ssh-keygen generator 3 broken

[Bernd Eckenfels]

Hello,

Sean wrote on 23. Dec 2023 20:52 (GMT +01:00):

> Hello, I was re-generating the moduli for SSH, and during that process I
> noticed that, when running the following command:
> 
> ssh-keygen -M screen -O prime-tests=600 -O generator=3 -f
> moduli-2048-01.candidates moduli-2048-01c
> 
> 
> It does not produce any errors, only the following:
> ebug2:    1467763: (4) Sophie-Germain 
> debug2:    1467763: generator 0 != 3 

According to this 

https://github.com/openssh/openssh-portable/blob/1036d77b34a5fa15e56f516b81b9928006848cbd/moduli.c#L718

It only guesses 2 (p mod 24 == 11 aka quadratic no residue) or 5 (p mod 10 == 3, 7).
Seems to miss the p mod 12 == 5 check for g=3.
(And also p mod 24 = 23 for g=2 quadratic residue)

Not sure what the idea behind ignoring 3 is, but certainly should be documented if not fixed,

I also wonder if it should if a generator is specified instead only test its matching remainder, that way
It will catch all candidates not only the ones which did not fail the g=2 test.

Gruss
Bernd
— 
https://bernd.eckenfels.net