There is a huge need for sending information. In everyday life we nd a greater need for encryption and cryptosistems. In this work we will nd about the basic concept of cryptology, explain the dierence between cryptography and cryptanalysis, dene plaintext, ciphertext and cryptosystem. We will familiarize with RSA cryptosystem and their implementation. In the fourth chapter we will cover, in short, RSA security, the cryptoanalisis of RSA, and the semantic security. However, the fth chapter we will dedicade to the eciency of RSA and modular exponentiation. In the last chapter we will analyze some of the earlier attacks on RSA, such as common modulus attack, Håsdat's broadcast attack and cycling attacks.