# What is the NIST recommended maximum bias for random number generators?

What is the maximum bias recommended by NIST for random number generators?

This answer says that it is $$2^{-64}$$.

Is it same for all applications? Does NIST have a publication with more information?

I tried to browse through NIST Recommendation for Random Bit Generator Constructions, but couldn't find it.

## 1 Answer

Yes, NIST recommends $$\epsilon \le 2^{-64}$$. They consider such a sequence to have "full entropy". It's in the definitions (page 4) of SP800-90C.

Converting that to a probability bias, $$P(x_i = 0, x_i = 1) \approx 0.5 \pm 2^{-66}$$.

The interesting thing is that if the Leftover Hash Lemma is used, $$\epsilon$$ can be set by the designer. ID Quantique TRNGs are designed with extractors such that $$\epsilon \approx 2^{-100}$$.