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I have been studying C/C++ and I read that if one wants unpredictable random data in a program, it is needed that a random generation function be supplied with truly and unpredictable random data (as of /dev/hwrng).

But this confused me because for cryptographic things a normal and non-cryptographic PRNG should be avoided.

Does supplying a truly random and unpredictable seed to a non-cryptographic PRNG (such as MT19937) will result in a unpredictable stream?

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No. Let's say the PRNG of period $N$ has linear complexity $L,$ where for LFSRs and LFSR derived PRNGs with nonlinear mixing functions we have $L=n^c$ for some constant $c\geq 1.$ The Mersenne Twister itself is predictable, given a long enough output of bits, namely $624$ bits, while its period is $N=2^{19937} − 1.$

So the output stream is definitely predictable.

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  • $\begingroup$ And what if we only output 500 bits per seeding? $\endgroup$
    – Paul Uszak
    Commented Dec 8, 2022 at 5:06
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No, it does not guarantee security.

For PRNG, to be secure, it surely needs a random seed and good probability properties. However, it is also required to have predictable values (both future and previous).

For example Mersene-Twister algorithm you mentioned, generates linearly dependent random outputs. With enough data you can solve a linear equation of next output.

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