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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).

2.2 Binary System In the binary numeral system or base-2 number system, we represents each value with 0 and 1. To convert a decimal numeral system or base-10 number system into binary system, we need to represent a decimal in terms of sums of a n2n. That is, if x is the said decimal number then we wish to have x = X n2N a n2 n The coe cients a

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