Diffie-Hellman question

[Peter Fairbrother]

Thomas Shaddack wrote:

> 
> I have a standard implementation of OpenSSL, with Diffie-Hellman prime in
> the SSL certificate. The DH cipher suite is enabled.
> 
> Is it safe to keep one prime there forever, or should I rather
> periodically regenerate it? Why? If yes, what's some sane period to do so:
> day, week, month?

No need. 

Kinda.

The best known discreet logarithm attacks are such that if they succeed in
the attack then they can easily apply their solution to anything encrypted
with the same prime. A shared prime attracts attacks. Widely used primes can
become a big target.

These attacks are generally supposed to be beyond capability for the next X
zillion years though. Or perhaps for ten years.

This might seem garubonsendese in the naive ""it's safe' or 'it's not safe""
crypto paradigm. However, that isn't how crypto works.

Cryptanalysis (the revealing of plaintext against the wishes of the
encryptor) is an economic activity. No-one will bother putting in enough
resources to break your 2k-bit modexp-based crypto unless they think it
worthwhile.

But if your prime is shared with several other people who are sending
nuclear secrets, then your prime might become subject to attack.

> If the adversary has a log of a passively intercepted DHE-RSA-AES256-SHA
> secured SSL communication, presuming the ephemeral key was correctly
> generated and disposed of after the transaction, will the eventual
> physical retrieval of the DH prime (and the rest of the certificate) allow
> him to decode the captured log?

The prime is public - anyone can know it  - so it's retrieval won't affect
anything. 

The question I think you are asking is "if the secret key is retrieved, will
I lose forward security", to which the answer is "yes".

For long-term forward secrecy you need to change the public key every every
day or so. Use a long-term key to sign the daily keys. PGP does this.

Once you have deleted the day's public key, you are OK (but see belaw!).

The ephemeral keys cannot (or should not) be retrive(able)d.




(below!) Or perhaps the question you were asking was "if finding DL's mod
_this prime_ becomes possible, will I lose forward security?", in which case
the answer is "yer fukked" - as are we all - if one prime gets broken, they
all will, sooner or later.



-- 
Peter Fairbrother
(Who is right now composing a talk about the uses of modexp in crypto, for
those far more knowledgeable than I)