Algebro-Geometric Aspects of the Classical Yang-Baxter Equation

In this thesis we consider algebro-geometric aspects of the Classical Yang-Baxter Equation and the Generalised Classical Yang-Baxter Equation. In chapter one we present a method to construct solutions of the Generalised Classical Yang-Baxter Equation starting with certain sheaves of Lie algebras on algebraic curves. Furthermore we discuss a criterion to check unitarity of such solutions. In chapter two we consider the special class of solutions coming from sheaves of traceless endomorphisms of simple vector bundles on the nodal cubic curve. These solutions are quasi-trigonometric and we describe how they fit into the classification scheme of such solutions. Moreover, we describe a concrete formula for these solutions. In the third and final chapter we show that any unitary, rational solution of the Classical Yang-Baxter Equation can be obtained via the method of chapter one applied to a sheaf of Lie algebras on the cuspidal cubic curve.

Elliptic curves, group law, and efficient computation

This thesis is about the derivation of the addition law on an arbitrary elliptic curve and efficiently adding points on this elliptic curve using the derived addition law. The outcomes of this research guarantee practical speedups in higher level operations which depend on point additions. In particular, the contributions immediately find applications in cryptology. Mastered by the 19th century mathematicians, the study of the theory of elliptic curves has been active for decades. Elliptic curves over finite fields made their way into public key cryptography in late 1980’s with independent proposals by Miller [Mil86] and Koblitz [Kob87]. Elliptic Curve Cryptography (ECC), following Miller’s and Koblitz’s proposals, employs the group of rational points on an elliptic curve in building discrete logarithm based public key cryptosystems. Starting from late 1990’s, the emergence of the ECC market has boosted the research in computational aspects of elliptic curves. This thesis falls into this same area of research where the main aim is to speed up the additions of rational points on an arbitrary elliptic curve (over a field of large characteristic). The outcomes of this work can be used to speed up applications which are based on elliptic curves, including cryptographic applications in ECC. The aforementioned goals of this thesis are achieved in five main steps. As the first step, this thesis brings together several algebraic tools in order to derive the unique group law of an elliptic curve. This step also includes an investigation of recent computer algebra packages relating to their capabilities. Although the group law is unique, its evaluation can be performed using abundant (in fact infinitely many) formulae. As the second step, this thesis progresses the finding of the best formulae for efficient addition of points. In the third step, the group law is stated explicitly by handling all possible summands. The fourth step presents the algorithms to be used for efficient point additions. In the fifth and final step, optimized software implementations of the proposed algorithms are presented in order to show that theoretical speedups of step four can be practically obtained. In each of the five steps, this thesis focuses on five forms of elliptic curves over finite fields of large characteristic. A list of these forms and their defining equations are given as follows: (a) Short Weierstrass form, y2 = x3 + ax + b, (b) Extended Jacobi quartic form, y2 = dx4 + 2ax2 + 1, (c) Twisted Hessian form, ax3 + y3 + 1 = dxy, (d) Twisted Edwards form, ax2 + y2 = 1 + dx2y2, (e) Twisted Jacobi intersection form, bs2 + c2 = 1, as2 + d2 = 1, These forms are the most promising candidates for efficient computations and thus considered in this work. Nevertheless, the methods employed in this thesis are capable of handling arbitrary elliptic curves. From a high level point of view, the following outcomes are achieved in this thesis. - Related literature results are brought together and further revisited. For most of the cases several missed formulae, algorithms, and efficient point representations are discovered. - Analogies are made among all studied forms. For instance, it is shown that two sets of affine addition formulae are sufficient to cover all possible affine inputs as long as the output is also an affine point in any of these forms. In the literature, many special cases, especially interactions with points at infinity were omitted from discussion. This thesis handles all of the possibilities. - Several new point doubling/addition formulae and algorithms are introduced, which are more efficient than the existing alternatives in the literature. Most notably, the speed of extended Jacobi quartic, twisted Edwards, and Jacobi intersection forms are improved. New unified addition formulae are proposed for short Weierstrass form. New coordinate systems are studied for the first time. - An optimized implementation is developed using a combination of generic x86-64 assembly instructions and the plain C language. The practical advantages of the proposed algorithms are supported by computer experiments. - All formulae, presented in the body of this thesis, are checked for correctness using computer algebra scripts together with details on register allocations.

An analysis of the RC4 family of stream ciphers against algebraic attacks

To date, most applications of algebraic analysis and attacks on stream ciphers are on those based on lin- ear feedback shift registers (LFSRs). In this paper, we extend algebraic analysis to non-LFSR based stream ciphers. Specifically, we perform an algebraic analysis on the RC4 family of stream ciphers, an example of stream ciphers based on dynamic tables, and inves- tigate its implications to potential algebraic attacks on the cipher. This is, to our knowledge, the first pa- per that evaluates the security of RC4 against alge- braic attacks through providing a full set of equations that describe the complex word manipulations in the system. For an arbitrary word size, we derive alge- braic representations for the three main operations used in RC4, namely state extraction, word addition and state permutation. Equations relating the inter- nal states and keystream of RC4 are then obtained from each component of the cipher based on these al- gebraic representations, and analysed in terms of their contributions to the security of RC4 against algebraic attacks. Interestingly, it is shown that each of the three main operations contained in the components has its own unique algebraic properties, and when their respective equations are combined, the resulting system becomes infeasible to solve. This results in a high level of security being achieved by RC4 against algebraic attacks. On the other hand, the removal of an operation from the cipher could compromise this security. Experiments on reduced versions of RC4 have been performed, which confirms the validity of our algebraic analysis and the conclusion that the full RC4 stream cipher seems to be immune to algebraic attacks at present.

A new approach for finding an appropriate combination of texture parameters for classification

This paper suggests an approach for finding an appropriate combination of various parameters for extracting texture features (e.g. choice of spectral band for extracting texture feature, size of the moving window, quantization level of the image, and choice of texture feature etc.) to be used in the classification process. Gray level co-occurrence matrix (GLCM) method has been used for extracting texture from remotely sensed satellite image. Results of the classification of an Indian urban environment using spatial property (texture), derived from spectral and multi-resolution wavelet decomposed images have also been reported. A multivariate data analysis technique called ‘conjoint analysis’ has been used in the study to analyze the relative importance of these parameters. Results indicate that the choice of texture feature and window size have higher relative importance in the classification process than quantization level or the choice of image band for extracting texture feature. In case of texture features derived using wavelet decomposed image, the parameter ‘decomposition level’ has almost equal relative importance as the size of moving window and the decomposition of images up to level one is sufficient and there is no need to go for further decomposition. It was also observed that the classification incorporating texture features improves the overall classification accuracy in a statistically significant manner in comparison to pure spectral classification.

An exploration of affine group laws for elliptic curves

Several forms of elliptic curves are suggested for an efficient implementation of Elliptic Curve Cryptography. However, a complete description of the group law has not appeared in the literature for most popular forms. This paper presents group law in affine coordinates for three forms of elliptic curves. With the existence of the proposed affine group laws, stating the projective group law for each form becomes trivial. This work also describes an automated framework for studying elliptic curve group law, which is applied internally when preparing this work.

Analysis of stream cipher based authenticated encryption schemes

Authenticated Encryption (AE) is the cryptographic process of providing simultaneous confidentiality and integrity protection to messages. This approach is more efficient than applying a two-step process of providing confidentiality for a message by encrypting the message, and in a separate pass providing integrity protection by generating a Message Authentication Code (MAC). AE using symmetric ciphers can be provided by either stream ciphers with built in authentication mechanisms or block ciphers using appropriate modes of operation. However, stream ciphers have the potential for higher performance and smaller footprint in hardware and/or software than block ciphers. This property makes stream ciphers suitable for resource constrained environments, where storage and computational power are limited. There have been several recent stream cipher proposals that claim to provide AE. These ciphers can be analysed using existing techniques that consider confidentiality or integrity separately; however currently there is no existing framework for the analysis of AE stream ciphers that analyses these two properties simultaneously. This thesis introduces a novel framework for the analysis of AE using stream cipher algorithms. This thesis analyzes the mechanisms for providing confidentiality and for providing integrity in AE algorithms using stream ciphers. There is a greater emphasis on the analysis of the integrity mechanisms, as there is little in the public literature on this, in the context of authenticated encryption. The thesis has four main contributions as follows. The first contribution is the design of a framework that can be used to classify AE stream ciphers based on three characteristics. The first classification applies Bellare and Namprempre's work on the the order in which encryption and authentication processes take place. The second classification is based on the method used for accumulating the input message (either directly or indirectly) into the into the internal states of the cipher to generate a MAC. The third classification is based on whether the sequence that is used to provide encryption and authentication is generated using a single key and initial vector, or two keys and two initial vectors. The second contribution is the application of an existing algebraic method to analyse the confidentiality algorithms of two AE stream ciphers; namely SSS and ZUC. The algebraic method is based on considering the nonlinear filter (NLF) of these ciphers as a combiner with memory. This method enables us to construct equations for the NLF that relate the (inputs, outputs and memory of the combiner) to the output keystream. We show that both of these ciphers are secure from this type of algebraic attack. We conclude that using a keydependent SBox in the NLF twice, and using two different SBoxes in the NLF of ZUC, prevents this type of algebraic attack. The third contribution is a new general matrix based model for MAC generation where the input message is injected directly into the internal state. This model describes the accumulation process when the input message is injected directly into the internal state of a nonlinear filter generator. We show that three recently proposed AE stream ciphers can be considered as instances of this model; namely SSS, NLSv2 and SOBER-128. Our model is more general than a previous investigations into direct injection. Possible forgery attacks against this model are investigated. It is shown that using a nonlinear filter in the accumulation process of the input message when either the input message or the initial states of the register is unknown prevents forgery attacks based on collisions. The last contribution is a new general matrix based model for MAC generation where the input message is injected indirectly into the internal state. This model uses the input message as a controller to accumulate a keystream sequence into an accumulation register. We show that three current AE stream ciphers can be considered as instances of this model; namely ZUC, Grain-128a and Sfinks. We establish the conditions under which the model is susceptible to forgery and side-channel attacks.

Meltdown : a tool to help in the interpretation of thermal melt curves acquired by differential scanning fluorimetry

The output of a differential scanning fluorimetry (DSF) assay is a series of melt curves, which need to be interpreted to get value from the assay. An application that translates raw thermal melt curve data into more easily assimilated knowledge is described. This program, called “Meltdown,” conducts four main activities—control checks, curve normalization, outlier rejection, and melt temperature (Tm) estimation—and performs optimally in the presence of triplicate (or higher) sample data. The final output is a report that summarizes the results of a DSF experiment. The goal of Meltdown is not to replace human analysis of the raw fluorescence data but to provide a meaningful and comprehensive interpretation of the data to make this useful experimental technique accessible to inexperienced users, as well as providing a starting point for detailed analyses by more experienced users.

Structure matters: Adoption of structured classification Approach in the context of cognitive presence classification

Within online learning communities, receiving timely and meaningful insights into the quality of learning activities is an important part of an effective educational experience. Commonly adopted methods – such as the Community of Inquiry framework – rely on manual coding of online discussion transcripts, which is a costly and time consuming process. There are several efforts underway to enable the automated classification of online discussion messages using supervised machine learning, which would enable the real-time analysis of interactions occurring within online learning communities. This paper investigates the importance of incorporating features that utilise the structure of on-line discussions for the classification of "cognitive presence" – the central dimension of the Community of Inquiry framework focusing on the quality of students' critical thinking within online learning communities. We implemented a Conditional Random Field classification solution, which incorporates structural features that may be useful in increasing classification performance over other implementations. Our approach leads to an improvement in classification accuracy of 5.8% over current existing techniques when tested on the same dataset, with a precision and recall of 0.630 and 0.504 respectively.

Site classification and estimation of surface level seismic hazard using geophysical data and probabilistic approach

This paper presents the site classification of Bangalore Mahanagar Palike (BMP) area using geophysical data and the evaluation of spectral acceleration at ground level using probabilistic approach. Site classification has been carried out using experimental data from the shallow geophysical method of Multichannel Analysis of Surface wave (MASW). One-dimensional (1-D) MASW survey has been carried out at 58 locations and respective velocity profiles are obtained. The average shear wave velocity for 30 m depth (Vs(30)) has been calculated and is used for the site classification of the BMP area as per NEHRP (National Earthquake Hazards Reduction Program). Based on the Vs(30) values major part of the BMP area can be classified as ``site class D'', and ``site class C'. A smaller portion of the study area, in and around Lalbagh Park, is classified as ``site class B''. Further, probabilistic seismic hazard analysis has been carried out to map the seismic hazard in terms spectral acceleration (S-a) at rock and the ground level considering the site classes and six seismogenic sources identified. The mean annual rate of exceedance and cumulative probability hazard curve for S. have been generated. The quantified hazard values in terms of spectral acceleration for short period and long period are mapped for rock, site class C and D with 10% probability of exceedance in 50 years on a grid size of 0.5 km. In addition to this, the Uniform Hazard Response Spectrum (UHRS) at surface level has been developed for the 5% damping and 10% probability of exceedance in 50 years for rock, site class C and D These spectral acceleration and uniform hazard spectrums can be used to assess the design force for important structures and also to develop the design spectrum.

Porn, censorship, classification and free speech: Global paradoxes in the governance of media content

In this presentation, I reflect upon the global landscape surrounding the governance and classification of media content, at a time of rapid change in media platforms and services for content production and distribution, and contested cultural and social norms. I discuss the tensions and contradictions arising in the relationship between national, regional and global dimensions of media content distribution, as well as the changing relationships between state and non-state actors. These issues will be explored through consideration of issues such as: recent debates over film censorship; the review of the National Classification Scheme conducted by the Australian Law Reform Commission; online controversies such as the future of the Reddit social media site; and videos posted online by the militant group ISIS.

On Random Planar Curves and Their Scaling Limits

Planar curves arise naturally as interfaces between two regions of the plane. An important part of statistical physics is the study of lattice models. This thesis is about the interfaces of 2D lattice models. The scaling limit is an infinite system limit which is taken by letting the lattice mesh decrease to zero. At criticality, the scaling limit of an interface is one of the SLE curves (Schramm-Loewner evolution), introduced by Oded Schramm. This family of random curves is parametrized by a real variable, which determines the universality class of the model. The first and the second paper of this thesis study properties of SLEs. They contain two different methods to study the whole SLE curve, which is, in fact, the most interesting object from the statistical physics point of view. These methods are applied to study two symmetries of SLE: reversibility and duality. The first paper uses an algebraic method and a representation of the Virasoro algebra to find common martingales to different processes, and that way, to confirm the symmetries for polynomial expected values of natural SLE data. In the second paper, a recursion is obtained for the same kind of expected values. The recursion is based on stationarity of the law of the whole SLE curve under a SLE induced flow. The third paper deals with one of the most central questions of the field and provides a framework of estimates for describing 2D scaling limits by SLE curves. In particular, it is shown that a weak estimate on the probability of an annulus crossing implies that a random curve arising from a statistical physics model will have scaling limits and those will be well-described by Loewner evolutions with random driving forces.

Modeling Efficient Classification as a Process of Confidence Assessment and Delegation

In visual object detection and recognition, classifiers have two interesting characteristics: accuracy and speed. Accuracy depends on the complexity of the image features and classifier decision surfaces. Speed depends on the hardware and the computational effort required to use the features and decision surfaces. When attempts to increase accuracy lead to increases in complexity and effort, it is necessary to ask how much are we willing to pay for increased accuracy. For example, if increased computational effort implies quickly diminishing returns in accuracy, then those designing inexpensive surveillance applications cannot aim for maximum accuracy at any cost. It becomes necessary to find trade-offs between accuracy and effort. We study efficient classification of images depicting real-world objects and scenes. Classification is efficient when a classifier can be controlled so that the desired trade-off between accuracy and effort (speed) is achieved and unnecessary computations are avoided on a per input basis. A framework is proposed for understanding and modeling efficient classification of images. Classification is modeled as a tree-like process. In designing the framework, it is important to recognize what is essential and to avoid structures that are narrow in applicability. Earlier frameworks are lacking in this regard. The overall contribution is two-fold. First, the framework is presented, subjected to experiments, and shown to be satisfactory. Second, certain unconventional approaches are experimented with. This allows the separation of the essential from the conventional. To determine if the framework is satisfactory, three categories of questions are identified: trade-off optimization, classifier tree organization, and rules for delegation and confidence modeling. Questions and problems related to each category are addressed and empirical results are presented. For example, related to trade-off optimization, we address the problem of computational bottlenecks that limit the range of trade-offs. We also ask if accuracy versus effort trade-offs can be controlled after training. For another example, regarding classifier tree organization, we first consider the task of organizing a tree in a problem-specific manner. We then ask if problem-specific organization is necessary.

An accurate method for the experimental evaluation of the acoustical impedance of a black box

Among different methods, the transmission-line or the impedance tube method has been most popular for the experimental evaluation of the acoustical impedance of any termination. The current state of method involves extrapolation of the measured data to the reflecting surface or exact locations of the pressure maxima, both of which are known to be rather tricky. The present paper discusses a method which makes use of the positions of the pressure minima and the values of the standing-wave ratio at these points. Lippert's concept of enveloping curves has been extended. The use of Smith or Beranek charts, with their inherent inaccuracy, has been altogether avoided. The existing formulas for the impedance have been corrected. Incidentally, certain other errors in the current literature have also been brought to light.Subject Classification: 85.20.

Combination of similarity measures for time series classification using genetic algorithms

Time series classification deals with the problem of classification of data that is multivariate in nature. This means that one or more of the attributes is in the form of a sequence. The notion of similarity or distance, used in time series data, is significant and affects the accuracy, time, and space complexity of the classification algorithm. There exist numerous similarity measures for time series data, but each of them has its own disadvantages. Instead of relying upon a single similarity measure, our aim is to find the near optimal solution to the classification problem by combining different similarity measures. In this work, we use genetic algorithms to combine the similarity measures so as to get the best performance. The weightage given to different similarity measures evolves over a number of generations so as to get the best combination. We test our approach on a number of benchmark time series datasets and present promising results.

Efficient method of moving shadow detection and vehicle classification

Moving shadow detection and removal from the extracted foreground regions of video frames, aim to limit the risk of misconsideration of moving shadows as a part of moving objects. This operation thus enhances the rate of accuracy in detection and classification of moving objects. With a similar reasoning, the present paper proposes an efficient method for the discrimination of moving object and moving shadow regions in a video sequence, with no human intervention. Also, it requires less computational burden and works effectively under dynamic traffic road conditions on highways (with and without marking lines), street ways (with and without marking lines). Further, we have used scale-invariant feature transform-based features for the classification of moving vehicles (with and without shadow regions), which enhances the effectiveness of the proposed method. The potentiality of the method is tested with various data sets collected from different road traffic scenarios, and its superiority is compared with the existing methods. (C) 2013 Elsevier GmbH. All rights reserved.