https://github.com/kostadinlambov/the-galois-field-in-cryptography
This project is about Galois fields, what properties they have and how they can be used in cryptography.
https://github.com/kostadinlambov/the-galois-field-in-cryptography
aes-encryption asymmetric-cryptography encryption-decryption extension-fields finite-fields galois-fields numpy prime-fields python symmetric-cryptography
Last synced: 3 months ago
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This project is about Galois fields, what properties they have and how they can be used in cryptography.
- Host: GitHub
- URL: https://github.com/kostadinlambov/the-galois-field-in-cryptography
- Owner: kostadinlambov
- License: mit
- Created: 2024-06-13T18:24:35.000Z (over 1 year ago)
- Default Branch: master
- Last Pushed: 2024-07-03T18:44:34.000Z (over 1 year ago)
- Last Synced: 2025-04-06T05:32:59.057Z (6 months ago)
- Topics: aes-encryption, asymmetric-cryptography, encryption-decryption, extension-fields, finite-fields, galois-fields, numpy, prime-fields, python, symmetric-cryptography
- Language: Jupyter Notebook
- Homepage:
- Size: 604 KB
- Stars: 0
- Watchers: 1
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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README
# 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)