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Galois Field in Cryptography

Galois Field in CryptographyChristoforus Juan BenvenutoMay 31, 2012 AbstractThis paper introduces the basics of Galois Field as well as its im-plementation in storing data. This paper shows and helps visualizesthat storing data in Galois Fields allows manageable and effectivedata manipulation, where it focuses mainly on application in com-puter Cryptography . Details on the algorithm for Advanced Encryp-tion Standard (AES), which is an examples of computer cryptographythat utilizes Galois Field , will also be Introduction22 Galois Field .. Binary System .. Bit and Byte .. ASCII .. Finite Field Arithmetic .. and Subtraction .. and Multiplicative Inverse ..53 Application in Advanced Encryption Standard (AES) .. 1011 IntroductionGalois Field , named after Evariste Galois , also known as finite Field , refers toa Field in which there exists finitely many elements.

ASCII stands for American Standard Code for Information Interchange. Since there are exactly 255 characters in ASCII, we can uniquely assign 3. each character to an element in gf(28) or represent it as a byte. The most frequently used ASCII codes and their values are given in …

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