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Arithmétique - Licence 1

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Author(s): Eric Hoffbeck
Year: 2015

Language: French
Commentary: Downloaded from https://www.math.univ-paris13.fr/~hoffbeck/Arith/poly-L1.pdf

Introduction : Un peu de cryptographie
I. Division euclidienne et congruences
I.1. Division euclidienne
I.2. Divisibilité
I.3. Définition de la relation de congruence (Rappel)
I.4. Congruences et opérations
I.5. Application : les carrés itérés
II. Plus grand commun diviseur
II.1. Définition
II.2. Algorithme d'Euclide
II.3. Théorèmes de Bézout
II.4. Applications
III. Le théorème d'Euler
III.1. Rappels et notations
III.2. Fonction indicatrice d'Euler
III.3. Le théorème d'Euler
IV. Le système RSA
IV.1. Préliminaires arithmétiques
IV.2. Les fonctions de cryptage et de décryptage
IV.3. Clé publique et clé secrète
IV.4. Sécurité du système RSA