The Galois Field in Cryptography

This project is about Galois fields, what properties they have and how they can be used in cryptography.

The project starts with the basics of Galois fields. Some of the basics of Groups, Rings and Fields and how they are used to define a Galois field are discussed. The difference between prime and extension fields is explained.

This is followed by an introduction to symmetric/asymmetric cryptography.

At the end, some example implementations of symmetric encryption using Galois fields are shown.

1. Group, Ring and Field

2. Finite Fields. Galois field - GF(2)

• Construction of Finite Fields
• Prime Fields - GF(p)
• Extension Fields GF(p^n)

3. Symmetric vs. Asymmetric Cryptography

4. Example of Symmetric Encryption

• One-Time Pad (OTP) for One-Bit Messages
• Extension one-bit encryption system to many bits
• AES (Advanced Encryption Standard)

5. Applications of encryption over GF(2)