On Saturday, 21 August 2021 12:06:52 CEST, Damien Miller wrote:
On Wed, 18 Aug 2021, Hubert Kario wrote:
Hello everybody!
For the past few years we've used a tool to double-check the security of
the primes shipped in the OpenSSH moduli file:
https://github.com/tomato42/ecpp-verifier
In short, it uses primality certificates to mathematically prove that all
the
parameters use safe primes and a bit of simple maths to check if they're
not
vulnerable to Special Number Field Sieve.
I wrote an article on why it's necessary, a high level overview how it
does it and how you can run it yourself:
https://www.redhat.com/en/blog/understanding-and-verifying-security-diffie-hellman-parameters
Excellent - one question: how do you generate/prove safe primes? I was
never able to figure out how to prove that both N and (N-1)/2 are prime
(though I thought it might be possible using Pocklington's criteria).
You generate safe primes by selecting numbers at random, and checking if
they are a safe prime using something like Miller-Rabin test. Repeat until
you
get a safe prime.
You prove the primality of them using Atkin-Goldwasser-Kilian-Morain
certificates (and few others as shortcuts, but Atkin ones do the heavy
lifting).
--
Regards,
Hubert Kario
Senior 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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