| Line 85: | Line 85: | ||
| <math>B_{15}</math> || <math>B_3</math> || <math>B_7</math> || <math>B_{11}</math> | | <math>B_{15}</math> || <math>B_3</math> || <math>B_7</math> || <math>B_{11}</math> | ||
|} | |} | ||
| + | |||
| + | Now <math> B_0 </math> remains in the same place, but <math> B_1 </math> goes to where <math> B_13</math> was and so on. | ||
| + | |||
| + | '''*MixColumn Layer''' | ||
Revision as of 06:23, 19 June 2015
Internal Structure of AES
A slecture by students Katie Marsh and Divya Agarwal
Based on the Cryptography lecture material of Prof. Paar.
Contents
Link to video on youtube
Accompanying Notes
Overview of AES
- AES is a block cipher
- information is handled 128 bits at a time, divided into 16 bytes.
- key can be 128, 192, or 256 bits long
- number of rounds depends on the key length (can be 10/12/14 rounds respectively)
Rounds
Within each round of AES are different layers. The first iteration starts with a Key Addition Layer and then follows this pattern for the remaining rounds:
- Byte Substitution Layer
- ShiftRows Layer
- MixColumn Layer
- Key Addition Layer
The Byte Substitution layer acts as the confusion element, and the ShiftRows and MixColumn Layers act as the diffusion element. In the final round, the MixColumn layer is omitted.
We will now examine each layer separately.
Layers
*Byte Substitution Layer (S) This layer consists of 16 identical S-box which take in 8 bits and output 8 bits. Let $ A_i $ be one byte of input. Then $ S(A_i)=B_i $
But what is the function S? First, the $ A_i^{-1} \in GF(2^8) $ is calculated. Then, an affine transformation is applied.
In software, S-boxes are usually a look up table.
*ShiftRows Layer This transformation looks fairly random until we write it in a new way. First, we write the input bits in a four byte by four byte grid as follows.
| $ B_0 $ | $ B_4 $ | $ B_8 $ | $ B_{12} $ |
| $ B_1 $ | $ B_5 $ | $ B_9 $ | $ B_{13} $ |
| $ B_2 $ | $ B_6 $ | $ B_{10} $ | $ B_{14} $ |
| $ B_3 $ | $ B_7 $ | $ B_{11} $ | $ B_{15} $ |
Then we shift the second row 3 positions to the right, the third row 2 positions to the right and the fourth row 1 position to the right and achieve the following result:
| $ B_0 $ | $ B_4 $ | $ B_8 $ | $ B_{12} $ |
| $ B_5 $ | $ B_9 $ | $ B_{13} $ | $ B_1 $ |
| $ B_{10} $ | $ B_{14} $ | $ B_2 $ | $ B_6 $ |
| $ B_{15} $ | $ B_3 $ | $ B_7 $ | $ B_{11} $ |
Now $ B_0 $ remains in the same place, but $ B_1 $ goes to where $ B_13 $ was and so on.
*MixColumn Layer
References
Questions and comments
If you have any questions, comments, etc. please post them here.
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