Predict MT19937 PRNG, from preceding 624 generated numbers. There is a specialization for the "random" of Python standard library.

$ pip install mersenne-twister-predictor

This library has the special feature for CPython's standard random. Try below one:

import random
from mt19937predictor import MT19937Predictor

predictor = MT19937Predictor()
for _ in range(624):
    x = random.getrandbits(32)
    predictor.setrandbits(x, 32)

assert random.getrandbits(32) == predictor.getrandbits(32)

This is useful for some CTF tasks, e.g. TokyoWesterns CTF 4th 2018: mixed cipher, Tokyo Westerns CTF 3rd: 2017, etc. For more details, read the document.

Give the 624 32-bit integers, as unsigned decimal integers, line by line.

$ wc data.txt
 624  624 6696 data.txt

$ head -n 4 data.txt
734947730
363401994
806921074
790218357

$ cat data.txt | mt19937predict > predicted.txt

This is an example of a pseudorandom number generator using the Mersenne Twister.

// generator.cpp
#include <iostream>
#include <random>
using namespace std;
int main() {
    random_device seed_gen;
    mt19937 mt(seed_gen());
    for (int i = 0; i < 1000; ++i) {
        cout << mt() << endl;
    }
    return 0;
}

Compile it and let it generate 1000 numbers.

$ g++ -std=c++11 generator.cpp

$ ./a.out > data.txt

$ head data.txt
734947730
363401994
806921074
790218357
1766244801
680628322
1972477509
4015123394
2848130362
3481789813

Take the 624 consecutive numbers. We will predict the rest, 376 numbers.

$ head -n 624 data.txt > known.txt

$ tail -n 376 data.txt > correct.txt

$ wc known.txt
 624  624 6696 known.txt

Predict.

$ cat known.txt | mt19937predict | head -n 376 > predicted.txt

Compare the predict numbers and the original ones. If diff outputs nothing, it means the prediction was succeeded.

$ diff predicted.txt correct.txt

thanks to

• http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/mt.html
• http://herumi.in.coocan.jp/diary/1505.html#18
• https://oupo.hatenadiary.com/entries/2014/10/16