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→Creating the Template: Added section on sorting traces
== Sorting the Traces ==
With the data in-hand, our next task is to group the data according to our model. We're attacking an intermediate result in the AES algorithm where
<pre>
intermediate = sbox[plaintext ^ key]
</pre>
In our attack, we're going to try to look at a trace and decide what the Hamming weight of this intermediate result is. To set up the templates, we need to sort our template traces into 9 groups. The first group will be all of the traces that have an intermediate Hamming weight of 0. The next group has a Hamming weight of 1, etc..., and the last group has a Hamming weight of 8.
To find which group a trace belongs in, we can calculate the intermediate result from the plaintext and key. Some Python code to do this is:
<pre>
sbox=(
0x63,0x7c,0x77,0x7b,0xf2,0x6b,0x6f,0xc5,0x30,0x01,0x67,0x2b,0xfe,0xd7,0xab,0x76,
0xca,0x82,0xc9,0x7d,0xfa,0x59,0x47,0xf0,0xad,0xd4,0xa2,0xaf,0x9c,0xa4,0x72,0xc0,
0xb7,0xfd,0x93,0x26,0x36,0x3f,0xf7,0xcc,0x34,0xa5,0xe5,0xf1,0x71,0xd8,0x31,0x15,
0x04,0xc7,0x23,0xc3,0x18,0x96,0x05,0x9a,0x07,0x12,0x80,0xe2,0xeb,0x27,0xb2,0x75,
0x09,0x83,0x2c,0x1a,0x1b,0x6e,0x5a,0xa0,0x52,0x3b,0xd6,0xb3,0x29,0xe3,0x2f,0x84,
0x53,0xd1,0x00,0xed,0x20,0xfc,0xb1,0x5b,0x6a,0xcb,0xbe,0x39,0x4a,0x4c,0x58,0xcf,
0xd0,0xef,0xaa,0xfb,0x43,0x4d,0x33,0x85,0x45,0xf9,0x02,0x7f,0x50,0x3c,0x9f,0xa8,
0x51,0xa3,0x40,0x8f,0x92,0x9d,0x38,0xf5,0xbc,0xb6,0xda,0x21,0x10,0xff,0xf3,0xd2,
0xcd,0x0c,0x13,0xec,0x5f,0x97,0x44,0x17,0xc4,0xa7,0x7e,0x3d,0x64,0x5d,0x19,0x73,
0x60,0x81,0x4f,0xdc,0x22,0x2a,0x90,0x88,0x46,0xee,0xb8,0x14,0xde,0x5e,0x0b,0xdb,
0xe0,0x32,0x3a,0x0a,0x49,0x06,0x24,0x5c,0xc2,0xd3,0xac,0x62,0x91,0x95,0xe4,0x79,
0xe7,0xc8,0x37,0x6d,0x8d,0xd5,0x4e,0xa9,0x6c,0x56,0xf4,0xea,0x65,0x7a,0xae,0x08,
0xba,0x78,0x25,0x2e,0x1c,0xa6,0xb4,0xc6,0xe8,0xdd,0x74,0x1f,0x4b,0xbd,0x8b,0x8a,
0x70,0x3e,0xb5,0x66,0x48,0x03,0xf6,0x0e,0x61,0x35,0x57,0xb9,0x86,0xc1,0x1d,0x9e,
0xe1,0xf8,0x98,0x11,0x69,0xd9,0x8e,0x94,0x9b,0x1e,0x87,0xe9,0xce,0x55,0x28,0xdf,
0x8c,0xa1,0x89,0x0d,0xbf,0xe6,0x42,0x68,0x41,0x99,0x2d,0x0f,0xb0,0x54,0xbb,0x16)
intermediate = sbox[tempPText[0][0] ^ tempKey[0][0]]
</pre>
This will calculate the intermediate value for trace 0, looking only at subkey 0. This calculation can be repeated using list comprehension:
<pre>
tempSbox = [sbox[tempPText[i][0] ^ tempKey[i][0]] for i in range(len(tempPText))]
</pre>
Then, we need to get the Hamming weight of all of these intermediate values. We can do this using the same lookup table as the previous tutorial:
<pre>
hw = [bin(x).count("1") for x in range(256)]
tempHW = [hw[s] for s in tempSbox]
</pre>
Confirm that these look correct by printing them. (Would I ever steer you wrong?)
With these Hamming weights, we can look at every trace and decide which group it belongs in. Let's make a list of lists of traces:
<pre>
tempTracesHW = [[] for _ in range(9)]
</pre>
Then, we can loop through our list of traces and append each trace to the right category:
<pre>
for i in range(len(tempTraces)):
HW = tempHW[i]
tempTracesHW[HW].append(tempTraces[i])
</pre>
Now, <code>tempTracesHW[y]</code> is a list of all of the traces with an intermediate Hamming weight of <code>y</code>. As our last step, let's turn this into a NumPy array to make the math easier in the rest of the tutorial:
<pre>
tempTracesHW = np.array(tempTracesHW)
</pre>
== Points of Interest ==
== Covariance Matrices ==