<http://purl.org/dc/terms/description>
"Cryptography is defined to be the practice and studying of hiding information\nand is used in applications present today; examples include the security of ATM\ncards and computer passwords ([34]). In order to transform information to make it\nunreadable, one needs a series of algorithms. Many of these algorithms are based on\nelliptic curves because they require fewer bits. To use such algorithms, one must find\nthe rational points on an elliptic curve. The study of Algebraic Number Theory, and\nin particular, rare objects known as power bases, help determine what these rational\npoints are. With such broad applications, studying power bases is an interesting\ntopic with many research opportunities, one of which is given below.\nThere are many similarities between Cyclic and Dihedral fields of prime degree;\nmore specifically, the structure of their field discriminants is comparable. Since the\nexistence of power bases (i.e. monogenicity) is based upon finding solutions to the\nindex form equation - an equation dependant on field discriminants - does this imply\nmonogenic properties of such fields are also analogous?\nFor instance, in [14], Marie-Nicole Gras has shown there is only one monogenic\ncyclic field of degree 5. Is there a similar result for dihedral fields of degree 5? The\npurpose of this thesis is to show that there exist infinitely many monogenic dihedral\nquintic fields and hence, not just one or finitely many. We do so by using a well-\nknown family of quintic polynomials with Galois group D\u2085. Thus, the main theorem\ngiven in this thesis will confirm that monogenic properties between cyclic and dihedral\nquintic fields are not always correlative."@en
<https://open.library.ubc.ca/cIRcle/collections/ubctheses/24/items/1.0066793>