Re: [tor-dev] Padding prop224 REND1 cells to blend them with legacy cells

[Ian Goldberg <iang@xxxxxxxxxxxxxxx>]

On Tue, Sep 19, 2017 at 08:29:41PM -0400, Nick Mathewson wrote:
> > Is your goal that someone who sees the *plaintext* of that cell won't be
> > able to tell if it's a legacy RENDEZVOUS1 cell or a new one?  If so,
> > life is a bit complicated, since the g^y field will always be in the
> > prime-order subgroup.  (Note: I'm not actually 100% sure Tor uses a
> > generator of the prime-order subgroup for g in this part of the spec.
> > But it should have, and so hopefully did.)
> >
> > If HANDSHAKE_INFO || PADDING_64 (the latter being the first 64 bytes of
> > the padding) is _not_ in the prime-order subgroup, the observer will be
> > sure it's a prop224 cell.  If it _is_, the observer can't tell.
> >
> > If that's undesirable, you could always insist that PADDING_64 be chosen
> > such that HANDSHAKE_INFO || PADDING_64 _is_ in the prime-order subgroup.
> > Raise it to the power of the prime order q to check; if the result is
> > 1, you're good.  You'll need to try on average (p-1)/q random values of
> > PADDING_64 before you get a good one.  (NOTE: *NOT* CONSTANT TIME.)  If
> > p = 2q+1, that's just 2, so not *terrible*, but 2 1024-bit modexps might
> > still be annoying.  If for some reason p is a DSA modululus or something
> > bizarre like that, life is much more annoying.  (I hope it's not.)  This
> > is all assuming p is of the form 2^1024 - (some number at most say
> > 2^960), so that HANDSHAKE_INFO || PADDING_64 won't be larger than p
> > itself, which would be another problem.
> >
> > To be sure, what are the g and p values used in this particular
> > Diffie-Hellman?
> 
> This is the old, old, old group:
> 
>    For Diffie-Hellman, unless otherwise specified, we use a generator
>    (g) of 2.  For the modulus (p), we use the 1024-bit safe prime from
>    rfc2409 section 6.2 whose hex representation is:
> 
>      "FFFFFFFFFFFFFFFFC90FDAA22168C234C4C6628B80DC1CD129024E08"
>      "8A67CC74020BBEA63B139B22514A08798E3404DDEF9519B3CD3A431B"
>      "302B0A6DF25F14374FE1356D6D51C245E485B576625E7EC6F44C42E9"
>      "A637ED6B0BFF5CB6F406B7EDEE386BFB5A899FA5AE9F24117C4B1FE6"
>      "49286651ECE65381FFFFFFFFFFFFFFFF"

I confirm that both things I supposed about the group above are true: g
generates the prime-order subgroup, and p is near to 2^1024.
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