Essays about: "Elliptiska kurvor"

Found 4 essays containing the words Elliptiska kurvor.

  1. 1. Scheme Theory & Weak Mordell-Weil for Elliptic Curves Over Number Fields

    University essay from Lunds universitet/Matematik LTH; Lunds universitet/Matematik (naturvetenskapliga fakulteten)

    Author : Carl-Fredrik Lidgren; [2021]
    Keywords : algebraic geometry; schemes; scheme theory; elliptic curves; Mordell-Weil; weak Mordell-Weil; algebraic number theory; arithmetic geometry; number theory; geometry; Mathematics and Statistics;

    Abstract : We provide an introduction to scheme-theoretic algebraic geometry, which studies spaces that are in essence locally solutions to systems of polynomial equations, and prove the weak Mordell-Weil theorem. The weak Mordell-Weil theorem states that for an elliptic curve $E$ over a number field $K$, the quotient $E(K)/mE(K)$ is finite for all $m\geq 2$. 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. Some Nonlinear Diophantine Equations

    University essay from Lunds universitet/Matematik (naturvetenskapliga fakulteten)

    Author : Alexander Koronen; [2017]
    Keywords : Diophantine Equations; Congruences; Euclidean Domains; Mathematics and Statistics;

    Abstract : This thesis deals with some special types of Diophantine equations. Two classic cases of Fermat's equation are shown to have no nontrivial integer solutions, using two different approaches. The rest of the thesis deals with some instances of y^2=x^3+k, commonly known as Mordell's equation. In most cases, no integer solutions exist. READ MORE

  5. 4. Elliptic Curve Digital Signatures in RSA Hardware

    University essay from Informationskodning; Tekniska högskolan

    Author : Martin Krisell; [2012]
    Keywords : Cryptography; Digital Signatures; Elliptic Curves; ECC; ECDSA; ECIES; RSA; Kryptering; Digitala signaturer; Elliptiska kurvor; ECC; ECSDA; ECIES; RSA;

    Abstract : A digital signature is the electronic counterpart to the hand written signature. It can prove the source and integrity of any digital data, and is a tool that is becoming increasingly important as more and more information is handled electronically. Digital signature schemes use a pair of keys. READ MORE