That is a fact that the increasing volume of data brings security problems. Encryption measures taken against these emerging and increasing security problems have been examined, and it has been seen that encryption approaches are performed mainly in the areas of neural and quantum cryptography. According to these two of the advanced cryptography techniques are discussed and analyzed with their advantages and disadvantages. This article is committed to paper to be able to provide solutions for big data privacy and big data security problems with Neural and Quantum Cryptography techniques when questioning their feasibility.