University Sétif 1 FERHAT ABBAS Faculty of Sciences
Détail de l'auteur
Auteur Hasna Chouli |
Documents disponibles écrits par cet auteur
Ajouter le résultat dans votre panier Affiner la recherche
Titre : Elliptic Curve Cryptography defined on Finite Fields Type de document : texte imprimé Auteurs : Affaf Mechakou, Auteur ; Hasna Chouli ; Ahmed Djamal Eddine Bouzidi, Directeur de thèse Editeur : Sétif:UFA1 Année de publication : 2024 Importance : 1 vol (39 f.) Format : 29 cm Langues : Français (fre) Catégories : Thèses & Mémoires:Mathématique Mots-clés : Elliptic curve Finite Filed Index. décimale : 510-Mathématique Résumé : This memory is a map that guides us through understanding ECC and why it is so promising , we’ve split it into three main chapters that progressively explore finite fields, elliptic curves, and their cryptographic applications.
The first chapter introduces the fundamentals by examining the structure and proper- ties of finite fields.
The second chapter delves into elliptic curves, their geometric and algebraic repre- sentations, and the arithmetic operations defined over finite fields.
Building on these concepts, the third chapter focuses on elliptic curve cryptography, a powerful approach to secure communication and data protection based on the hard- ness of the elliptic curve discrete logarithm problem, Key exchange protocols, and other cryptographic schemes utilizing elliptic curves are covered.Through this logical progres- sion, a comprehensive understanding of these fundamental topics is developed.Note de contenu : Contents
1 Introduction 7
2 Finite Filed 9
2.1 Finite Filed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2 Irreducible Polynomial ........................................................................................ 11
2.3 Construction of Finite Fields .............................................................................. 12
3 Elliptic curve 15
3.1 Curves ................................................................................................................. 15
3.2 Elliptic Curves ..................................................................................................... 17
3.2.1 Group Law ............................................................................................... 18
3.2.2 Elliptic Curves over Finite Fields ...................................................... 22
4 Elliptic Curves Cryptography 25
4.1 Asymmetric Cryptography .................................................................................. 25
4.1.1 Cryptography ........................................................................................... 25
4.1.2 Asymmetric Encryption ........................................................................... 25
4.2 The Discrete Logarithm Problem ....................................................................... 25
4.2.1 Finite Field DLP .............................................................................. 26
4.2.2 Elliptic Curve DLP .......................................................................... 26
4.3 Fast Exponentiation Algorithm ........................................................................... 27
4.3.1 Over Finite Field .............................................................................. 27
4.3.2 Fast Exponentation on Elliptic Curve ................................................... 29
4.4 Asymmetric Cryptography Based on Diffie–Hellman....................................... 29
4.4.1 Diffie–Hellman Key Exchange Over Finite Fields ................................. 29
4.4.2 Diffie–Hellman Key Exchange Over Elliptic Curves ............................... 30
4.5 Baby step giant step attack ........................................................ 32
4.5.1 Over finite fields ................................................................ 32
4.5.2 Over Elliptic curve ................................................................. 34Côte titre : MAM/0761 Elliptic Curve Cryptography defined on Finite Fields [texte imprimé] / Affaf Mechakou, Auteur ; Hasna Chouli ; Ahmed Djamal Eddine Bouzidi, Directeur de thèse . - [S.l.] : Sétif:UFA1, 2024 . - 1 vol (39 f.) ; 29 cm.
Langues : Français (fre)
Catégories : Thèses & Mémoires:Mathématique Mots-clés : Elliptic curve Finite Filed Index. décimale : 510-Mathématique Résumé : This memory is a map that guides us through understanding ECC and why it is so promising , we’ve split it into three main chapters that progressively explore finite fields, elliptic curves, and their cryptographic applications.
The first chapter introduces the fundamentals by examining the structure and proper- ties of finite fields.
The second chapter delves into elliptic curves, their geometric and algebraic repre- sentations, and the arithmetic operations defined over finite fields.
Building on these concepts, the third chapter focuses on elliptic curve cryptography, a powerful approach to secure communication and data protection based on the hard- ness of the elliptic curve discrete logarithm problem, Key exchange protocols, and other cryptographic schemes utilizing elliptic curves are covered.Through this logical progres- sion, a comprehensive understanding of these fundamental topics is developed.Note de contenu : Contents
1 Introduction 7
2 Finite Filed 9
2.1 Finite Filed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2 Irreducible Polynomial ........................................................................................ 11
2.3 Construction of Finite Fields .............................................................................. 12
3 Elliptic curve 15
3.1 Curves ................................................................................................................. 15
3.2 Elliptic Curves ..................................................................................................... 17
3.2.1 Group Law ............................................................................................... 18
3.2.2 Elliptic Curves over Finite Fields ...................................................... 22
4 Elliptic Curves Cryptography 25
4.1 Asymmetric Cryptography .................................................................................. 25
4.1.1 Cryptography ........................................................................................... 25
4.1.2 Asymmetric Encryption ........................................................................... 25
4.2 The Discrete Logarithm Problem ....................................................................... 25
4.2.1 Finite Field DLP .............................................................................. 26
4.2.2 Elliptic Curve DLP .......................................................................... 26
4.3 Fast Exponentiation Algorithm ........................................................................... 27
4.3.1 Over Finite Field .............................................................................. 27
4.3.2 Fast Exponentation on Elliptic Curve ................................................... 29
4.4 Asymmetric Cryptography Based on Diffie–Hellman....................................... 29
4.4.1 Diffie–Hellman Key Exchange Over Finite Fields ................................. 29
4.4.2 Diffie–Hellman Key Exchange Over Elliptic Curves ............................... 30
4.5 Baby step giant step attack ........................................................ 32
4.5.1 Over finite fields ................................................................ 32
4.5.2 Over Elliptic curve ................................................................. 34Côte titre : MAM/0761 Exemplaires (1)
Code-barres Cote Support Localisation Section Disponibilité MAM/0761 MAM/0761 Mémoire Bibliothéque des sciences Anglais Disponible
Disponible
