Abstarct: Distributing a secure key between two legitimate users over a distance, is the main task of cryptography. In classical cryptography, security of secret key is baxsed on the difficulty of math functions, while, in quantum cryptography or quantum key distribution(QKD), security depends on fundamental principals of quantum mechanics. Several protocols have been introduced for QKD which almost all of them use carrying particle to send information from sender to receiver. The security of QKD protocols provided by several steps such as authentication, sifting process and privacy amplification processes. In 2003, Bostrom and Felbinger presented a direct two-way quantum communication baxsed on entangled qubits. Since the information is transferred in a deterministic manner, no qubits have to be discarded and therefore, the information can be decoded after the transmission. In this protocol security against eavesdropping attacks is provided by the control mode in quantum communication. In this thesis, first we have review some basic concepts used in cryptography. Then we have a general overview of quantum key distribution and some well-known quantum key distribution protocols. Finally we presented a complete explanation of Ping-Pong protocol and investigate its security against different kinds of attacks.