Essays about: "gaussian integers"

Found 5 essays containing the words gaussian integers.

  1. 1. Gaussian Integers and Other Quadratic Integer Rings

    University essay from KTH/Skolan för teknikvetenskap (SCI)

    Author : Erik Landin; Seif Hussein; [2021]
    Keywords : ;

    Abstract : 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. READ MORE

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

    University essay from Linnéuniversitetet/Institutionen för matematik (MA)

    Author : Alessia Pina; [2017]
    Keywords : ;

    Abstract : 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. READ MORE

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

    University essay from KTH/Matematik (Inst.)

    Author : Alice Hedenlund; [2013]
    Keywords : ;

    Abstract : 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. READ MORE

  5. 4. On Quadratic Extensionsand Gaussian Primes

    University essay from KTH/Fysik

    Author : Henrik Löfberg; [2013]
    Keywords : ;

    Abstract : 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. READ MORE

  6. 5. Computations in Prime Fields using Gaussian Integers

    University essay from Institutionen för systemteknik

    Author : Adam Engström; [2006]
    Keywords : gaussian integers; prime fields; arithmetic; logic minimization;

    Abstract : 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. READ MORE