Advanced Encryption Standard: Difference between revisions

Revision as of 14:46, 26 November 2024

Revision as of 14:47, 26 November 2024

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In more general sense, each column is treated as a polynomial over <math>\operatorname{GF}(2^8)</math> and is then multiplied modulo <math>{01}_{16} \cdot z^4+{01}_{16}</math> with a fixed polynomial <math>c(z) = {03}_{16} \cdot z^3 + {01}_{16} \cdot z^2 +{01}_{16} \cdot z + {02}_{16}</math>. The coefficients are displayed in their [[hexadecimal]] equivalent of the binary representation of bit polynomials from <math>\operatorname{GF}(2)[x]</math>. The {{mono | MixColumns}} step can also be viewed as a multiplication by the shown particular [[MDS matrix]] in the [[finite field]] <math>\operatorname{GF}(2^8)</math>. This process is described further in the article [[Rijndael MixColumns]].

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=== The {{mono|AddRoundKey}} ===

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[[Image:AES-AddRoundKey.svg|right|320px|thumbnail|In the {{mono | AddRoundKey}} step, each byte of the state is combined with a byte of the round subkey using the [[Exclusive or|XOR]] operation (⊕).]]

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In the {{mono | AddRoundKey}} step, the subkey is combined with the state. For each round, a subkey is derived from the main [[key (cryptography)|key]] using [[Rijndael key schedule|Rijndael's key schedule]]; each subkey is the same size as the state. The subkey is added by combining of the state with the corresponding byte of the subkey using bitwise [[Exclusive or|XOR]].

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=== Optimization of the cipher ===