Essays about: "Applications of Elliptic Curves."

Showing result 1 - 5 of 6 essays containing the words Applications of Elliptic Curves..

  1. 1. The Elliptic Curve Method : A Modern Approach to Integer Factorization

    University essay from KTH/Skolan för teknikvetenskap (SCI)

    Author : Felix Cao; [2023]
    Keywords : Pollard s p-1 method; Factorization; Elliptic curves; Lentra s; Elliptic curve method;

    Abstract : In this paper, we present a study of elliptic curves, focusing on theirunderlying mathematical concepts, properties and applications in numbertheory. We begin by introducing elliptic curves and their unique features,discussing their algebraic structure, and exploring their group law, pro-viding examples and geometric interpretations. READ MORE

  3. 2. On Intersections of Algebraic Curves and Applications to Elliptic Curves

    University essay from Lunds universitet/Matematik (naturvetenskapliga fakulteten)

    Author : Karl Lindén; [2018]
    Keywords : Bezout s theorem; Max Noether s fundamental theorem; Pappus s theorem; Pascal s theorem; Chasles theorem; algebraic curves; elliptic curves; Mathematics and Statistics;

    Abstract : In this thesis we state and give elementary proofs for some fundamental results about intersections of algebraic curves, namely Bezout's, Max Noether's, Pappus's, Pascal's and Chasles' theorems. Our main tools are linear algebra and basic ring theory. We conclude the thesis by applying the results to elliptic curves.. READ MORE

  4. 3. Degree Project in Engineering Physics, First Level Department of Mathematics KTH Royal Institute of Technology

    University essay from KTH/Skolan för teknikvetenskap (SCI)

    Author : Tomas Petkov; [2016]
    Keywords : ;

    Abstract : The study of elliptic curves is an important part of the elds of algebraic geometry and number theory, with many applications in areas such as cryptography. While much of the groundwork has already been laid out, the results often times fall short of giving an easily digestible overview of the subject as a whole. READ MORE

  5. 4. Empirical testing of pseudo random number generators based on elliptic curves

    University essay from Linnéuniversitetet/Institutionen för matematik (MA)

    Author : Reinaudo Alice; [2015]
    Keywords : elliptic curves; cryptography; pseudo random; number generation;

    Abstract : An introduction on random numbers, their history and applications is given, along with explanations of different methods currently used to generate them. Such generators can be of different kinds, and in particular they can be based on physical systems or algorithmic procedures. READ MORE

  6. 5. Elliptic Curves Cryptography

    University essay from Institutionen för datavetenskap, fysik och matematik, DFM

    Author : Zunera Idrees; [2012]
    Keywords : Group Theory and Number Theory; Elliptic Curves; Elliptic Curves over Finite Fields; Applications of Elliptic Curves.;

    Abstract : In the thesis we study the elliptic curves and its use in cryptography. Elliptic curvesencompasses a vast area of mathematics. Elliptic curves have basics in group theory andnumber theory. The points on elliptic curve forms a group under the operation of addition. READ MORE