Sökning: "gaussian integers"

Hittade 5 uppsatser innehållade orden gaussian integers.

1. 1. Gaussian Integers and Other Quadratic Integer Rings

   Kandidat-uppsats, KTH/Skolan för teknikvetenskap (SCI)

   Författare :Erik Landin; Seif Hussein; [2021]
   Nyckelord :;

   Sammanfattning : This thesis deals with quadratic integer rings, in particular the Gaussian integers Z}[i]. Concepts such as quadratic extensions, Euclidean domains and unique factorization domains will be introduced to the reader. LÄS MER

3. 2. RSA in extensions of the ring of integers

   Master-uppsats, Linnéuniversitetet/Institutionen för matematik (MA)

   Författare :Alessia Pina; [2017]
   Nyckelord :;

   Sammanfattning : The aim of this work is to create a variant of the RSA classical algorithm, through extensions from the ring of integers Z to two Euclidean domains:the domain of Gaussian integers, Z[i], and the domain generated by p2, Z[p2]. To achieve this purpose, the study of the theory behind both these sets becomes necessary, to ensure that all the properties are preserved when moving into extensions and so that the construction of the algorithm is possible. LÄS MER

4. 3. On Integers, Primes and UniqueFactorization in Quadratic Fields

   Kandidat-uppsats, KTH/Matematik (Inst.)

   Författare :Alice Hedenlund; [2013]
   Nyckelord :;

   Sammanfattning : Abstract. This thesis will deal with quadratic elds. The prob- lem is to study such elds and their properties including, but not limited to, determining integers, nding primes and deciding which quadratic elds have unique factorization. LÄS MER

5. 4. On Quadratic Extensionsand Gaussian Primes

   Kandidat-uppsats, KTH/Fysik

   Författare :Henrik Löfberg; [2013]
   Nyckelord :;

   Sammanfattning : Abstract. This thesis will deal with algebraic extensions. The goal is to give the reader an introduction to algebraic extensions, euclidian domains, unique factorization domains as well as more specic theories for example how to nd primes in the gaussian integers. LÄS MER

7. 5. Computations in Prime Fields using Gaussian Integers

   Uppsats för yrkesexamina på grundnivå, Institutionen för systemteknik

   Författare :Adam Engström; [2006]
   Nyckelord :gaussian integers; prime fields; arithmetic; logic minimization;

   Sammanfattning : In this thesis it is investigated if representing a field Zp, p = 1 (mod 4) prime, by another field Z[i]/ < a + bi > over the gaussian integers, with p = a2 + b2, results in arithmetic architectures using a smaller number of logic gates. Only bit parallell architectures are considered and the programs Espresso and SIS are used for boolean minimization of the architectures. LÄS MER