Cryptography in the quantum world

We survey a number of results concerning transmission of quantum information secretly. First of all, we present the basic concepts of quantum information and the rules guiding it. Then we consider quantum teleportation which is the quantum equivalent of the classical one-time-pad, showing the possibility of transmission of perfectly secret quantum messages as long as the users have exchanged a (quantum) secret key before end of a special Einstein-Podolsky-Rosen type. Then we consider quantum cryptography, a technique used to secretly exchange a cryptographic key using the uncertainty principle to determine the amount of tempering on the communication. We unveil a technique known as entanglement purification that publicly allows amplification of the privacy of a random secret key. Combined with quantum cryptography this technique allows users to exchange EPR particles publicly and purify them after tempering of an adversary in order to transmit secret information through teleportation. Finally, the quantum equivalent of Shamir´s secret sharing is presented