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I'm looking at D.3.2 Verifiably Random Base Points of NIST SP 800-186. Looks like step 5 is there to ensure that $hashlen > bitLen(q)+1$ and (potentially) discard big $e$, so $t$ is distributed properly. However, the generation method won't work in if $hashlen < bitLen(q)$ (say SHA256 and Curve448). Is there any way to fix it?

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    $\begingroup$ The step only checks that the division is not the same. You may choose a large hash like SHA-512. $\endgroup$
    – kelalaka
    Apr 7, 2022 at 18:43
  • $\begingroup$ @kelalaka, yes but when hashlen is smaller than qbitLen, it's an infinite loop, no? With a bigger hashlen there is no problem, but I wonder how to make it work with a smaller one $\endgroup$
    – pintor
    Apr 8, 2022 at 8:10

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