Proven Primes

[Tero Kivinen]

Ben Laurie writes:
> > I actually just finished finding the 16384 bit Diffie-Helman group
> > with same kind of parameters. It took about 9.5 months to generate.
> > The 12288 bit group took only about 15 days to generate.
> I have to admit to surprise at the time involved - what s/w are you 
> using to do the generating?

We have our own software and crypto library to generate those primes.
To create ~500 bit group it takes about 10 seconds. To create ~1000
bit group it takes about minute. Here are ike style primes between
512-1024 where the bits is incremented by 32 every time. These are not
proven, but running primo or similar on them shouldn't take that long,
so you can do it yourself if you need a proven prime:

SOPHIE GERMAIN PRIME SEARCH
FIXED 64 bits.
INDEX 0: 
PRIME (bits 512), index = 131, 0.989151 seconds: 
0xffffffffffffffffc90fdaa22168c234c4c6628b80dc1cd129024e088a67cc74020bbea63b139b22514a08798e3404ddef9519b3cd3a439dffffffffffffffff
PRIME (bits 544), index = 11486, 2.32198 seconds: 
0xffffffffffffffffc90fdaa22168c234c4c6628b80dc1cd129024e088a67cc74020bbea63b139b22514a08798e3404ddef9519b3cd3a431b302b374affffffffffffffff
PRIME (bits 576), index = 145480, 17.2525 seconds: 
0xffffffffffffffffc90fdaa22168c234c4c6628b80dc1cd129024e088a67cc74020bbea63b139b22514a08798e3404ddef9519b3cd3a431b302b0a6df2614c7effffffffffffffff
PRIME (bits 608), index = 37293, 5.66688 seconds: 
0xffffffffffffffffc90fdaa22168c234c4c6628b80dc1cd129024e088a67cc74020bbea63b139b22514a08798e3404ddef9519b3cd3a431b302b0a6df25f14374fe1c719ffffffffffffffff
PRIME (bits 640), index = 335775, 42.4739 seconds: 
0xffffffffffffffffc90fdaa22168c234c4c6628b80dc1cd129024e088a67cc74020bbea63b139b22514a08798e3404ddef9519b3cd3a431b302b0a6df25f14374fe1356d6d56e1e3ffffffffffffffff
PRIME (bits 672), index = 5214, 2.83781 seconds: 
0xffffffffffffffffc90fdaa22168c234c4c6628b80dc1cd129024e088a67cc74020bbea63b139b22514a08798e3404ddef9519b3cd3a431b302b0a6df25f14374fe1356d6d51c245e485c9d3ffffffffffffffff
PRIME (bits 704), index = 65808, 10.8744 seconds: 
0xffffffffffffffffc90fdaa22168c234c4c6628b80dc1cd129024e088a67cc74020bbea63b139b22514a08798e3404ddef9519b3cd3a431b302b0a6df25f14374fe1356d6d51c245e485b576625f7fd5ffffffffffffffff
PRIME (bits 736), index = 229946, 34.0901 seconds: 
0xffffffffffffffffc90fdaa22168c234c4c6628b80dc1cd129024e088a67cc74020bbea63b139b22514a08798e3404ddef9519b3cd3a431b302b0a6df25f14374fe1356d6d51c245e485b576625e7ec6f44fc522ffffffffffffffff
PRIME (bits 768), index = 149686, 24.5593 seconds: 
0xffffffffffffffffc90fdaa22168c234c4c6628b80dc1cd129024e088a67cc74020bbea63b139b22514a08798e3404ddef9519b3cd3a431b302b0a6df25f14374fe1356d6d51c245e485b576625e7ec6f44c42e9a63a3620ffffffffffffffff
PRIME (bits 800), index = 168625, 28.5964 seconds: 
0xffffffffffffffffc90fdaa22168c234c4c6628b80dc1cd129024e088a67cc74020bbea63b139b22514a08798e3404ddef9519b3cd3a431b302b0a6df25f14374fe1356d6d51c245e485b576625e7ec6f44c42e9a637ed6b0c01ef66ffffffffffffffff
PRIME (bits 832), index = 13056, 5.62474 seconds: 
0xffffffffffffffffc90fdaa22168c234c4c6628b80dc1cd129024e088a67cc74020bbea63b139b22514a08798e3404ddef9519b3cd3a431b302b0a6df25f14374fe1356d6d51c245e485b576625e7ec6f44c42e9a637ed6b0bff5cb6f406eaecffffffffffffffff
PRIME (bits 864), index = 173063, 32.9709 seconds: 
0xffffffffffffffffc90fdaa22168c234c4c6628b80dc1cd129024e088a67cc74020bbea63b139b22514a08798e3404ddef9519b3cd3a431b302b0a6df25f14374fe1356d6d51c245e485b576625e7ec6f44c42e9a637ed6b0bff5cb6f406b7edee3b1001ffffffffffffffff
PRIME (bits 896), index = 26718, 9.01863 seconds: 
0xffffffffffffffffc90fdaa22168c234c4c6628b80dc1cd129024e088a67cc74020bbea63b139b22514a08798e3404ddef9519b3cd3a431b302b0a6df25f14374fe1356d6d51c245e485b576625e7ec6f44c42e9a637ed6b0bff5cb6f406b7edee386bfb5a8a0802ffffffffffffffff
PRIME (bits 928), index = 636907, 119.4 seconds: 
0xffffffffffffffffc90fdaa22168c234c4c6628b80dc1cd129024e088a67cc74020bbea63b139b22514a08798e3404ddef9519b3cd3a431b302b0a6df25f14374fe1356d6d51c245e485b576625e7ec6f44c42e9a637ed6b0bff5cb6f406b7edee386bfb5a899fa5aea8dbfbffffffffffffffff
PRIME (bits 960), index = 139761, 31.0893 seconds: 
0xffffffffffffffffc90fdaa22168c234c4c6628b80dc1cd129024e088a67cc74020bbea63b139b22514a08798e3404ddef9519b3cd3a431b302b0a6df25f14374fe1356d6d51c245e485b576625e7ec6f44c42e9a637ed6b0bff5cb6f406b7edee386bfb5a899fa5ae9f24117c4d41d6ffffffffffffffff
PRIME (bits 992), index = 15349, 8.29022 seconds: 
0xffffffffffffffffc90fdaa22168c234c4c6628b80dc1cd129024e088a67cc74020bbea63b139b22514a08798e3404ddef9519b3cd3a431b302b0a6df25f14374fe1356d6d51c245e485b576625e7ec6f44c42e9a637ed6b0bff5cb6f406b7edee386bfb5a899fa5ae9f24117c4b1fe64928a245ffffffffffffffff

FINISHED (0 primes found in the interval 512 to 1024).
-- 
kivinen at ssh.fi
SSH Communications Security                  http://www.ssh.fi/
SSH IPSEC Toolkit                            http://www.ssh.fi/ipsec/

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