From bc068c75a4fb3eb02f5bbcd968791d8d88adb459 Mon Sep 17 00:00:00 2001 From: haskal Date: Sun, 25 Apr 2021 23:04:48 -0400 Subject: [PATCH] optimize --- sca/ascad/attack.py | 120 ++++++++++++++++++++++--------------- sca/ascad/first_order.png | Bin 26415 -> 23790 bytes sca/ascad/second_order.png | Bin 0 -> 39126 bytes 3 files changed, 71 insertions(+), 49 deletions(-) create mode 100644 sca/ascad/second_order.png diff --git a/sca/ascad/attack.py b/sca/ascad/attack.py index d539562..d111a17 100644 --- a/sca/ascad/attack.py +++ b/sca/ascad/attack.py @@ -66,49 +66,50 @@ def align(db, ntraces): 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 + return traces[:, max_start:min_end] -def main(db): - ntraces = 1000 - traces = align(db, ntraces) +# 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 +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() - # for i in range(10): - # plt.plot(traces[i], color=numpy.hstack((numpy.random.random(3), [0.5]))) - # plt.show() + 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 - logger.info("making model") + +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") - - # O - (n,t) array of n traces with t samples each - # P - (n,m) array of n predictions for each of the m candidates - # returns an (m,t) correaltion matrix of m traces t samples each - def corr_submatrix(O, P): - O -= numpy.mean(O, axis=0) - P -= numpy.mean(P, axis=0) - - numerator = numpy.einsum("nm,nt->mt", P, O, optimize='optimal') - denominator = numpy.sqrt(numpy.outer((P * P).sum(axis=0), (O * O).sum(axis=0))) - - return numerator / denominator + 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 - coefs = corr_submatrix(traces, model.transpose()) + correlator = Correlator(model) + coefs = correlator.corr_submatrix(traces) # plot absmax coefs = numpy.abs(coefs) @@ -116,35 +117,56 @@ def main(db): plt.plot(max_by_key) plt.show() - # logger.info("making 2nd order") - # traces = traces.transpose() - # traces_x = numpy.zeros((700*699//2, ntraces), 'double') - # tx_i = 0 - # for i in tqdm.trange(700): - # for j in range(i+1, 700): - # traces_x[tx_i, :] = numpy.abs(traces[i, :] - traces[j, :]) - # tx_i += 1 - # - # logger.info("doing corr") - # ncolumns = 100 - # step = traces_x.shape[0] // ncolumns - # all_coefs = None - # for i in tqdm.trange(ncolumns): - # start = i * step - # end = (i + 1) * step - # input_matrix = numpy.vstack((model, traces_x[start:end, :])) - # coefs = numpy.corrcoef(input_matrix)[0:256, 256:] - # if all_coefs is None: - # all_coefs = coefs - # else: - # all_coefs = numpy.hstack((all_coefs, coefs)) - # - # - # all_coefs = numpy.abs(all_coefs) - # max_by_key = numpy.max(all_coefs, axis=1) - # plt.plot(max_by_key) + +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] + mask_v = mask[15] + 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 = 10 + 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 = 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 diff --git a/sca/ascad/first_order.png b/sca/ascad/first_order.png index 2acd3ffdf83ddc6b790c601a1cf840e627156ff3..6d866937b76e62e1f96cb47aacb8e3be4ff5a454 100644 GIT binary patch literal 23790 zcmeFYXIN8PyEPoTB7%wtQbk1+HlWf$iXtE)pg`zVr1uhf6$Pa#RcS#wBsA%vx)G2X zS^%jcQUjqAI`0hV-sgJW_nhP?^*6~k1^)T+o#I%XDJyeArQz}g+~un zArNAJ2!!azDRS_MV9)3;@K4l5R?9`r-ps|#*vS;4WbEQ#WA9>P`TUBjsgtv%y&XTV z0Pmf@u2{IZI5>;(@!9@!0k6H2Ip6nwnpDupX@^JJ&JYNVG2xFWM=IMA0@2e|cz9pk zJ!xso!&`l`_GlIV#Pz|YsCVbCy!uwxdLc&EF+NTse^@tnJk7Q&R>Ss|>-y{x#&hI3 z{jKs#v3X^oy5oWJ(HQFj;MwX(hJHno8I@mZV%5o!=agfT;2Ztk-cWn>Y3|FZ?qPGK;|?+q>LgCMsC9Cx*KmGTF;(+ 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