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Mathematical foundations of cryptography including Galois Fields and AES S-box implementation.
Overview
Lab 5 explores the mathematical foundations underlying modern cryptography, with focus on algebraic structures, finite fields (Galois Fields), and their application in AES. The project implements Galois Field arithmetic (GF(2^8)), generates multiplication and addition tables, and builds the AES S-box substitution layer. This provides deep understanding of the mathematical principles that make AES secure and efficient.
Technologies Used
Key Features
Galois Field GF(2^8) arithmetic implementation
Finite field multiplication and addition
Multiplication table generation for GF(2^8)
AES S-box generation using multiplicative inverse
Affine transformation implementation
Irreducible polynomial operations
Showing 6 of 8 features
Challenges
Understanding abstract algebra concepts, implementing finite field arithmetic correctly, computing multiplicative inverses in GF(2^8), ensuring mathematical correctness of S-box generation.
Outcome & Impact
Successfully implemented GF(2^8) arithmetic operations, generated correct AES S-box matching specification, gained deep mathematical understanding of AES security properties.
How I Grew
Mastered finite field arithmetic and Galois Field theory
Learned mathematical foundations of AES cipher
Understood the role of irreducible polynomials in cryptography
Gained expertise in polynomial arithmetic over finite fields
Developed skills in implementing abstract mathematical concepts
Learned how S-box design contributes to cipher security