Algebra and Cryptography
Euclidean algorithm; Single factorization, Fermat algorithm, primes, Mersenne and Fermat, Sieve of Eratosthenes; Modular arithmetic, divisibility criteria, Diophantine equations; Modular division; Fermat's Little Theorem; Pseudocousins; Congruence systems; sharing passwords; Groups; Lagrange's Theorem; Mersenne and Fermat; Primitive roots; RSA Encryption.
Basic Information
Workload
60
Requirements
Discrete Mathematics
Mandatory:
- Coutinho, S. Collier. Números Inteiros e Criptografia. Coleção Computação e Matemática. IMPA
- Hefez, Abramo. Elementos de Aritmética. SBM.
- Gonçalves, Adilson. Introdução a Álgebra. IMPA.
Complementary:
- Codes and Ciphers: Julius Caesar, the Enigma, and the Internet R. F. Churchhouse;
- An Introduction to Cryptography Richard A. Mollin;
- RSA and Public-Key Cryptography Richard A.
- A Course in Number Theory and Cryptography NEAL Koblitz;
- Algebraic Aspects of Cryptography NEAL Koblitz.