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1
from https://habr.com/ru/post/704750/
2
====
3
from scipy.fftpack import dct
4
def max_step(D):
5
    return 1 / np.max(np.sum(np.abs(D), axis=1))
6
D_8 = dct(np.identity(8), norm='ortho', axis=0)
7
D_8x8 = np.kron(D_8, D_8)
8
ID_8x8 = D_8x8.T
9
step = max_step(ID_8x8)
10
====
11
12
13
rounding DCT 8x8 attack
14-
target [63]
14+
target [0]
15-
error[63] = 0.36345122165219323
15+
error[0] = 0.4903774985577911
16
17
x0 = 
18-
[ 3.21570e+04  7.54310e+04  1.90400e+04 -2.65290e+04 -1.41840e+04
18+
[  45042.   49802.    -388.    3762.   -3316.   34708.   -6698.   27018.
19-
 -7.37000e+02  3.42740e+04  2.04780e+04  3.82150e+04 -5.29930e+04
19+
  -41219.  -17662. -118901.    1831.    9137.  -42023.  -13850.  -10845.
20-
  5.60780e+04  9.04390e+04  3.95360e+04  2.91800e+04 -2.65180e+04
20+
   23379.  -27018.   23699.   13219.   -1786.   52937.  -58440.   19318.
21-
 -7.12580e+04 -7.40000e+01 -3.43890e+04  6.71220e+04  5.44200e+04
21+
  -18008.   75903.  -48954.   -7870.  114001.  -19152.   10159.  -13026.
22-
  2.68740e+04  1.14120e+04  1.35259e+05 -3.38130e+04  4.96000e+03
22+
   60418.   45511.   36168.  100336.  -35948.   22835.   96077.    1730.
23-
  1.03055e+05  2.64600e+04  7.50780e+04  1.09977e+05  3.70680e+04
23+
  -15922. -133054.   -3460.   -6655.  -48379.  -80695.  -72022.   37555.
24-
  2.06340e+04  3.48570e+04 -1.71090e+04  3.52050e+04 -4.82130e+04
24+
   -1090.   64528.   41440.   43964.  -23915.    -182.   23294.   27462.
25-
  9.05500e+03 -1.82850e+04 -1.03090e+04 -8.37100e+03 -2.52420e+04
25+
  103482.   94889.   32304.   30749.   53892.   40881.  100513.   81184.]
26-
  4.60700e+03 -4.47260e+04  3.15630e+04 -1.98000e+02  1.58800e+04
26+
27-
 -9.75700e+03 -1.71800e+04 -1.95440e+04  1.39380e+04  3.54700e+03
27+
28-
 -1.06690e+04 -4.08350e+04 -4.34850e+04 -1.01460e+04 -1.22600e+03
28+
29-
  2.97860e+04  5.17650e+04  7.53810e+04  5.72220e+04  8.14950e+04
29+
[ 674073.   53800.  218225.  -54378.  319611.    8035. -257778. -242650.
30-
  8.17560e+04  5.77570e+04  7.52880e+04  5.15530e+04]
30+
 -693212.  -54434. -255213.  410709.  132596. -361181.   -8871. -200692.
31
  408618.   -6658.  413722.   80224. -103591. -173971.   24160.  -99300.
32
 -584331.   17660.  102992. -427463.   81361.  486706.  250154.  -86881.
33
 1259213.  226041.  202529.  363315. -356449.  -71335. -550168.   77964.
34-
[ 1074830.   193736.  -338415.    13079.  -104230.   228263.  -233123.
34+
   77467.  207701. -172874.  -78605. -198860. -544405.  103635.   84479.
35-
   111786.    -7069.   179245.  -290551.    48850.  -129995.   285193.
35+
 -123598.   -4467.  126910.  -77316.  291086.   86719.  929863.  170559.
36-
   -30464.   106144.   323421.    98818.   351891.    -3202.   -75865.
36+
  847692.  297807.   90397. -134541. -518376.  516347.  363414. -418244.]
37-
    91163.   235911.    58042. -1102995.   197193.   526398.    -1243.
37+
38-
    22406.  -319711.   231321.  -132663.   671694.    75679.   265404.
38+
39-
   -15365.   -65723.  -702025.  -525226.  -357070.   107584.  -189676.
39+
[0.49617557 0.47420052 0.48957082 0.47507862 0.49163128 0.4865168
40-
   564141.  -154626.  -199856.  -378895.  -172348.    74769.   326091.
40+
 0.49642385 0.49678944 0.4972423  0.49134182 0.49103339 0.49237629
41-
  -242209.    10389.   -79499.  -245409.   285278.  -122416.   383915.
41+
 0.49355259 0.49590319 0.49743268 0.49390482 0.49467272 0.47830408
42-
  -531683.  -229808.   525138.    -8969.  -352765.   292531.  -213364.
42+
 0.49497682 0.49301821 0.49058334 0.48763356 0.49502501 0.47314813
43-
   -35115.]
43+
 0.49245933 0.49161419 0.48935522 0.49125884 0.48733352 0.49666805
44
 0.4999157  0.49382924 0.4945706  0.48928885 0.49132343 0.48228909
45
 0.49789887 0.48620763 0.49494931 0.49609369 0.49152199 0.48262616
46-
[ 0.40315882 -0.19870145  0.41718635 -0.42159535  0.38378994 -0.30594735
46+
 0.49165072 0.48969459 0.48877153 0.48997834 0.49213162 0.48938426
47-
  0.40698604 -0.11234968 -0.41041095  0.30005438 -0.40203765  0.37411043
47+
 0.49217561 0.48163395 0.48898808 0.47947837 0.49790445 0.49805074
48-
 -0.26800671  0.29769347 -0.41567793  0.32678877  0.41745705 -0.14799411
48+
 0.49200448 0.48096602 0.48670205 0.4960902  0.49680454 0.49715593
49-
  0.40002459 -0.45672981  0.38949022 -0.23573711  0.3956908  -0.3833918
49+
 0.49264483 0.49256263 0.49677621 0.49464604]
50-
 -0.40504443  0.4708772  -0.40249882  0.31336475 -0.47300105  0.43274495
50+
51-
 -0.40203625  0.41120419  0.41016877 -0.33179672  0.4119895  -0.30702097
51+
52-
  0.20380031 -0.39401525  0.4011217  -0.43956844 -0.40995583  0.30902218
52+
[  45041.5096225    49802.13522281    -388.10707774    3762.03674973
53-
 -0.38539845  0.4304962  -0.40184558  0.34851823 -0.40360952  0.32369982
53+
   -3316.0570494    34708.0042799    -6698.03350853   27017.98267656
54-
  0.40613151 -0.2464837   0.39681631 -0.34720649  0.48494332 -0.48595521
54+
  -41218.86612965  -17662.03685572 -118900.9713595     1830.99014012
55-
  0.40075047 -0.14012014 -0.41512128  0.24115339 -0.3938026   0.30064321
55+
    9137.01518245  -42023.0020703   -13849.99124395  -10844.99594931
56-
 -0.36229381  0.3768861  -0.39986288  0.31031769]
56+
   23378.89421016  -27017.97033732   23698.97709904   13219.00762467
57
   -1786.01218981   52937.00162524  -58440.00750826   19317.99592986
58
  -18007.96146653   75902.98979536  -48953.99311838   -7870.00269811
59-
[ 3.21569872e+04  7.54309918e+04  1.90399839e+04 -2.65290004e+04
59+
  114001.00305218  -19151.99931936   10159.0021093   -13025.99984388
60-
 -1.41839966e+04 -7.36987492e+02  3.42740060e+04  2.04780018e+04
60+
   60417.94194243   45511.01631003   36167.98584339  100336.00548459
61-
  3.82149912e+04 -5.29929957e+04  5.60779938e+04  9.04389857e+04
61+
  -35948.00755141   22835.00203295   96076.9964938     1729.99856434
62-
  3.95360043e+04  2.91800080e+04 -2.65179917e+04 -7.12580260e+04
62+
  -15921.99294015 -133054.00089018   -3459.99951989   -6655.0014809
63-
 -7.40024836e+01 -3.43889861e+04  6.71220043e+04  5.44200095e+04
63+
  -48378.99893657  -80694.99998904  -72022.00021801   37554.99950295
64-
  2.68739728e+04  1.14120176e+04  1.35259006e+05 -3.38130119e+04
64+
   -1090.03262392   64528.00892361   41439.99307846   43964.00387872
65-
  4.95999837e+03  1.03054995e+05  2.64600063e+04  7.50780102e+04
65+
  -23915.00376437    -182.00040394   23293.99741379   27461.99888187
66-
  1.09976997e+05  3.70679774e+04  2.06340072e+04  3.48569589e+04
66+
  103481.98701999   94889.00365117   32303.99753426   30749.00040944
67-
 -1.71089881e+04  3.52050022e+04 -4.82130075e+04  9.05501063e+03
67+
   53891.99837031   40881.0001226   100512.99927998   81183.99725001]
68-
 -1.82849970e+04 -1.03089961e+04 -8.37101724e+03 -2.52419709e+04
68+
69-
  4.60697699e+03 -4.47260036e+04  3.15629743e+04 -1.97994123e+02
69+
70-
  1.58799882e+04 -9.75699193e+03 -1.71799762e+04 -1.95440681e+04
70+
[-4.90377499e-01  1.35222810e-01 -1.07077738e-01  3.67497334e-02
71-
  1.39380062e+04  3.54701291e+03 -1.06690075e+04 -4.08349967e+04
71+
 -5.70493978e-02  4.27989701e-03 -3.35085314e-02 -1.73234385e-02
72-
 -4.34849930e+04 -1.01459724e+04 -1.22603755e+03  2.97861079e+04
72+
  1.33870350e-01 -3.68557240e-02  2.86404973e-02 -9.85987891e-03
73-
  5.17649577e+04  7.53809684e+04  5.72219754e+04  8.14949617e+04
73+
  1.51824467e-02 -2.07030145e-03  8.75605502e-03  4.05068910e-03
74-
  8.17560312e+04  5.77569288e+04  7.52881017e+04  5.15526365e+04]
74+
 -1.05789839e-01  2.96626757e-02 -2.29009568e-02  7.62467133e-03
75
 -1.21898092e-02  1.62524448e-03 -7.50826287e-03 -4.07013805e-03
76
  3.85334747e-02 -1.02046371e-02  6.88161718e-03 -2.69810834e-03
77-
[-1.28449759e-02 -8.23246132e-03 -1.60571352e-02 -3.51853178e-04
77+
  3.05217662e-03  6.80637568e-04  2.10929855e-03  1.56116002e-04
78-
  3.42800453e-03  1.25075628e-02  5.97447068e-03  1.76590946e-03
78+
 -5.80575706e-02  1.63100295e-02 -1.41566088e-02  5.48459390e-03
79-
 -8.82740255e-03  4.31740546e-03 -6.15852178e-03 -1.43198912e-02
79+
 -7.55141320e-03  2.03295266e-03 -3.50620023e-03 -1.43566074e-03
80-
  4.28251284e-03  7.99135982e-03  8.34500257e-03 -2.60377127e-02
80+
  7.05985346e-03 -8.90180905e-04  4.80108527e-04 -1.48090259e-03
81-
 -2.48356060e-03  1.38533741e-02  4.26753641e-03  9.52619359e-03
81+
  1.06342707e-03  1.09610264e-05 -2.18004890e-04 -4.97053588e-04
82-
 -2.71559989e-02  1.76128100e-02  5.50283250e-03 -1.19271616e-02
82+
 -3.26239171e-02  8.92361134e-03 -6.92153634e-03  3.87872399e-03
83-
 -1.62669418e-03 -5.40009190e-03  6.28752898e-03  1.02185548e-02
83+
 -3.76437412e-03 -4.03936477e-04 -2.58620775e-03 -1.11813122e-03
84-
 -2.64928071e-03 -2.26283147e-02  7.20483317e-03 -4.11015357e-02
84+
 -1.29800120e-02  3.65116999e-03 -2.46574024e-03  4.09439737e-04
85-
  1.18984529e-02  2.21740937e-03 -7.54117729e-03  1.06306715e-02
85+
 -1.62969298e-03  1.22601778e-04 -7.20019074e-04 -2.74998696e-03]