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This work presents a new concept to implement the elliptic curve point multiplication (PM). This computation is based on a new modular arithmetic over Gaussian integer fields. Gaussian integers are a subset of the complex numbers such that the real and imaginary parts are integers. Since Gaussian integer fields are isomorphic to prime fields, this arithmetic is suitable for many elliptic curves. Representing the key by a Gaussian integer expansion is beneficial to reduce the computational complexity and the memory requirements of secure hardware implementations, which are robust against attacks. Furthermore, an area-efficient coprocessor design is proposed with an arithmetic unit that enables Montgomery modular arithmetic over Gaussian integers. The proposed architecture and the new arithmetic provide high flexibility, i.e., binary and non-binary key expansions as well as protected and unprotected PM calculations are supported. The proposed coprocessor is a competitive solution for a compact ECC processor suitable for applications in small embedded systems.
Shared Field, Divided Field
(2020)
In my research sabbatical I was working on three different topics, namely orthogonal polynomials in geometric modeling, re-parametrized univariate subdivision curves, and reconstruction of 3d-fish-models and other zoological artifacts. In the subsequent Sections, I will describe my particular activity in these different fields. The sections are meant to present an overview of my research activities, leaving out the technical details.
Section 1 is on orthogonal polynomials and other related generating systems for functions systems of smooth function.
In Section 2, I will discuss the application of various re-parametrization schemes for interpolatory subdivision algorithms for the generation of space curves.
The next Section 3 is concerned with my research at the University of Queensland, Brisbane, in collaboration with Dr. Ulrike Siebeck from the School of Biomedical Sciences on fish behavior and reconstruction of 3d-fish models in particular.
In the last Section 4, I will describe what effects this research will have on in my subsequent teaching at the University of Applied Science Konstanz (HTWG).
The actual task of electrocardiographic examinations is to increase the reliability of diagnosing the condition of the heart. Within the framework of this task, an important direction is the solution of the inverse problem of electrocardiography, based on the processing of electrocardiographic signals of multichannel cardio leads at known electrode coordinates in these leads (Titomir et al. Noninvasiv electrocardiotopography, 2003), (Macfarlane et al. Comprehensive Electrocardiology, 2nd ed. (Chapter 9), 2011).