In the near future, general quantum computers could become a reality. Because of this we have a need for updating our public key infrastructure to resist quantum attacks. Among the many proposed cryptosystems that we could use to replace our modern cryptosystems are the four cryptosystems we will be analysing: McEliece, Classic McEliece, McNie, and NTRUEncrypt. We will cover the cryptosystems in full detail before analysing how secure and how efficient the cryptosystems are