Algebra and Cryptography

Basic information

Workload: 

60 hours

Prerequisite: 

Discrete Mathematics

Syllabus: 

Euclidean algorithm; Single factorization, Fermat algorithm, primes, Mersenne and Fermat, Eratosthenes sieve; Modular arithmetic, Divisibility criteria, Diophantine equations; Modular division; Small Fermat theorem; Pseudoprimes; Congruence systems; Password sharing; Groups; Lagrange's theorem; Mersenne and Fermat; Primitive roots; RSA encryption.

 

Teaching Plan

Bibliography

Mandatory: 

•    Coutinho, S. Collier. Integers and Cryptography. Computing and Mathematics Collection. IMPA
•    Hefez, Abramo. Elements of Arithmetic. SBM.
•    Gonçalves, Adilson. Introduction to Algebra. 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.