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CorrelationPowerAnalysis.py
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CorrelationPowerAnalysis.py
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import numpy as np
import matplotlib.pyplot as plt
class CpaOnAES128:
sboxTable = (
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
)
def __init__(self):
self.allKeyBytes = []
self.firstKeyByte = None
self.nthKeyByte = None
self.isAllKeyBytes = False
self.isFirstKeyByte = False
self.isNthKeyByte = False
self.plainTexts = None
self.powerTraces = None
self.plainTextsTemp = None
self.powerTracesTemp = None
self.hypothesisMatrix = None
self.correlationMatrix = None
self.maxCorrForEachKeyHypo = None
self.gradualMaxCorrForEachKeyHypo = []
self.stepSizes = []
def GetKey(self):
return self.key
def SetPowerTraces(self, powerTraces):
self.powerTraces = powerTraces
def SetPlainTexts(self, plainTexts):
self.plainTexts = plainTexts
def GetPlainTexts(self):
return self.plainTexts
def GetPowerTraces(self):
return self.powerTraces
def Sbox(self, inp):
return self.sboxTable[inp]
def HammingWeight(self, num):
return bin(num).count("1")
def HammingDistance(self, num1, num2):
return self.HammingWeight(num1^num2)
def CreateHypothesisMatrix(self, byteNumber):
keyHypo = [i for i in range(256)]
self.hypothesisMatrix = np.zeros((len(self.plainTexts), len(keyHypo)))
for i in range(len(self.plainTexts)):
for j in range(len(keyHypo)):
sboxResult = self.Sbox(self.plainTexts[i][byteNumber] ^ keyHypo[j])
self.hypothesisMatrix[i][j] = self.HammingWeight(sboxResult)
def GradualCreateHypothesisMatrix(self, byteNumber):
keyHypo = [i for i in range(256)]
self.hypothesisMatrix = np.zeros((len(self.plainTextsTemp), len(keyHypo)))
for i in range(len(self.plainTextsTemp)):
for j in range(len(keyHypo)):
sboxResult = self.Sbox(self.plainTextsTemp[i][byteNumber] ^ keyHypo[j])
self.hypothesisMatrix[i][j] = self.HammingWeight(sboxResult)
def NumpyPearsonCorrelation(self, h , p):
return np.corrcoef(h , p)[0][1]
def CreateCorrelationMatrix(self):
self.correlationMatrix = np.zeros([256,self.powerTraces.shape[1]])
for i in range(256):
for j in range(self.powerTraces.shape[1]):
self.correlationMatrix[i][j] = self.NumpyPearsonCorrelation(self.hypothesisMatrix[:,i] , self.powerTraces[:,j])
def GradualCreateCorrelationMatrix(self):
self.correlationMatrix = np.zeros([256,self.powerTracesTemp.shape[1]])
for i in range(256):
for j in range(self.powerTracesTemp.shape[1]):
self.correlationMatrix[i][j] = self.NumpyPearsonCorrelation(self.hypothesisMatrix[:,i] , self.powerTracesTemp[:,j])
def FindMaxCorrValueForEachKeyHypo(self):
self.maxCorrForEachKeyHypo = np.zeros([256])
for i in range(256):
maxCorrValIndex = np.argmax(abs(self.correlationMatrix[i]))
self.maxCorrForEachKeyHypo[i]=self.correlationMatrix[i][maxCorrValIndex]
def FindKeyHypoWithMaxCorr(self):
KeyVal = np.argmax(abs(self.maxCorrForEachKeyHypo))
if(self.isAllKeyBytes):
self.allKeyBytes.append(KeyVal)
if(self.isFirstKeyByte):
self.firstKeyByte = KeyVal
if(self.isNthKeyByte):
self.nthKeyByte = KeyVal
def PlotGradualCorrelationGraph(self):
xmax = np.argmax(self.maxCorrForEachKeyHypo)
ymax = self.maxCorrForEachKeyHypo.max()
ymin = self.maxCorrForEachKeyHypo.min()
fig, (ax1,ax2) = plt.subplots(2,1,figsize=(8, 8))
ax1.set_title("Final Correlation Value for Each Hypothesis")
ax1.set_xlabel("Key Byte Hypothesis")
ax1.set_ylabel("correlation value")
ax1.set_ylim(ymin-0.2, ymax+0.2)
ax1.stem(self.maxCorrForEachKeyHypo)
text= "x={}, y={:.3f}".format(xmax, ymax)
bbox_props = dict(boxstyle="square,pad=0.3", fc="w", ec="k", lw=0.72)
arrowprops=dict(arrowstyle="->",connectionstyle="angle,angleA=0,angleB=60")
kw = dict(xycoords='data',textcoords="axes fraction",
arrowprops=arrowprops, bbox=bbox_props, ha="right", va="top")
ax1.annotate(text, xy=(xmax, ymax), xytext=(0.99,0.99), **kw)
ax2.set_title("Gradual Correlation Value for Each Hypothesis")
ax2.set_xlabel("Number of Traces Used")
ax2.set_ylabel("correlation value")
gradualCorrForEachKeyHypo = np.zeros([256,len(self.gradualMaxCorrForEachKeyHypo)])
for j in range(256):
for i in range(len(self.gradualMaxCorrForEachKeyHypo)):
gradualCorrForEachKeyHypo[j][i]= (self.gradualMaxCorrForEachKeyHypo)[i][j]
for i in range(256):
if i==xmax:
ax2.plot(self.stepSizes, gradualCorrForEachKeyHypo[i], color="red")
else:
ax2.plot(self.stepSizes, gradualCorrForEachKeyHypo[i], color="gray")
fig.subplots_adjust(hspace=0.5)
plt.figure(figsize=(100,60))
plt.show()
def CpaOnFirstKeyByte(self):
self.isFirstKeyByte = True
self.isAllKeyBytes = False
self.isNthKeyByte = False
self.CreateHypothesisMatrix(0)
self.CreateCorrelationMatrix()
self.FindMaxCorrValueForEachKeyHypo()
self.FindKeyHypoWithMaxCorr()
print(f"First Key Byte Value: Dec: {self.firstKeyByte}, Hex: {hex(self.firstKeyByte)}")
#plt.plot(self.maxCorrForEachKeyHypo)
def GradualCpaOnFirstKeyByte(self, stepSize):
self.isFirstKeyByte = True
self.isAllKeyBytes = False
self.isNthKeyByte = False
self.gradualMaxCorrForEachKeyHypo = []
self.stepSizes = []
currentStepSize = 0
for numOfTracesUsed in range(stepSize,len(self.plainTexts),stepSize):
print(f"Running CPA with {numOfTracesUsed} number of traces")
self.plainTextsTemp = np.zeros([numOfTracesUsed,self.plainTexts.shape[1]])
self.plainTextsTemp = self.plainTexts[0:numOfTracesUsed,:]
self.powerTracesTemp = np.zeros([numOfTracesUsed,self.powerTraces.shape[1]])
self.powerTracesTemp = self.powerTraces[0:numOfTracesUsed,:]
self.GradualCreateHypothesisMatrix(0)
self.GradualCreateCorrelationMatrix()
self.FindMaxCorrValueForEachKeyHypo()
self.gradualMaxCorrForEachKeyHypo.append(self.maxCorrForEachKeyHypo)
currentStepSize = currentStepSize + stepSize
self.stepSizes.append(currentStepSize)
self.FindKeyHypoWithMaxCorr()
print(f"First Key Byte Value for {numOfTracesUsed} number of traces: Dec: {self.firstKeyByte}, Hex: {hex(self.firstKeyByte)}")
print(f"First Key Byte Value: Dec: {self.firstKeyByte}, Hex: {hex(self.firstKeyByte)}")
self.PlotGradualCorrelationGraph()
def CpaOnDesiredKeyByte(self, keyByteNum):
self.isFirstKeyByte = False
self.isAllKeyBytes = False
self.isNthKeyByte = True
self.CreateHypothesisMatrix(keyByteNum-1)
self.CreateCorrelationMatrix()
self.FindMaxCorrValueForEachKeyHypo()
self.FindKeyHypoWithMaxCorr()
print(f"Key Byte Num{keyByteNum} Value: Dec: {self.nthKeyByte}, Hex: {hex(self.nthKeyByte)}")
plt.plot(self.maxCorrForEachKeyHypo)