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Galois Fields 1 Fields Designtheory  Form

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okay so let's look at galwa fields and understand how they are used in cryptography so what we basically have is that we might have a vector so let's say we've got four three four six as a vector it is possible to represent that Vector as a as a polynomial so we might Define this as three plus four X plus six x squared and it's these polynomials that we perform our operations and it allows us to simplify our cryptographic operations so we represent our binary values or we can represent our binary values as a polynomial so for example if we have say 0 1 2 and 3 then we have zero zero zero one zero zero zero one one zero and one one this has a degree of two and we would Define that as a gawa field 2 to the power of two for this and we always have zero and this we can represent as X and this we can this we can represent as one this we can represent this X and this will be X plus one if we have a gawa field of three then we could go all the way up from zeros

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