This thesis provides a survey of the attacks on multivariate cryptosystems. We begin by providing an outline of the general multivariate cryptosystem. Proceeding from there, we show that even with this level of detail, there are several attacks that are possible, including the method of Groebner bases, the XL method, and the recently announced method of Dixon resultants. Less general attack techniques also exist, such as MinRank attacks and differential analysis. These attacks lack the universality of the first three mentioned. In order to explore these less general attacks further, more details are required, so we present four different multivariate cryptosystems. Then, we attack them, using the less general attacks of MinRank, differential analysis and even an attack specific to one system. This concludes our study of the attacks themselves, and we move on to note that not all routes of attack are promising. Specifically, quantum computing does not seem to be helpful beyond the quadratic speed-up of Grover's algorithm. We also note that not all multivariate cryptosystems have been successfully attacked as of the writing of this thesis. We conclude with the fact that multivariate cryptography is gaining more and more active study.

This thesis provides a survey of the attacks on multivariate cryptosystems. We begin by providing an outline of the general multivariate cryptosystem. Proceeding from there, we show that even with this level of detail, there are several attacks that are possible, including the method of Groebner bases, the XL method, and the recently announced method of Dixon resultants. Less general attack techniques also exist, such as MinRank attacks and differential analysis. These attacks lack the universality of the first three mentioned. In order to explore these less general attacks further, more details are required, so we present four different multivariate cryptosystems. Then, we attack them, using the less general attacks of MinRank, differential analysis and even an attack specific to one system. This concludes our study of the attacks themselves, and we move on to note that not all routes of attack are promising. Specifically, quantum computing does not seem to be helpful beyond the quadratic speed-up of Grover's algorithm. We also note that not all multivariate cryptosystems have been successfully attacked as of the writing of this thesis. We conclude with the fact that multivariate cryptography is gaining more and more active study.

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Deriving low-dimensional perceptual spaces from data consisting of many variables is of crucial interest in strategic market planning. A frequently used method in this context is Principal Components Analysis, which finds uncorrelated directions in the data. This methodology which supports the identification of competitive structures can gainfully be utilized for product (re)positioning or optimal product (re)design. In our paper, we investigate the usefulness of a novel technique, Independent Component Analysis, to discover market structures. Independent Component Analysis is an extension of Principal Components Analysis in the sense that it looks for directions in the data that are not only uncorrelated but also independent. Comparing the two approaches on the basis of an empirical data set, we find that Independent Component Analysis leads to clearer and sharper structures than Principal Components Analysis. Furthermore, the results of Independent Component Analysis have a reasonable marketing interpretation. / Series: Working Papers SFB "Adaptive Information Systems and Modelling in Economics and Management Science"

The generation of random variates from multivariate binary distributions has not gained as much interest in the literature as, e.g., multivariate normal or Poisson distributions. Binary variables are important in many types of applications. Our main interest is in the segmentation of marketing data, where data come from customer questionnaires with "yes/no" questions. Artificial data provide a valuable tool for the analysis of segmentation tools, because data with known structure can be constructed to mimic situations from the real world (Dolnicar et al. 1998). Questionnaire data can be highly correlated, when several questions covering the same field are likely to be answered similarly by a subject. In this paper we present a computationally fast method to simulate multivariate binary distributions with a given correlation structure. The implementation of the algorithm in R, an implementation of the S statistical language, is described in the appendix. / Series: Working Papers SFB "Adaptive Information Systems and Modelling in Economics and Management Science"