import numpy as np from scipy import stats import matplotlib.pyplot as plt from tqdm import tqdm HW = np.array([bin(x).count('1') for x in range(0x100)], dtype=np.uint8) # Rijndael S-box sbox = np.array([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],dtype=np.uint8) class ConditionalAveragerAesSbox: def __init__(self, numValues, traceLength): '''Allocate the matrix of averaged traces''' self.avtraces = np.zeros((numValues, traceLength)) self.counters = np.zeros(numValues) print('ConditionalAverager: initialized for %d values and trace length %d' % (numValues, traceLength)) def addTrace(self, data, trace): '''Add a single trace with corresponding single chunk of data''' if (self.counters[data] == 0): self.avtraces[data] = trace self.counters[data] += 1 else: self.counters[data] += 1 self.avtraces[data] = self.avtraces[data] + (trace - self.avtraces[data]) / self.counters[data] def getSnapshot(self): ''' return a snapshot of the average matrix''' avdataSnap = np.flatnonzero(self.counters) # get an vector of only _observed_ values avtracesSnap = self.avtraces[avdataSnap] # remove lines corresponding to non-observed values return avdataSnap, avtracesSnap class CPA_AES(object): def __init__(self, n_traces, tracelen, knownKeyByte, encrypt=True, evolutionStep=1, Nskip=20): self.knownKeyByte = knownKeyByte self.Nskip = Nskip self.numsamples = tracelen self.numtraces = n_traces self.numkeys = 256 self.ranking = None self.correctPos = np.zeros((int(self.numtraces/evolutionStep)), dtype=np.uint8) self.correlation_values = np.empty((self.numkeys,self.numsamples), dtype=np.float32) self.correlation_evol = np.empty((self.numkeys,int(self.numtraces/evolutionStep)), dtype=np.float32) self.CondAver = ConditionalAveragerAesSbox(self.numkeys,self.numsamples) self.stepCount = 0 self.evolutionStep = evolutionStep # AES encryption intermediate is SBOX[in^k] def compute_intermediates(self, i, k): return sbox[i^k] def power_model(self, x): return HW[x] ##Hamming weight # Construct a matrix of predictions based on the power model of the intermediate value for each trace/plaintext with all key candidates. def compute_predictions(self, data): H = np.zeros((256, len(data)), dtype='uint8') # intermediate variable predictions for k in range(self.numkeys): H[k,:] = self.compute_intermediates(data,k) HL = np.vectorize(self.power_model)(H).T return HL # Naive correlation computation between traces and prediction matrix. def compute_correlation(self, traces, H): n_total = len(traces) * self.numkeys for s in range(self.numsamples): for k in range(self.numkeys): print("progress: {:.1f}%".format(100*(k + s*self.numkeys)/n_total), end='\r') self.correlation_values[k,s] = abs(stats.pearsonr(H[:,k], traces[:,s])[0]) # A faster correlation computation by taking the full matrix of predictions instead of just a column. # ref: https://github.com/ikizhvatov/efficient-columnwise-correlation def correlationTraces(self, traces, H): (n, t) = traces.shape # n traces of t samples (n_bis, m) = H.shape # n predictions for each of m candidates assert n_bis == n DO = traces - (np.einsum("nt->t", traces, dtype='float64', optimize='optimal') / np.double(n)) # compute O - mean(O) DP = H - (np.einsum("nm->m", H, dtype='float64', optimize='optimal') / np.double(n)) # compute P - mean(P) numerator = np.einsum("nm,nt->mt", DP, DO, optimize='optimal') tmp1 = np.einsum("nm,nm->m", DP, DP, optimize='optimal') tmp2 = np.einsum("nt,nt->t", DO, DO, optimize='optimal') tmp = np.einsum("m,t->mt", tmp1, tmp2, optimize='optimal') denominator = np.sqrt(tmp) self.correlation_values = numerator / denominator # Get the ranking of every key candidates by taking the the maximum absolute value for all correaltion results. # Get the position of the knownKeyByte. def rank(self): self.ranking = np.flip(np.argsort(np.amax(self.correlation_values,1)),0) self.correctPos[self.stepCount] = np.argwhere(self.knownKeyByte == self.ranking)[0,0] # Plot the correlation values for visualization. def show_graph(self, fontsize=11): fig = plt.figure() axCPA = plt.subplot2grid((2, 2), (0, 0), colspan=2) axEvol = plt.subplot2grid((2, 2), (1, 0)) axCorrectPos = plt.subplot2grid((2, 2), (1, 1)) x = range(self.numsamples) for i in range(self.numkeys): axCPA.plot(x, self.correlation_values[i], color="blue") axCPA.plot(x, self.correlation_values[self.ranking[0]], color="red") axCPA.set_ylabel('Correlation', fontsize=fontsize) axCPA.set_xlabel('Time sample', fontsize=fontsize) x = range(0, self.numtraces, self.evolutionStep) axCorrectPos.plot(x, self.correctPos) axCorrectPos.set_ylabel('Correct key candidate rank', fontsize=fontsize) axCorrectPos.set_xlabel('Number of traces', fontsize=fontsize) for i in range(self.correlation_evol.shape[0]): axEvol.plot(x, self.correlation_evol[i], color='gray') axEvol.plot(x, self.correlation_evol[self.knownKeyByte], color='red') axEvol.set_ylabel('Correlation', fontsize=fontsize) axEvol.set_xlabel('Number of traces', fontsize=fontsize) plt.tight_layout() plt.show() def run(self, data, traces): for i in range(self.Nskip): self.CondAver.addTrace(data[i], traces[i]) for i in tqdm(range(self.Nskip, self.numtraces+self.Nskip)): self.CondAver.addTrace(data[i], traces[i]) if (((i + 1) % self.evolutionStep == 0) or ((i + 1) == self.numtraces+self.Nskip)): (avdata, avtraces) = self.CondAver.getSnapshot() H = self.compute_predictions(avdata) self.correlationTraces(avtraces, H) self.correlation_evol[:,self.stepCount] = np.max(np.abs(self.correlation_values), axis=1) self.rank() self.stepCount += 1 self.show_graph() if __name__ == "__main__": tracesetFilename = "traces/Xoodyak_FVR3000_20240214_124156.npz" knownKey = bytes.fromhex("CAFEBABEDEADBEEF0001020304050607") # the correct key #knownKey = b"0xE8\0x77\0xD5\0x9C\0x2D\0x47\0xB4\0x18\0x8F\0x2F\0x70\0x34\0xB2\0x5E\0xDA\0x89" # the correct key npzfile = np.load(tracesetFilename) N = 1500 # number of traces to attack (less or equal to the amount of traces in the file) Nskip = 0 #number of traces to skip to avoid warning in correlation for division by 0 SboxNum = 0 # S-box to attack, counting from 0 data = npzfile['data'][:N+Nskip,SboxNum] # selecting only the required plaintext byte #traces = npzfile['traces'][:N+Nskip, 800:1500] #data = npzfile['data'][:N] traces = npzfile['traces'][:N,:250000] evolutionStep = 10 print("Construct object...") cpa_aes = CPA_AES(N, traces.shape[1], knownKey[SboxNum], evolutionStep=evolutionStep, Nskip=Nskip) print("Running Analysis...") cpa_aes.run(data, traces)