Cryptography is a branch of applied mathematics whose main focus represents safeness of messages sent through the communication channel. RSA is an asymmetric public key algorithm and it is one of the most famous cryptographic algorithms nowadays. Due to the asymmetry, it is considerably slower and therefore not used for encryption of larger contents. It is applied in the secret key exchange, which is then used to encrypt larger content. Encryption and decryption functions, e_K and d_K, are one-way functions that are based on modular arithmethics. Safeness of this cryptosystem is based on complexity of large number factorization and on the fact that e_K and d_K are one-way functions. The key is to properly choose the parameters that form the secret and public key. An unwary user can make the cracking much easier for the attacker if he does not follow the recommendations when choosing parameters. Cryptoanalysis is a branch of applied mathematics that deals with the detection of ciphers and methods of cracking encrypted data. There are many common methods for attacking the RSA cryptosystem, but in the end, all of them rely on a combination of circumstances in which the user has chosen a poor set of parameters. RSA still hasn’t been cracked, and for now, it can be considered safe, even though there is no mathematical proof of that.