Computer Security Fundamentals, 5th Edition by William Chuck Easttom

Author:William Chuck Easttom [William Chuck Easttom]
Language: eng
Format: epub
Publisher: Pearson IT Certification
Published: 2023-02-15T00:00:00+00:00

Figure 8.5 ShiftRows.

▪ MixColumns: This is a mixing operation that operates on the columns of the state, combining the 4 bytes in each column. In the MixColumns process, each column of the state is multiplied with a fixed polynomial. Each column in the state (remember the matrix we are working with) is treated as a polynomial within the Galois field (28). The result is multiplied with a fixed polynomial c(x) = 3x3 + x2 + x +2 modulo x4 + 1. The MixColumns process can also be viewed as a multiplication by the shown particular MDS matrix in the finite field GF(28).

These processes are executed multiple times in the Rijndael cipher. For 128-bit keys, there are 10 rounds. For 192-bit keys, there are 12 rounds. For 256-bit keys, there are 14 rounds.

These last few steps may be leaving you a bit confused if you don’t have a background in number theory. You may be asking questions like “What is a Galois field?” and “What is a fixed polynomial?” A general overview of the math needed to understand this is provided in the next section.

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