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Added script in appendix and mentioned scipy include
** Calculate the log of the PDF (<math>\log f(\mathbf{a})</math>) and add it to the running total
* List the best guesses we've seen so far
Make sure you've included the multivariate stats from SciPy:
<pre>
from scipy.stats import multivariate_normal
</pre>
Our implementation is:
<pre>
If you ran into numerical problems while working through this tutorial, try recording another bigger data set. Instead of capturing 1000 template traces, try 5000 (on your coffee break), 10000 (on your lunch break), or 100000 (overnight). You'll probably find that the extra data makes the statistics work out better.
= Appendix: Full Script =
If you got lost, here's our full implementation:
<pre>
# manualTemplate.py
# A script to perform a template attack
# Will attack one subkey of AES-128
import numpy as np
from scipy.stats import multivariate_normal
import matplotlib.pyplot as plt
# Useful utilities
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)
hw = [bin(x).count("1") for x in range(256)]
def cov(x, y):
# Find the covariance between two 1D lists (x and y).
# Note that var(x) = cov(x, x)
return np.cov(x, y)[0][1]
# Uncomment to check
#print sbox
#print [hw[s] for s in sbox]
# Start calculating template
# 1: load data
tempTraces = np.load(r'C:\chipwhisperer\software\temp_attack\rand_key_data\traces\2016.05.24-12.53.15_traces.npy')
tempPText = np.load(r'C:\chipwhisperer\software\temp_attack\rand_key_data\traces\2016.05.24-12.53.15_textin.npy')
tempKey = np.load(r'C:\chipwhisperer\software\temp_attack\rand_key_data\traces\2016.05.24-12.53.15_keylist.npy')
#print tempPText
#print len(tempPText)
#print tempKey
#print len(tempKey)
#plt.plot(tempTraces[0])
#plt.show()
# 2: Find HW(sbox) to go with each input
# Note - we're only working with the first byte here
tempSbox = [sbox[tempPText[i][0] ^ tempKey[i][0]] for i in range(len(tempPText))]
tempHW = [hw[s] for s in tempSbox]
#print tempSbox
#print tempHW
# 2.5: Sort traces by HW
# Make 9 blank lists - one for each Hamming weight
tempTracesHW = [[] for _ in range(9)]
# Fill them up
for i in range(len(tempTraces)):
HW = tempHW[i]
tempTracesHW[HW].append(tempTraces[i])
# Switch to numpy arrays
tempTracesHW = [np.array(tempTracesHW[HW]) for HW in range(9)]
#print len(tempTracesHW[8])
# 3: Find averages
tempMeans = np.zeros((9, len(tempTraces[0])))
for i in range(9):
tempMeans[i] = np.average(tempTracesHW[i], 0)
#plt.plot(tempMeans[2])
#plt.grid()
#plt.show()
# 4: Find sum of differences
tempSumDiff = np.zeros(len(tempTraces[0]))
for i in range(9):
for j in range(i):
tempSumDiff += np.abs(tempMeans[i] - tempMeans[j])
#plt.plot(tempSumDiff)
#plt.grid()
#plt.show()
# 5: Find POIs
POIs = []
numPOIs = 5
POIspacing = 5
for i in range(numPOIs):
# Find the max
nextPOI = tempSumDiff.argmax()
POIs.append(nextPOI)
# Make sure we don't pick a nearby value
poiMin = max(0, nextPOI - POIspacing)
poiMax = min(nextPOI + POIspacing, len(tempSumDiff))
for j in range(poiMin, poiMax):
tempSumDiff[j] = 0
#print POIs
# 6: Fill up mean and covariance matrix for each HW
meanMatrix = np.zeros((9, numPOIs))
covMatrix = np.zeros((9, numPOIs, numPOIs))
for HW in range(9):
for i in range(numPOIs):
# Fill in mean
meanMatrix[HW][i] = tempMeans[HW][POIs[i]]
for j in range(numPOIs):
x = tempTracesHW[HW][:,POIs[i]]
y = tempTracesHW[HW][:,POIs[j]]
covMatrix[HW,i,j] = cov(x, y)
#print meanMatrix
#print covMatrix[0]
# Template is ready!
# 1: Load attack traces
atkTraces = np.load(r'C:\chipwhisperer\software\temp_attack\fixed_key_data\traces\2016.05.24-12.10.07_traces.npy')
atkPText = np.load(r'C:\chipwhisperer\software\temp_attack\fixed_key_data\traces\2016.05.24-12.10.07_textin.npy')
atkKey = np.load(r'C:\chipwhisperer\software\temp_attack\fixed_key_data\traces\2016.05.24-12.10.07_knownkey.npy')
#print atkTraces
#print atkPText
print atkKey
# 2: Attack
# Running total of log P_k
P_k = np.zeros(256)
for j in range(len(atkTraces)):
# Grab key points and put them in a small matrix
a = [atkTraces[j][POIs[i]] for i in range(len(POIs))]
# Test each key
for k in range(256):
# Find HW coming out of sbox
HW = hw[sbox[atkPText[j][0] ^ k]]
# Find p_{k,j}
rv = multivariate_normal(meanMatrix[HW], covMatrix[HW])
p_kj = rv.pdf(a)
# Add it to running total
P_k[k] += np.log(p_kj)
# Print our top 5 results so far
# Best match on the right
print P_k.argsort()[-5:]
</pre>
{{Template:Tutorials}}
