When a random-number generator passes a standard statistical test suite, what should you conclude about its safety before trusting it in cryptography?

Answer: It is only a first screening; model, entropy, and seed secrecy still need checking.

It is only a first screening; model, entropy, and seed secrecy still need checking. ✓ — Passing statistical tests is useful evidence, but it is only a first screening. NIST SP 800-22 warns that test suites cannot certify a generator's cryptographic suitability or replace cryptanalysis. The source model, available entropy, implementation details, and threat model still decide whether the output is safe. A clean report is encouraging, not a guarantee.

It proves future bits are unpredictable, so the generator is safe for cryptography. — It is tempting to treat a passed test as proof that future bits cannot be predicted, and the output's normal-looking statistics is what makes that idea feel right. But a flawed physical device can contain predictable noise, and a deterministic generator can pass many tests until its internal state is exposed. For cryptography, you need a reason an adversary could not have known the bits in advance, not just a clean histogram.

It makes seed secrecy unnecessary because the output already looks random. — Passing tests can make the output look independent, so it is tempting to think the seed no longer needs protection. For pseudorandom generators, however, the goal is next-output unpredictability even after previous outputs, as long as the seed stays unknown. If the seed becomes known, the whole argument changes; a battery of tests does not make seed exposure harmless.