Foundations of Security Week11 Lecture

Lecture Outline#

1. Review of AES encryption structure
2. ShiftRows transformation in AES
3. MixColumns transformation in AES
4. AddRoundKey transformation

Learning Outcomes#

By the end of this lecture, students should be able to:

1. Describe how rows in the AES state matrix are shifted
2. Describe how columns are transformed using matrix multiplication
3. Understand how AES operations are performed in $GF(2^8)$
4. Perform basic MixColumns calculations using polynomial operations

Advanced Encryption Standard (AES)#

Main Rounds - ShiftRows

It shifts the bytes in each row of the subbytes result to the left by a specific number of positions.

Main Rounds - Mix Columns

• It transforms each column using matrix multiplication in Galois Field ($\textcolor{blue}{GF(2^8)}$) to ensure that changes to one byte affect all four bytes in the column.
• This multiplication is not traditional matrix multiplication.
• Each column of the state matrix (consisting of 4 bytes) is treated as a 4-byte vector and is multiplied by a fixed 4 $\times$ 4 matrix
• This is done in $GF(2^8)$ using modulo operations with the irreducible polynomial $x^8+x^4+x^3+x+1$

• Convert to binary and Reduce using the irreducible polynomial $\textcolor{blue}{x^8+x^4+x^3+x+1}$

or

• Compute for all, cross out and Reduce using the irreducible polynomial $\textcolor{blue}{x^8+x^4+x^3+x+1}$

• Convert to binary and Reduce using the irreducible polynomial $\textcolor{blue}{x^8+x^4+x^3+x+1}$

Main Rounds – AddRoundKey