@phdthesis{Malik,
  author    = {Malik, Irfan},
  title     = {An adaptive contact formulation for Isogeometric Finite Element Analysis},
  doi       = {10.25643/bauhaus-universitaet.4612},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20220324-46129},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  pages     = {124},
  abstract  = {Numerical simulation of physical phenomena, like electro-magnetics, structural and fluid mechanics is essential for the cost- and time-efficient development of mechanical products at high quality. It allows to investigate the behavior of a product or a system far before the first prototype of a product is manufactured. This thesis addresses the simulation of contact mechanics. Mechanical contacts appear in nearly every product of mechanical engineering. Gearboxes, roller bearings, valves and pumps are only some examples. Simulating these systems not only for the maximal/minimal stresses and strains but for the stress-distribution in case of tribo-contacts is a challenging task from a numerical point of view. Classical procedures like the Finite Element Method suffer from the nonsmooth representation of contact surfaces with discrete Lagrange elements. On the one hand, an error due to the approximate description of the surface is introduced. On the other hand it is difficult to attain a robust contact search because surface normals can not be described in a unique form at element edges. This thesis introduces therefore a novel approach, the adaptive isogeometric contact formulation based on polynomial Splines over hierarchical T-meshes (PHT-Splines), for the approximate solution of the non-linear contact problem. It provides a more accurate, robust and efficient solution compared to conventional methods. During the development of this method the focus was laid on the solution of static contact problems without friction in 2D and 3D in which the structures undergo small deformations. The mathematical description of the problem entails a system of partial differential equations and boundary conditions which model the linear elastic behaviour of continua. Additionally, it comprises side conditions, the Karush-Kuhn-Tuckerconditions, to prevent the contacting structures from non-physical penetration. The mathematical model must be transformed into its integral form for approximation of the solution. Employing a penalty method, contact constraints are incorporated by adding the resulting equations in weak form to the overall set of equations. For an efficient space discretization of the bulk and especially the contact boundary of the structures, the principle of Isogeometric Analysis (IGA) is applied. Isogeometric Finite Element Methods provide several advantages over conventional Finite Element discretization. Surface approximation with Non-Uniform Rational B-Splines (NURBS) allow a robust numerical solution of the contact problem with high accuracy in terms of an exact geometry description including the surface smoothness. The numerical evaluation of the contact integral is challenging due to generally non-conforming meshes of the contacting structures. In this work the highly accurate Mortar Method is applied in the isogeometric setting for the evaluation of contact contributions. This leads to an algebraic system of equations that is linearized and solved in sequential steps. This procedure is known as the Newton Raphson Method. Based on numerical examples, the advantages of the isogeometric approach with classical refinement strategies, like the p- and h-refinement, are shown and the influence of relevant algorithmic parameters on the approximate solution of the contact problem is verified. One drawback of the Spline approximations of stresses though is that they lack accuracy at the contact edge where the structures change their boundary from contact to no contact and where the solution features a kink. The approximation with smooth Spline functions yields numerical artefacts in the form of non-physical oscillations. This property of the numerical solution is not only a drawback for the simulation of e.g. tribological contacts, it also influences the convergence properties of iterative solution procedures negatively. Hence, the NURBS discretized geometries are transformed to Polynomial Splines over Hierarchical T-meshes (PHT-Splines), for the local refinement along contact edges to reduce the artefact of pressure oscillations. NURBS have a tensor product structure which does not allow to refine only certain parts of the geometrical domain while leaving other parts unchanged. Due to the B{\´e}zier Extraction, lying behind the transformation from NURBS to PHT-Splines, the connected mesh structure is broken up into separate elements. This allows an efficient local refinement along the contact edge. Before single elements are refined in a hierarchical form with cross-insertion, existing basis functions must be modified or eliminated. This process of truncation assures local and global linear independence of the refined basis which is needed for a unique approximate solution. The contact boundary is a priori unknown. Local refinement along the contact edge, especially for 3D problems, is for this reason not straight forward. In this work the use of an a posteriori error estimation procedure, the Super Convergent Recovery Solution Based Error Estimation Scheme, together with the D{\"o}rfler Marking Method is suggested for the spatial search of the contact edge. Numerical examples show that the developed method improves the quality of solutions along the contact edge significantly compared to NURBS based approximate solutions. Also, the error in maximum contact pressures, which correlates with the pressure artefacts, is minimized by the adaptive local refinement. In a final step the practicability of the developed solution algorithm is verified by an industrial application: The highly loaded mechanical contact between roller and cam in the drive train of a high-pressure fuel pump is considered.},
  subject      = {Isogeometrische Analyse},
  language  = {en}
}
@phdthesis{List,
  author    = {List, Eik},
  title     = {Design, Analysis, and Implementation of Symmetric-key (Authenticated) Ciphers},
  doi       = {10.25643/bauhaus-universitaet.4523},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20211103-45235},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  pages     = {258},
  abstract  = {Modern cryptography has become an often ubiquitous but essential part of our daily lives. Protocols for secure authentication and encryption protect our communication with various digital services, from private messaging, online shopping, to bank transactions or exchanging sensitive information. Those high-level protocols can naturally be only as secure as the authentication or encryption schemes underneath. Moreover, on a more detailed level, those schemes can also at best inherit the security of their underlying primitives. While widespread standards in modern symmetric-key cryptography, such as the Advanced Encryption Standard (AES), have shown to resist analysis until now, closer analysis and design of related primitives can deepen our understanding. The present thesis consists of two parts that portray six contributions: The first part considers block-cipher cryptanalysis of the round-reduced AES, the AES-based tweakable block cipher Kiasu-BC, and TNT. The second part studies the design, analysis, and implementation of provably secure authenticated encryption schemes. In general, cryptanalysis aims at finding distinguishable properties in the output distribution. Block ciphers are a core primitive of symmetric-key cryptography which are useful for the construction of various higher-level schemes, ranging from authentication, encryption, authenticated encryption up to integrity protection. Therefore, their analysis is crucial to secure cryptographic schemes at their lowest level. With rare exceptions, block-cipher cryptanalysis employs a systematic strategy of investigating known attack techniques. Modern proposals are expected to be evaluated against these techniques. The considerable effort for evaluation, however, demands efforts not only from the designers but also from external sources. The Advanced Encryption Standard (AES) is one of the most widespread block ciphers nowadays. Therefore, it is naturally an interesting target for further analysis. Tweakable block ciphers augment the usual inputs of a secret key and a public plaintext by an additional public input called tweak. Among various proposals through the previous decade, this thesis identifies Kiasu-BC as a noteworthy attempt to construct a tweakable block cipher that is very close to the AES. Hence, its analysis intertwines closely with that of the AES and illustrates the impact of the tweak on its security best. Moreover, it revisits a generic tweakable block cipher Tweak-and-Tweak (TNT) and its instantiation based on the round-reduced AES. The first part investigates the security of the AES against several forms of differential cryptanalysis, developing distinguishers on four to six (out of ten) rounds of AES. For Kiasu-BC, it exploits the additional freedom in the tweak to develop two forms of differential-based attacks: rectangles and impossible differentials. The results on Kiasu-BC consider an additional round compared to attacks on the (untweaked) AES. The authors of TNT had provided an initial security analysis that still left a gap between provable guarantees and attacks. Our analysis conducts a considerable step towards closing this gap. For TNT-AES - an instantiation of TNT built upon the AES round function - this thesis further shows how to transform our distinguisher into a key-recovery attack. Many applications require the simultaneous authentication and encryption of transmitted data. Authenticated encryption (AE) schemes provide both properties. Modern AE schemes usually demand a unique public input called nonce that must not repeat. Though, this requirement cannot always be guaranteed in practice. As part of a remedy, misuse-resistant and robust AE tries to reduce the impact of occasional misuses. However, robust AE considers not only the potential reuse of nonces. Common authenticated encryption also demanded that the entire ciphertext would have to be buffered until the authentication tag has been successfully verified. In practice, this approach is difficult to ensure since the setting may lack the resources for buffering the messages. Moreover, robustness guarantees in the case of misuse are valuable features. The second part of this thesis proposes three authenticated encryption schemes: RIV, SIV-x, and DCT. RIV is robust against nonce misuse and the release of unverified plaintexts. Both SIV-x and DCT provide high security independent from nonce repetitions. As the core under SIV-x, this thesis revisits the proof of a highly secure parallel MAC, PMAC-x, revises its details, and proposes SIV-x as a highly secure authenticated encryption scheme. Finally, DCT is a generic approach to have n-bit secure deterministic AE but without the need of expanding the ciphertext-tag string by more than n bits more than the plaintext. From its first part, this thesis aims to extend the understanding of the (1) cryptanalysis of round-reduced AES, as well as the understanding of (2) AES-like tweakable block ciphers. From its second part, it demonstrates how to simply extend known approaches for (3) robust nonce-based as well as (4) highly secure deterministic authenticated encryption.},
  subject      = {Kryptologie},
  language  = {en}
}