Sökning: "elliptic curves"

Visar resultat 1 - 5 av 21 uppsatser innehållade orden elliptic curves.

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

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

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

    Sammanfattning : 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. LÄS MER

  3. 2. Elliptic Curves and Cryptography

    Kandidat-uppsats, Uppsala universitet/Sannolikhetsteori och kombinatorik

    Författare :David Ahlqvist; [2022]
    Nyckelord :;

    Sammanfattning : .... LÄS MER

  4. 3. Effective quasiparallelogram laws on elliptic curves over number fields

    Master-uppsats, Göteborgs universitet/Institutionen för matematiska vetenskaper

    Författare :Douglas Molin; [2021-05-21]
    Nyckelord :height; elliptic curve; quasiparallelogram law; canonical height; difference bounds;

    Sammanfattning : We introduce the classical theory of heights on projective space and prove explicit quasiparallelogram laws for the ordinary height and the naive height on elliptic curves over number fields with shortWeierstrass equations. As corollaries, we obtain bounds for the differences between the classical heights and the canonical height, similar to the well-known Silverman bounds. LÄS MER

  5. 4. Pairing-Based Cryptography in Theory and Practice

    Kandidat-uppsats, Umeå universitet/Institutionen för matematik och matematisk statistik

    Författare :Hannes Salin; [2021]
    Nyckelord :cryptography; pairings; elliptic curves; algebra; provable security; algebraic geometry;

    Sammanfattning : In this thesis we review bilinear maps and their usage in modern cryptography, i.e. the theoretical framework of pairing-based cryptography including the underlying mathematical hardness assumptions. The theory is based on algebraic structures, elliptic curves and divisor theory from which explicit constructions of pairings can be defined. LÄS MER

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

    Kandidat-uppsats, Lunds universitet/Matematik LTH; Lunds universitet/Matematik (naturvetenskapliga fakulteten)

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

    Sammanfattning : 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 $m\geq 2$. LÄS MER