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A random-number generator passes a standard statistical test suite, so what is the safest conclusion before trusting it for cryptography?

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Answer: Only a first screening

Only a first screening ✓ — Passing statistical tests is useful evidence, but it is only a first screening. NIST SP 800-22 explicitly warns that tests cannot certify a generator's cryptographic suitability or replace cryptanalysis. A clean test report is encouraging, yet the source model, entropy, implementation, and threat model still matter.

Proof of future bits — Future bits are not proven merely because past output looked statistically normal. A flawed physical device can contain predictable noise, and a deterministic generator can pass many tests until its state is exposed. Certification needs a reason that an adversary could not have known the bits in advance, not just a clean histogram.

No need for seed secrecy — Seed secrecy still matters for pseudorandom generators. SP 800-22 frames the goal as next-output unpredictability despite previous outputs when the seed is unknown. If the seed becomes known, the argument changes completely; passing a battery of tests does not make seed exposure harmless.

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