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Date: Tue, 20 Oct 2015 20:26:55 +0300
Subject: Re: Prime example of a can of worms

On 2015-10-20 10:22:40 -0600, Kurt Seifried wrote:

 > 1) in openssl does the -2/-5 option matter with respect to
 > security?

Actually, no: it's just a "generator", so it can be almost any small
prime number - say, 3 or 7 or whatever. It can even be just co-prime
to group modulo base.

However, the value 2 is the default in OpenSSL, so there may be some
space for experiments with birthdays paradox... especially when the
modulo is small.

 > 2) Openssl/gnutls (and likely others) all apparently have
 > slight variations on how they generate/test primes [...]
 > this worries me, diversity is good, but if not implemented
 > correctly. Do any best practices actually exist?

All implementations I know of simply use the randomized algorithms
with Miller-Rabin primality test.

 > 3) in testing for primeness how sure are we? Reading
[wikipedia: "Miller-Rabin primality test"]
 > and so on these tests are all "probably prime" but I can't find
 > any data to show that e.g. given this set of large primes, tested
 > against the various traditional primality methods, and then brute
 > forced to confirm they are prime/not prime, what % failed?

There's the Agrawal-Kayal-Saxena primality test, but I'm unaware of
any attempts to use it for checking the prime candidates which passed
the Miller-Rabin primality test.

Alexey V. Vissarionov aka Gremlin from Kremlin <gremlin ПРИ gremlin ТЧК ru>
GPG: 8832FE9FA791F7968AC96E4E909DAC45EF3B1FA8 @ hkp://

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