Hiermit versichere ich, die vorliegende Diplomarbeit selbstständig und unter ausschliesslicher Verwendung der angegebenen Quellen und Hilfsmittel angefertigt zu haben. Diese Arbeit hat in gleicher oder ähnlicher Form noch keiner Prüfungsbehörde vorgelegen. Darmstadt, 14. Februar 2006

by an ultrasonic transducer at a distance of 0.5 cm in the X-direction, and is biased by 60 Vdc, indicating the energy harvesting capability of 21.4 nW in the X-direction. When excited along the Y-axis, the harvester has an energy-harvesting capacity of 22.7 nW. The harvester was modeled and simulated using

First and foremost, I would like to thank my advisor, Prof. Jennifer E. Michaels. I am most appreciative of your guidance over the last four years, from the basics of elastic waves to both short- and long-term career advice. I have grown a tremendous amount, both profes-sionally and personally, and am deeply grateful for your mentorship, patience, and support. I would also like to thank my Ph.D. committee for their valuable insight and sugges-

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1.1 Private and Public Key Cryptography..................... 5

RECHERCHES Elastographie par ondes de cisaillement

I declare that this thesis is my own account of my research and contains as its main content work which has not previously been submitted for a degree at any tertiary education institution.

I would like to thank some people who were involved in the creation of this thesis: • Berry Schoenmakers of TU Eindhoven for introducing me to the topic of cryptographic voting protocols. • Evangelos Karatsiolis for his work in guiding me through the process of writing this thesis and his constant motivation. • Roberto Samarone Araujo for hours of discussing various protocols with Evengelos and me. • Warren D. Smith for providing with a preliminary version of his upcoming book »How Mathematics can Improve Democracy«. • Ute Günther and Christian Burgmann for their proof-reading. Nonetheless, any remaing errors shall be blamed on me. • Andrea Peter for her love and for cheering me up when I was down. • Last but not least my parents, Jacqueline Herrnkind and Hans Peter Klink – without their love and continuous support, this thesis would never have been written.

Recent developments of new medical treatment techniques put challenging demands on ultrasound imaging systems in terms of both image quality and raw data size. Traditional sampling methods result in very large amounts of data, thus, increasing demands on processing hardware and limiting the flexibility in the post-processing stages. In this paper, we apply Compressed Sensing (CS) techniques to analog ultrasound signals, following the recently developed Xampling framework. The result is a system with significantly reduced sampling rates which, in turn, means significantly reduced data size while maintaining the quality of the resulting images.

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