[+ Douglas, Berkant]
On Fri, May 06, 2011 at 10:50:05AM -0400, Nick Mathewson wrote:
Crypto people who have been following threads about the circuit-establishment handshake will be interested in the new paper, "Anonymity and one-way authentication in key-exchange protocols", by Goldberg, Stebila, and Ostaoglu. Here's the version they updated today:
http://www.cacr.math.uwaterloo.ca/techreports/2011/cacr2011-11.pdf
If we're moving to an improved handshake, this might be a good candidate to consider. The protocol itself is on page 14.
Some notes, written by a guy who knows less crypto than everybody involved:
- It's a pure Diffie-Hellman based system, which would lend itself
nicely to use with ECC.
- It seems to require the same number of exponentiations as our
current system, but Ian Goldberg notes that if you want to compute X^a and X^b at the same time you can do so more efficiently by taking into account the shared base.
- The security proof requires that the Gap DH assumption holds over
the group -- basically, that computing the Decisional DH problem is easy, but computing the Computational DH problem is hard. This assumption isn't true of most basic ECC groups -- I think it means you need to use a pairing-based system instead for the proof to hold. I'd bet that the authors aren't seriously suggesting that we use pairing-based crypto, but I'm wondering how much they were able to prove in a groups where DDH is hard.
Not quite: it's saying that, if you can break the protocol (_with or without_ the ability to solve DDH), then if you _do_ have a DDH oracle, you can also solve CDH. Since being able to solve CDH given a DDH oracle (the "GDH problem") would be extremely surprising, we conclude the protocol is secure.
- I haven't read over the security model closely yet; folks should
review it for reasonableness.
- I'm hoping to write this up as a proposed spec soon, unless Ian or
somebody wants to give it a shot.
Please go ahead.
- Ian