>A colleague of mine told me about a website that, given a sufficient quantity of output from an PRNG, had been able to deduce which application the PRNG was from.

As you correctly identified this would present an immediate and probably devastating attack to any cryptographic PRNG as it indeed would allow you to easily distinguish a random string from a PRNG output, something cryptographers try to make impossible eficiently.


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However, there _might_ be some truth to the story. Here are the two cases I know of where it would be possible:

 - The website identifies the output to be from the [infamous OpenSSL Debian bug][1].
 - The site is given an RSA publi key and can tell which implementation produced it as the prime-search strategies vary a bit in a secure way between different libraries. This was presented at [Usenix Security 2016 (PDF)][2] and perhaps someone converted this into a website.


  [1]: https://threatpost.com/how-debian-openssl-bug-almost-spawned-disaster-051809/72669/
  [2]: https://www.usenix.org/system/files/conference/usenixsecurity16/sec16_paper_svenda.pdf