Theory of Numbers in Cryptography and Its Weakness to the Possible Quantum Computer Age

The main application of cryptography is to protect information and to prevent it from being accessible to non-authorized observers. However, it also has other applications, for example to verify that a message has not been intentionally modified by a third party, verify that someone is who they really say they are. The aim of this paper is to show how mathematics plays an important role in modern cryptography as it takes advantage of the difficult problems (in the computational sense) that exist in number theory to develop cryptographic protocols. We also mention what would happen to the cryptographic protocols based on the theory of numbers if there were to be a quantum computer.