Explorando os números primos e uma das suas aplicações atuais: a criptografia

Abstract

Prime numbers are a great mystery in Mathematics with many questions and curiosities about them. Is there a function which give us all prime numbers? How can one know wether a given number is prime or not? How useful are prime numbers? Questions like those motivated us to write about this topic which is not so much discussed in basic education and has huge relevance, especially nowadays. One of its applications with direct influence in everyday life is encryption. When we make a bank transaction, exchange a message or even when we write a note using codes, we are using encryption and consequently Mathematics. In this dissertation we work, first, with concepts about prime numbers, generating functions, primality tests, special primes and some fundamental theorems about them. Next, we present RSA and ElGamal encryption systems, including their encoding, decryption and authenticity. We also present the Diffie- Hellman Protocol, an advance in key exchange. Lastly, we suggest activities to arouse the interest of students of basic education and to reinforce the importance of Mathematics in the life of everybody.