dct round error attack 0->0.49

from https://habr.com/ru/post/704750/
====
from scipy.fftpack import dct
def max_step(D):
    return 1 / np.max(np.sum(np.abs(D), axis=1))
D_8 = dct(np.identity(8), norm='ortho', axis=0)
D_8x8 = np.kron(D_8, D_8)
ID_8x8 = D_8x8.T
step = max_step(ID_8x8)
====


rounding DCT 8x8 attack
target [0]
error[0] = 0.4903774985577911

x0 =
[  45042.   49802.    -388.    3762.   -3316.   34708.   -6698.   27018.
  -41219.  -17662. -118901.    1831.    9137.  -42023.  -13850.  -10845.
   23379.  -27018.   23699.   13219.   -1786.   52937.  -58440.   19318.
  -18008.   75903.  -48954.   -7870.  114001.  -19152.   10159.  -13026.
   60418.   45511.   36168.  100336.  -35948.   22835.   96077.    1730.
  -15922. -133054.   -3460.   -6655.  -48379.  -80695.  -72022.   37555.
   -1090.   64528.   41440.   43964.  -23915.    -182.   23294.   27462.
  103482.   94889.   32304.   30749.   53892.   40881.  100513.   81184.]

t = np.dot(x0, D_8x8) / step
x1 = round(t) =
[ 674073.   53800.  218225.  -54378.  319611.    8035. -257778. -242650.
 -693212.  -54434. -255213.  410709.  132596. -361181.   -8871. -200692.
  408618.   -6658.  413722.   80224. -103591. -173971.   24160.  -99300.
 -584331.   17660.  102992. -427463.   81361.  486706.  250154.  -86881.
 1259213.  226041.  202529.  363315. -356449.  -71335. -550168.   77964.
   77467.  207701. -172874.  -78605. -198860. -544405.  103635.   84479.
 -123598.   -4467.  126910.  -77316.  291086.   86719.  929863.  170559.
  847692.  297807.   90397. -134541. -518376.  516347.  363414. -418244.]

e_round = t - x1 =
[0.49617557 0.47420052 0.48957082 0.47507862 0.49163128 0.4865168
 0.49642385 0.49678944 0.4972423  0.49134182 0.49103339 0.49237629
 0.49355259 0.49590319 0.49743268 0.49390482 0.49467272 0.47830408
 0.49497682 0.49301821 0.49058334 0.48763356 0.49502501 0.47314813
 0.49245933 0.49161419 0.48935522 0.49125884 0.48733352 0.49666805
 0.4999157  0.49382924 0.4945706  0.48928885 0.49132343 0.48228909
 0.49789887 0.48620763 0.49494931 0.49609369 0.49152199 0.48262616
 0.49165072 0.48969459 0.48877153 0.48997834 0.49213162 0.48938426
 0.49217561 0.48163395 0.48898808 0.47947837 0.49790445 0.49805074
 0.49200448 0.48096602 0.48670205 0.4960902  0.49680454 0.49715593
 0.49264483 0.49256263 0.49677621 0.49464604]

x2 = np.dot(x1 * step, ID) =
[  45041.5096225    49802.13522281    -388.10707774    3762.03674973
   -3316.0570494    34708.0042799    -6698.03350853   27017.98267656
  -41218.86612965  -17662.03685572 -118900.9713595     1830.99014012
    9137.01518245  -42023.0020703   -13849.99124395  -10844.99594931
   23378.89421016  -27017.97033732   23698.97709904   13219.00762467
   -1786.01218981   52937.00162524  -58440.00750826   19317.99592986
  -18007.96146653   75902.98979536  -48953.99311838   -7870.00269811
  114001.00305218  -19151.99931936   10159.0021093   -13025.99984388
   60417.94194243   45511.01631003   36167.98584339  100336.00548459
  -35948.00755141   22835.00203295   96076.9964938     1729.99856434
  -15921.99294015 -133054.00089018   -3459.99951989   -6655.0014809
  -48378.99893657  -80694.99998904  -72022.00021801   37554.99950295
   -1090.03262392   64528.00892361   41439.99307846   43964.00387872
  -23915.00376437    -182.00040394   23293.99741379   27461.99888187
  103481.98701999   94889.00365117   32303.99753426   30749.00040944
   53891.99837031   40881.0001226   100512.99927998   81183.99725001]

err = x2 - x0 =
[-4.90377499e-01  1.35222810e-01 -1.07077738e-01  3.67497334e-02
 -5.70493978e-02  4.27989701e-03 -3.35085314e-02 -1.73234385e-02
  1.33870350e-01 -3.68557240e-02  2.86404973e-02 -9.85987891e-03
  1.51824467e-02 -2.07030145e-03  8.75605502e-03  4.05068910e-03
 -1.05789839e-01  2.96626757e-02 -2.29009568e-02  7.62467133e-03
 -1.21898092e-02  1.62524448e-03 -7.50826287e-03 -4.07013805e-03
  3.85334747e-02 -1.02046371e-02  6.88161718e-03 -2.69810834e-03
  3.05217662e-03  6.80637568e-04  2.10929855e-03  1.56116002e-04
 -5.80575706e-02  1.63100295e-02 -1.41566088e-02  5.48459390e-03
 -7.55141320e-03  2.03295266e-03 -3.50620023e-03 -1.43566074e-03
  7.05985346e-03 -8.90180905e-04  4.80108527e-04 -1.48090259e-03
  1.06342707e-03  1.09610264e-05 -2.18004890e-04 -4.97053588e-04
 -3.26239171e-02  8.92361134e-03 -6.92153634e-03  3.87872399e-03
 -3.76437412e-03 -4.03936477e-04 -2.58620775e-03 -1.11813122e-03
 -1.29800120e-02  3.65116999e-03 -2.46574024e-03  4.09439737e-04
 -1.62969298e-03  1.22601778e-04 -7.20019074e-04 -2.74998696e-03]