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"])