene Anwendung ist. Der zentrale Schritt des KDD-Prozesses ist das Data Mining. Eine der wichtigsten Aufgaben des Data Mining ist Clustering. Dabei sollen die Objekte einer Datenbank in Gruppen (Cluster) partitioniert werden, so dass Objekte eines Clusters möglichst ähnlich und Objekte verschiedener Cluster möglichst unähnlich zu einander sind. Das dichtebasierte Clustermodell und die darauf aufbauenden Algorithmen DBSCAN und OPTICS sind unter einer Vielzahl anderer Clustering-Ansätze eine der erfolgreichsten Methoden zum Clustering. Im Rahmen dieser Dissertation wollen wir den aktuellen Stand der Technik im Bereich Clustering und speziell im Bereich dichtebasiertes Clustering voranbringen. Dazu erarbeiten wir neue Herausforderungen für das dichtebasierte Clustermodell und schlagen dazu innovative Lösungen vor. Zunächst steht die Entwicklung des industriellen Prototyps BOSS (Browsing OPTICS plots for Similarity Search) im Mittelpunkt dieser Arbeit. BOSS ist ein erster Beitrag zu einer umfassenden, skalierbaren und verteilten Softwarelösung, die eine Nutzung der Effizienzvorteile und die analytischen Möglichkeiten des dichtebasierten, hierarchischen Clustering-Algorithmus OPTICS für ein breites Publikum ermöglichen. Zur Entwicklung von BOSS werden drei entscheidende Erweiterungen von OPTICS benötigt: Wir entwickeln eine inkrementelle Version von OPTICS um nach einem Update der Datenbank (Einfügen/Löschen einer Menge von Objekten) die hierarchische Clustering Struktur effizient zu reorganisieren. Anhand von Experimenten mit synthetischen und realen Daten zeigen wir, dass die vorgeschlagenen, inkrementellen Algorithmen deutliche Beschleunigungsfaktoren gegenüber dem originalen OPTICS-Algorithmus erzielen. Desweiteren schlagen wir einen neuen Algorithmus zur automatischen Clusterextraktion aus hierarchischen Repräsentationen und zwei innovative Methoden zur automatischen Auswahl geeigneter Clusterrepräsentaten vor. Unsere neuen Techniken erzielen bei Tests auf mehreren realen Datenbanken im Vergleich zu den konkurrierenden Verfahren bessere Ergebnisse. Eine weitere Herausforderung für Clustering-Verfahren stellen hochdimensionale Featureräume dar. Reale Datensätze beinhalten dank moderner Verfahren zur Datenerhebung häufig sehr viele Merkmale. Teile dieser Merkmale unterliegen oft Rauschen oder Abhängigkeiten und können meist nicht im Vorfeld ausgesiebt werden, da diese Effekte jeweils in Teilen der Datenbank unterschiedlich ausgeprägt sind. Daher muss die Wahl der Features mit dem Data-Mining-Verfahren verknüpft werden. Im Rahmen dieser Arbeit stellen wir innovative Erweiterungen des dichtebasierten Clustermodells für hochdimensionale Daten vor. Wir entwickeln SUBCLU (dichtebasiertes SUBspace CLUstering), ein auf DBSCAN basierender Subspace Clustering Algorithmus. SUBCLU erzeugt effizient alle Cluster, die gefunden werden, wenn man DBSCAN auf alle möglichen Teilräume des Datensatzes anwendet. Experimente auf realen Daten zeigen, dass SUBCLU effektiver als vergleichbare Algorithmen ist. RIS (Ranking Interesting Subspaces), eine semi-hierarchische Erweiterung von SUBCLU, wird vorgeschlagen, das nicht mehr direkt die Teilraumcluster berechnet, sondern eine Liste von Teilräumen geordnet anhand ihrer Clustering-Qualität erzeugt. Dadurch können hierarchische Partitionierungen auf ausgewählten Teilräumen erzeugt werden. Experimente belegen, dass RIS in Kombination mit OPTICS ein Informationsgewinn gegenüber SUBCLU erreicht. Außerdem stellen wir den neuartigen Korrelationscluster Algorithmus 4C (Computing Correlation Connected Clusters) vor. 4C basiert auf einem innovativen und wohldefinierten Clustermodell und erzielt in unseren Experimenten mit realen Daten bessere Ergebnisse als vergleichbare Clustering-Ansätze

Markov field models of molecular kinetics

Computer simulations such as molecular dynamics (MD) provide a possible means to understand protein dynamics and mechanisms on an atomistic scale. The resulting simulation data can be analyzed with Markov state models (MSMs), yielding a quantitative kinetic model that, e.g., encodes state populations and transition rates. However, the larger an investigated system, the more data is required to estimate a valid kinetic model. In this work, we show that this scaling problem can be escaped when decomposing a system into smaller ones, leveraging weak couplings between local domains. Our approach, termed independent Markov decomposition (IMD), is a first-order approximation neglecting couplings, i.e., it represents a decomposition of the underlying global dynamics into a set of independent local ones. We demonstrate that for truly independent systems, IMD can reduce the sampling by three orders of magnitude. IMD is applied to two biomolecular systems. First, synaptotagmin-1 is analyzed, a rapid calcium switch from the neurotransmitter release machinery. Within its C2A domain, local conformational switches are identified and modeled with independent MSMs, shedding light on the mechanism of its calcium-mediated activation. Second, the catalytic site of the serine protease TMPRSS2 is analyzed with a local drug-binding model. Equilibrium populations of different drug-binding modes are derived for three inhibitors, mirroring experimentally determined drug efficiencies. IMD is subsequently extended to an end-to-end deep learning framework called iVAMPnets, which learns a domain decomposition from simulation data and simultaneously models the kinetics in the local domains. We finally classify IMD and iVAMPnets as Markov field models (MFM), which we define as a class of models that describe dynamics by decomposing systems into local domains. Overall, this thesis introduces a local approach to Markov modeling that enables to quantitatively assess the kinetics of large macromolecular complexes, opening up possibilities to tackle current and future computational molecular biology questions