An Overview of the McEliece Cryptosystem with Mathematica Implementation

George Leibowitz

Abstract

Data security is a rising topic that is becoming increasingly important with the integration of various “smart” devices into our lives. The ideas of data security in the most basic and fundamental underlying form lead me to exploring the subject of data encryption. After learning the basics of data security through research, I was led to the McEliece Cryptosystem. Although various types of cryptosystems exist, the McEliece Cryptosystem was one that was not as utilized as others in the field, which was quite interesting for me, as I saw great potential in the system. Although the
patterns that come from this system are finite due to the design of the system, the number of patterns is overwhelming. I decided to start this research project to replicate the McEliece Cryptosystem using Mathematica so that I could alter the system’s inputs and parameters and really explore how the security was created. Through the coding process, which involved plenty of troubleshooting and revisions, I could deeply get to understand the logic behind the system. The McEliece Cryptosystem could also be important in the future for quantum cryptography, a field that will expand when quantum computing has become mainstream.

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