What's the difference between a PRNG and a CSPRNG?
PRNG vs CSPRNG
What's the different between a pseudo-random number generator and a cryptographically-secure pseudo-random number generator? A recommendation from the NIST.
The NIST ran various tests (defined in a publication known as SP800-22) to determine which PRNG algorithms produced the best output given a certain criteria.
The result and recommendation for these tests can be read in another publication called SP800-90. Skip down to Appendix C (Informative) DRBG Mechanism Selection to see the good stuff.
Three algorithms are determined to be cryptographically-secure pseudo-random number generators:
So there you go. Those three algorithms are CSPRNG because they've been tested and recommended by the NIST*.
*There are other organizations and tests that determine a PRNG to be a CSPRNG, but the NIST is the 800-pound Gorilla.
It's worth noting that the original publication actually had 4 CSPRNG recommendations. The now infamous Dual_EC_DRBG was quietly removed in the revised publication SP800-9Ar1.
There has been a lot of controversy surrounding Dual_EC_DRBG. Whether or not any of the controversy is true, it's clear that trust in the NIST's authority has been undermined by its recommendation of Dual_EC_DRBG. I'm grateful that the NIST has removed the algorithm from its newest revision.
This also serves as a warning to anyone trying to influence these types of publications. The people that design, implement and critique this type of cryptography are smart. Very smart. Smarter than you and me -- and they don't like shenanigans!