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import logging
import random
logger = logging.getLogger(__name__)
import h5py
import matplotlib.pyplot as plt
import numpy
import scipy.fft
import scipy.signal
import tqdm
# import opt_einsum
import numpy_popcount
AES_SBOX = numpy.array([
# 0 1 2 3 4 5 6 7 8 9 A B C D E F
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='uint8')
def align(db, ntraces):
logger.info("aligning traces")
traces = db["traces"]
reference = traces[0].astype("double")
alignments = numpy.zeros(ntraces, "int64")
lags = scipy.signal.correlation_lags(len(reference), len(reference))
for i in tqdm.trange(1, ntraces):
trace = traces[i].astype("double")
corr = scipy.signal.correlate(reference, trace)
max_idxs = corr.argsort()[-10:][::-1]
max_corr = 0
max_idx = -1
for idx in max_idxs:
lag = lags[idx]
if lag == 0:
s_ref = reference
s_trs = trace
elif lag < 0:
s_ref = reference[:lag]
s_trs = trace[-lag:]
else:
s_ref = reference[lag:]
s_trs = trace[:-lag]
pcorr = numpy.corrcoef(s_ref, s_trs)[1,0]
if pcorr > max_corr:
max_corr = pcorr
max_idx = idx
lag = lags[max_idx]
alignments[i] = lag
alignments -= numpy.min(alignments)
max_start = max(alignments)
min_end = 700
traces = numpy.zeros((ntraces, 800), 'double')
for i in range(ntraces):
traces[i, alignments[i]:alignments[i]+700] = db["traces"][i]
return traces[:, max_start:min_end]
# P - (n,m) array of n predictions for each of the m candidates
# O - (n,t) array of n traces with t samples each
# returns an (m,t) correlation matrix of m traces t samples each
# TODO : is opt_einsum faster?
class Correlator:
def __init__(self, P):
self.P = P - numpy.mean(P, axis=0)
self.tmp1 = numpy.einsum("nm,nm->m", self.P, self.P, optimize='optimal')
self.P = self.P.transpose()
def corr_submatrix(self, O):
O -= numpy.mean(O, axis=0)
numerator = self.P @ O
tmp2 = numpy.einsum("nt,nt->t", O, O, optimize='optimal')
denominator = numpy.sqrt(numpy.outer(self.tmp1, tmp2))
return numerator / denominator
def attack_firstorder(db, traces, ntraces):
logger.info("making first order model")
model = numpy.repeat(numpy.arange(256, dtype='uint8'), ntraces).reshape((256, ntraces))
for i in tqdm.trange(ntraces):
(pt, ct, key, mask, desync) = db["metadata"][i]
pt_v = pt[2]
mask_v = mask[15]
model[:, i] = AES_SBOX[model[:, i] ^ pt_v] ^ mask_v
model = numpy_popcount.popcount(model).astype("double").transpose()
# boring, slow, uses too much RAM
# input_matrix = numpy.vstack((model, traces.transpose()))
# coefs = numpy.corrcoef(input_matrix)[0:256, 256:]
# uwu
correlator = Correlator(model)
coefs = correlator.corr_submatrix(traces)
# plot absmax
coefs = numpy.abs(coefs)
max_by_key = numpy.max(coefs, axis=1)
plt.plot(max_by_key)
plt.show()
def attack_firstorder_fft(db, traces, ntraces):
# lol
ntraces = 2000
db = h5py.File("./ASCAD_databases/ASCAD_desync100.h5", "r")["Attack_traces"]
traces = db["traces"][0:ntraces, :].astype("double")
logger.info("making first order model")
model = numpy.repeat(numpy.arange(256, dtype='uint8'), ntraces).reshape((256, ntraces))
for i in tqdm.trange(ntraces):
(pt, ct, key, mask, desync) = db["metadata"][i]
pt_v = pt[2]
mask_v = mask[15]
model[:, i] = AES_SBOX[model[:, i] ^ pt_v] ^ mask_v
model = numpy_popcount.popcount(model).astype("double").transpose()
logger.info("making fft traces")
fft_traces = numpy.zeros(traces.shape, traces.dtype)
for i in range(traces.shape[0]):
fft_traces[i, :] = numpy.abs(scipy.fft.fft(traces[i, :]))
traces = fft_traces[:, 1:350]
avg = numpy.mean(traces, axis=0)
peaks = avg.argsort()[-50:][::-1]
traces = numpy.hstack([traces[:, i:i+1] for i in peaks])
correlator = Correlator(model)
coefs = correlator.corr_submatrix(traces)
# plot absmax
coefs = numpy.abs(coefs)
max_by_key = numpy.max(coefs, axis=1)
plt.plot(max_by_key)
plt.show()
# def attack_secondorder_fft(db, traces, ntraces):
# # needs work
# # lol
# ntraces = 10000
# db = h5py.File("./ASCAD_databases/ASCAD.h5", "r")["Attack_traces"]
# traces = db["traces"][0:ntraces, :].astype("double")
#
# logger.info("making second order model")
# model = numpy.repeat(numpy.arange(256, dtype='uint8'), ntraces).reshape((256, ntraces))
# for i in tqdm.trange(ntraces):
# (pt, ct, key, mask, desync) = db["metadata"][i]
# pt_v = pt[2]
# mask_v = mask[15]
# model[:, i] = AES_SBOX[model[:, i] ^ pt_v] ^ mask_v
# model = numpy_popcount.popcount(model).astype("double").transpose()
#
# logger.info("making fft traces")
# fft_traces = numpy.zeros((traces.shape[0], traces.shape[1]), traces.dtype)
# for i in range(traces.shape[0]):
# fft_i = numpy.abs(scipy.fft.fft(traces[i, :]))
# conv_i = numpy.abs(numpy.conj(fft_i) * fft_i)
# fft_traces[i, :] = conv_i
#
# traces = fft_traces
# # traces = fft_traces[:, 1:350]
# # avg = numpy.mean(traces, axis=0)
# # peaks = avg.argsort()[-50:][::-1]
# # traces = numpy.hstack([traces[:, i:i+1] for i in peaks])
#
# correlator = Correlator(model)
# coefs = correlator.corr_submatrix(traces)
#
# # plot absmax
# coefs = numpy.abs(coefs)
# max_by_key = numpy.max(coefs, axis=1)
# plt.plot(max_by_key)
# plt.show()
def attack_secondorder(db, traces, ntraces):
logger.info("making second order model")
model = numpy.repeat(numpy.arange(256, dtype='uint8'), ntraces).reshape((256, ntraces))
for i in tqdm.trange(ntraces):
(pt, ct, key, mask, desync) = db["metadata"][i]
pt_v = pt[2]
model[:, i] = AES_SBOX[model[:, i] ^ pt_v]
model = numpy_popcount.popcount(model).astype("double").transpose()
logger.info("making second order combinations")
nticks = traces.shape[1]
traces_x = numpy.zeros((ntraces, nticks*(nticks - 1)//2), 'double')
tx_i = 0
for i in tqdm.trange(nticks):
for j in range(i+1, nticks):
traces_x[:, tx_i] = numpy.abs(traces[:, i] - traces[:, j])
tx_i += 1
logger.info("doing corr")
correlator = Correlator(model)
ncolumns = 4
step = traces_x.shape[1] // ncolumns
all_coefs = []
for i in tqdm.trange(ncolumns):
start = i * step
end = (i + 1) * step
coefs = correlator.corr_submatrix(traces_x[:, start:end])
all_coefs.append(coefs)
all_coefs = numpy.hstack(all_coefs)
all_coefs = numpy.abs(all_coefs)
max_by_key = numpy.max(all_coefs, axis=1)
plt.plot(max_by_key)
plt.show()
def main(db):
ntraces = 2000
# traces = None
# attack_firstorder_fft(db, traces, ntraces)
# return
traces = align(db, ntraces)
# for i in range(10):
# plt.plot(traces[i], color=numpy.hstack((numpy.random.random(3), [0.5])))
# plt.show()
attack_firstorder(db, traces, ntraces)
attack_secondorder(db, traces, ntraces)
if __name__ == "__main__":
from tqdm.contrib.logging import logging_redirect_tqdm
logging.basicConfig(level=logging.INFO)
with logging_redirect_tqdm():
db = h5py.File("./ASCAD_databases/ASCAD_desync100.h5", "r")
main(db["Attack_traces"])