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Learn you Galois fields for great good (2023)
you Galois Fields for Great Good (00) Introduction This is the introduction to a series on Abstract Algebra. In particular, our focus will be on Galois Fields (also known as Finite Fields) and their applications in Computer Science.
You interact with implementations of abstract algebra everyday: CRC, AES Encryption, Elliptic-Curve Cryptography, Reed-Solomon, Advanced Erasure Codes, Data Hashing/Fingerprinting, Zero-Knowledge Proofs, etc. In this series, we will start from the very basics of theory and build up step-by-step to interesting applications such as Reed-Solomon, AES, etc. Rabin Fingerprinting Extended Euclidean Algorithm Log and Invlog Tables Elliptic Curves Bit-matrix Representations Fast Multiplication with FFTs Vectorization Implementation Techniques
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