Matasano Crypto Challenge 23: Clone an MT19937 RNG From Its Output

matasano_text_art

Pada tulisan sebelumnya dibahas mengenai cara memecahkan MT19937 dan menemukan seed. Untuk tulisan hari ini akan dibahas mengenai duplikasi MT19937 RNG dari output yang dihasilkan.

Challenge

State internal dari MT19337 terdiri dari 624 32 bit integer.
Untuk setiap batch terdiri dari 624 output, lakukan permutasi MT pada state internal. Dengan melakukan permutasi secara reguler, MT19937 akan mencapai periode 2 **19937, ini sangat besar.

Setiap kali MT19937 dibuka, unsur dalam state internal dikenakan untuk fungsi temper yang mampu menyebarkan bit melalui hasil.

Fungsi temper, juga mempunyai kebalikan. Anda dapat menulis fungsi “untemper” yang diambil dari output dan mentransformasi kembali ke dalam elemen yang sama dengan array MT19937.

Untuk melakukan invert transformasi temper, lakukan invers untuk setiap operasi transformasi temper dalam urutan terbalik. Ada dua jenis operasi dalam transformasi temper dan masing-masing diterapkan dua kali. Pertama untuk melakukan XOR terhadap nilai right-shifted dan yang kedua adalah XOR terhadap nilai left-shifted kemudian operasi AND dengan nilai magic. Sehingga anda akan membutuhkan coding untuk melakukan operasi invers “right” dan “left”.

Ketika fungsi “untemper” anda berjalan, buat generator baru untuk MT19937, agar menghasilkan 624 output, dan lakukan fungsi “untemper” untuk setiap hasilnya, kemudian buat kembali generator state, dan sambung state tersebut kedalam instan baru dari generator MT19937.

Generator baru yang tersambung harus bisa memprediksi nilai aslinya.

Berhenti dan berpikir sejenak
Bagaimana anda memodifikasi MT19937 untuk melakukan serangan sulit ini? Apa yang terjadi jika dikenakan fungsi temper untuk setiap output ke dalam fungsi hash kriptografi?

Solved

Ini dia proses penyelesaiannya.

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Clone MT19937 RNG From Output
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----------------------------------------------------------------
[v] Obtain 624 Consecutive Outputs: 

[-] Output Array[0]: 1640418314

[-] Output Array[1]: 1593280314

[-] Output Array[2]: 713542454

[-] Output Array[3]: 489153168

[-] Output Array[4]: 412120820

[-] Output Array[5]: 2679220116

[-] Output Array[6]: 2958317078

[-] Output Array[7]: 3937115210

[-] Output Array[8]: 736966170

[-] Output Array[9]: 1479105876

[-] Output Array[10]: 3796964112

[-] Output Array[11]: 2663449447

[-] Output Array[12]: 4218689159

[-] Output Array[13]: 3093472839

[-] Output Array[14]: 872942083

[-] Output Array[15]: 3610298335

[-] Output Array[16]: 4149522021

[-] Output Array[17]: 3844897643

[-] Output Array[18]: 138850835

[-] Output Array[19]: 3214387506

[-] Output Array[20]: 740702168

[-] Output Array[21]: 1929901702

[-] Output Array[22]: 3428086495

[-] Output Array[23]: 594211351

[-] Output Array[24]: 2782594702

[-] Output Array[25]: 3139491467

[-] Output Array[26]: 109975401

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[-] Output Array[29]: 3250536856

[-] Output Array[30]: 713174823

[-] Output Array[31]: 3259317125

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[-] Output Array[233]: 3837280256

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[-] Output Array[273]: 454423452

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[-] Output Array[276]: 1444368279

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----------------------------------------------------------------
[v] Recover Internal States: 180607104

----------------------------------------------------------------
[v] Reset MT: 

[-] Reset MT [1]: 1640418314

[-] Reset MT [2]: 1593280314

[-] Reset MT [3]: 713542454

----------------------------------------------------------------
[v] Initialize New MT Instance with Recovered...

----------------------------------------------------------------
[v] Predict Next 624 RNG Outputs[-] Predict Output Array[0]: 2707207799

[-] Predict Output Array[1]: 2076045695

[-] Predict Output Array[2]: 214304123

[-] Predict Output Array[3]: 3066168560

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[-] Predict Output Array[468]: 2847591277

[-] Predict Output Array[469]: 1466722088

[-] Predict Output Array[470]: 525225894

[-] Predict Output Array[471]: 1812878630

[-] Predict Output Array[472]: 1096100576

[-] Predict Output Array[473]: 548520349

[-] Predict Output Array[474]: 2482583366

[-] Predict Output Array[475]: 2643046794

[-] Predict Output Array[476]: 1556371777

[-] Predict Output Array[477]: 644955460

[-] Predict Output Array[478]: 123482985

[-] Predict Output Array[479]: 1207704792

[-] Predict Output Array[480]: 1252681781

[-] Predict Output Array[481]: 2387792278

[-] Predict Output Array[482]: 127508380

[-] Predict Output Array[483]: 1077140097

[-] Predict Output Array[484]: 3483371482

[-] Predict Output Array[485]: 45173433

[-] Predict Output Array[486]: 1533595803

[-] Predict Output Array[487]: 2207463783

[-] Predict Output Array[488]: 3997283542

[-] Predict Output Array[489]: 800020734

[-] Predict Output Array[490]: 9297728

[-] Predict Output Array[491]: 4097628021

[-] Predict Output Array[492]: 1780200477

[-] Predict Output Array[493]: 3090095799

[-] Predict Output Array[494]: 2988203274

[-] Predict Output Array[495]: 3716000588

[-] Predict Output Array[496]: 1206962068

[-] Predict Output Array[497]: 2911871560

[-] Predict Output Array[498]: 635971261

[-] Predict Output Array[499]: 2268899381

[-] Predict Output Array[500]: 3018187304

[-] Predict Output Array[501]: 3756326181

[-] Predict Output Array[502]: 3895891337

[-] Predict Output Array[503]: 1143815282

[-] Predict Output Array[504]: 2433420198

[-] Predict Output Array[505]: 1634315874

[-] Predict Output Array[506]: 2036125171

[-] Predict Output Array[507]: 3844094465

[-] Predict Output Array[508]: 2589429948

[-] Predict Output Array[509]: 3060168270

[-] Predict Output Array[510]: 1518942019

[-] Predict Output Array[511]: 2439679230

[-] Predict Output Array[512]: 3897789797

[-] Predict Output Array[513]: 3403795809

[-] Predict Output Array[514]: 2308799837

[-] Predict Output Array[515]: 35637870

[-] Predict Output Array[516]: 3338287429

[-] Predict Output Array[517]: 2113099771

[-] Predict Output Array[518]: 3887674733

[-] Predict Output Array[519]: 183168430

[-] Predict Output Array[520]: 2267648856

[-] Predict Output Array[521]: 1441689104

[-] Predict Output Array[522]: 1859218488

[-] Predict Output Array[523]: 2575094438

[-] Predict Output Array[524]: 3340884162

[-] Predict Output Array[525]: 1071412385

[-] Predict Output Array[526]: 3070156090

[-] Predict Output Array[527]: 1731643687

[-] Predict Output Array[528]: 856490017

[-] Predict Output Array[529]: 1911687070

[-] Predict Output Array[530]: 1748164003

[-] Predict Output Array[531]: 3609251773

[-] Predict Output Array[532]: 3247385329

[-] Predict Output Array[533]: 3448035362

[-] Predict Output Array[534]: 910406169

[-] Predict Output Array[535]: 1475685766

[-] Predict Output Array[536]: 2791383269

[-] Predict Output Array[537]: 929025631

[-] Predict Output Array[538]: 2304861235

[-] Predict Output Array[539]: 2270793427

[-] Predict Output Array[540]: 1380975377

[-] Predict Output Array[541]: 4032592584

[-] Predict Output Array[542]: 810037286

[-] Predict Output Array[543]: 3781609389

[-] Predict Output Array[544]: 1899436523

[-] Predict Output Array[545]: 1703449419

[-] Predict Output Array[546]: 127625719

[-] Predict Output Array[547]: 2512686057

[-] Predict Output Array[548]: 2894516451

[-] Predict Output Array[549]: 947353843

[-] Predict Output Array[550]: 4175047866

[-] Predict Output Array[551]: 3540400599

[-] Predict Output Array[552]: 3549856769

[-] Predict Output Array[553]: 2249774196

[-] Predict Output Array[554]: 2536806609

[-] Predict Output Array[555]: 1700889295

[-] Predict Output Array[556]: 2403934849

[-] Predict Output Array[557]: 1873488369

[-] Predict Output Array[558]: 4180936040

[-] Predict Output Array[559]: 300832323

[-] Predict Output Array[560]: 2818460938

[-] Predict Output Array[561]: 1309333964

[-] Predict Output Array[562]: 181872930

[-] Predict Output Array[563]: 445494045

[-] Predict Output Array[564]: 3748569973

[-] Predict Output Array[565]: 658836749

[-] Predict Output Array[566]: 532563639

[-] Predict Output Array[567]: 1752133810

[-] Predict Output Array[568]: 2865527691

[-] Predict Output Array[569]: 4286798104

[-] Predict Output Array[570]: 4240352537

[-] Predict Output Array[571]: 1722754042

[-] Predict Output Array[572]: 2863065476

[-] Predict Output Array[573]: 4220752804

[-] Predict Output Array[574]: 1533870096

[-] Predict Output Array[575]: 1150133491

[-] Predict Output Array[576]: 920425483

[-] Predict Output Array[577]: 2464876522

[-] Predict Output Array[578]: 3221577745

[-] Predict Output Array[579]: 2371630503

[-] Predict Output Array[580]: 2337053519

[-] Predict Output Array[581]: 2894572635

[-] Predict Output Array[582]: 3808418451

[-] Predict Output Array[583]: 2569977547

[-] Predict Output Array[584]: 3016695897

[-] Predict Output Array[585]: 3672303812

[-] Predict Output Array[586]: 240756959

[-] Predict Output Array[587]: 4154707014

[-] Predict Output Array[588]: 2700776492

[-] Predict Output Array[589]: 2492653496

[-] Predict Output Array[590]: 310207483

[-] Predict Output Array[591]: 1906293471

[-] Predict Output Array[592]: 4077360126

[-] Predict Output Array[593]: 951273689

[-] Predict Output Array[594]: 730783078

[-] Predict Output Array[595]: 2714852542

[-] Predict Output Array[596]: 3772627284

[-] Predict Output Array[597]: 2949675102

[-] Predict Output Array[598]: 1446565583

[-] Predict Output Array[599]: 540482636

[-] Predict Output Array[600]: 1799890549

[-] Predict Output Array[601]: 1413418695

[-] Predict Output Array[602]: 2409408385

[-] Predict Output Array[603]: 1532906914

[-] Predict Output Array[604]: 1725699811

[-] Predict Output Array[605]: 4135649943

[-] Predict Output Array[606]: 2293818495

[-] Predict Output Array[607]: 3982308299

[-] Predict Output Array[608]: 2096384490

[-] Predict Output Array[609]: 911671827

[-] Predict Output Array[610]: 3295124991

[-] Predict Output Array[611]: 3821330809

[-] Predict Output Array[612]: 2157037312

[-] Predict Output Array[613]: 3338485446

[-] Predict Output Array[614]: 3526092151

[-] Predict Output Array[615]: 3798718115

[-] Predict Output Array[616]: 3385184675

[-] Predict Output Array[617]: 3930031594

[-] Predict Output Array[618]: 1515462361

[-] Predict Output Array[619]: 835305866

[-] Predict Output Array[620]: 869846291

[-] Predict Output Array[621]: 1104680209

[-] Predict Output Array[622]: 1816978544

[-] Predict Output Array[623]: 1486392435

----------------------------------------------------------------
[v] Predicted 624 Random Numbers

[v] Prediction Errors: 0


################################################################
End of | Clone MT19937 RNG From Output
################################################################

Mengapa hanya share prosesnya saja? Alasannya bisa anda lihat pada tulisan ikhtisar MCC sebelumnya.

Sekian tulisan hari ini, semoga bermanfaat.

Keep Fun Coding 😀

[1] Unknown. (????). Clone an MT19937 RNG From Its Output. Tersedia: cryptopals.com/sets/3/challenges/23/. [29 Januari 2015].

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2 thoughts on “Matasano Crypto Challenge 23: Clone an MT19937 RNG From Its Output

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