Changes

It is assumed you are experienced with Python development, or have at least run a Python program! If you are on Windows you'll probably use IDLE for as a code editor, although you can use any code editor you wish.

Note if you want to use matplotlib, and are running a native Python installation, you may need to install that package. If the <code>import matplotlib</code> command listed in the next section fails, you'll need to install these, which again for Windows you can get from the [http://www.lfd.uci.edu/~gohlke/pythonlibs/#pyparsing Pre-Built Windows Binaries].

The next step is to read the trace data. I assume If youdon've already t have performed a capture. You need to find the source trace filesany data yet, which have a <code>.npy</code> extension. You can you should follow the path of a <code>.cwp</code> steps in [[Tutorial B5 Breaking AES (ChipWhisperer ProjectStraightforward) file ]] to find the associated trace <code>.cfg</code> file. The same directory as the <code>.cfg</code> file will have the <code>.npy</code> filesrecord some traces.

You need to find the source trace files, which have a <code>.npy</code> extension. You can follow the path of a <code>.cwp</code> (ChipWhisperer Project) file to find the associated trace <code>.cfg</code> file. The same directory as the <code>.cfg</code> file will have the <code>.npy</code> files. As an example, consider say that our <code>.cwp</code> file contains this line:

This means our trace file is in <code>default-data-dir\traces\2013.11.18-16.40.58_traces.npy</code> for example, and the plaintext is in <code>default-data-dir\traces\2013.11.18-16.40.58_textin.npy</code>.

<blockquotepre>>>> traces = np.load(r'C:chipwhisperersoftwarechipwhisperercapturedefault-data-dirtraces2013.11.18-16.40.58_traces.npy') >>> pt = np.load(r'C:chipwhisperersoftwarechipwhisperercapturedefault-data-dirtraces2013.11.18-16.40.58_textin.npy')</blockquotepre>You can print , for example , the first plaintext sent to the device:

After executing <code>plotplt.show()</code> you should get a window to pop up with the single power trace.

Looking way back to how AES works, remember we are effectively attempint attemping to target the position at the bottom of this figure:

<blockquote>[[File:Sbox_cpa_detail.png|frame|none|alt=|caption The AES algorithm involves a number of rounds, this is a detail from the first round of operation. Each input byte is XOR'd with a byte of the (unknown) secret key. This is passed through an S-Box, which is simply a look-up table. The output of this S-Box is what we'll use to 'check' our guessed value of the key.]]

The objective is thus to determine the output of the SBoxS-Box, where the S-Box is defined as follows:

<math>sumnum = {\sum\nolimits_{d = 1}^D {\left[ {\left( {{h_{d,i}} - \overline {{h_i}} } \right)\left( {{t_{d,j}} - \overline {{t_j}} } \right)} \right]} }</math> <math>sumdem1 = \sum\nolimits_{d = 1}^D {{{\left( {{h_{d,i}} - \overline {{h_i}} } \right)}^2}}</math> <math>sumdem2 = \sum\nolimits_{d = 1}^D {{{\left( {{t_{d,j}} - \overline {{t_j}} } \right)}^2}}</math>

Tieing Tying it all together, we end up with the following:

The implementation of the correlation function runs as a loop over all traces. Ideally we'd like to implement this as a 'online' calculation; that is , we can add a trace in, observe the output, add another trace in, observe the output, etc. When generating plots of the Partial Guessing Entropy (PGE) vs. number of traces this is greatly preferred, since otherwise we need to run the loop many times!

We can use an alternate form of the [[File:rij.png]] correlation equation, which explicitly stores sums of the variables. This is easier to perform online calculation with, since when adding a new trace it's simple to update these sums. This form of the equation looks like: <math>r_{i,j} = \frac{D \sum_{d=1}^D h_{d,i}t_{d,j} - \sum_{d=1}^D h_{d,i} \sum_{d=1}^D t_{d,j}}{\sqrt{\Big(\big(\sum_{d=1}^D h_{d,i}\big)^2 - D\sum_{d=1}^D h_{d,i}^2\Big)\Big(\big(\sum_{d=1}^D t_{d,j}\big)^2 - D\sum_{d=1}^D t_{d,j}^2\Big)}}</math>