Stage en arithmétique et application à la cryptographie, introduction aux courbes elliptiques

Méthodologie

Durée : Deux semaines - Prix : 400.00€ - Lieu : Bordeaux (33000)Introduction
1 An Introduction to Cryptography 1
1.1 Simple substitution ciphers 1
1.2 Divisibility and greatest common divisors 10
1.3 Modular arithmetic 19
1.4 Prime numbers, unique factorization, and finite fields 26
1.5 Powers and primitive roots in finite fields 29
1.6 Cryptography before the computer age 34
1.7 Symmetric and asymmetric ciphers 36
Exercises 47


3 Integer Factorization and RSA 113
3.1 Euler's formula and roots modulo pq 113
3.2 The RSA public key cryptosystem 119
3.3 Implementation and security issues 122
3.4 Primality testing 124
3.5 Pollard's p — 1 factorization algorithm 133