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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] |