Weak DH primes and openssh

Hubert Kario hkario at redhat.com
Fri May 29 20:26:42 AEST 2015

On Friday 29 May 2015 09:23:59 Damien Miller wrote:
> On Thu, 28 May 2015, Hubert Kario wrote:
> > > If this is the only attack you're trying to address, and you've
> > > already limited yourself to safe primes, then NUMS properties don't
> > > really add anything. The NUMS approach is there are to try to avoid
> > > the possibility of other, unknown cryptanalytic attacks against some
> > > infrequent type of group, so that the entity who defines the group
> > > can't force you into this secret corner case if they have special
> > > knowledge.
> > 
> > that being said, how using NUMS seeds to generate safe prime would
> > hurt?
> If you're concerned about precomputation,

I'm afraid for precomputation only in 1024 bit case, 
/which we should strive not to use anyway/

> then it effectively gives the
> attackers a list of what you're going to use in the future.

Not really, no.

We can use this time an initial seed of "OpenSSH 1024 bit prime, attempt #1".
Next time we generate the primes we can use the initial seed of "2017 OpenSSH 
1024 bit prime, attempt #1", but we can use just as well a "2nd generation 
OpenSSH 1024 bit DH parameters, try number 1". Then we can also change the 
algorithm to use this seed for M-R witnesses, or not. Then we can use SHA-512 
instead of SHA-256, or some SHA-3 variant.

The space for possible selected values is rather large...
> > also, doesn't that require us to provide primality certificates for q
> > rather than p?
> IMO you'd want both to prove a safe prime

The process to prove primality of p when you know that q is prime[1] is rather 
simple, just use Pocklington Theorem to do that.

So the primality of q is basically a primality certificate for p.

 1 - continuing the nomenclature of q = (p-1)/2, where p and q are prime
Hubert Kario
Quality Engineer, QE BaseOS Security team
Web: www.cz.redhat.com
Red Hat Czech s.r.o., Purkyňova 99/71, 612 45, Brno, Czech Republic
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