Re: [MLS] Removing ART; maybe adding partial-tree

On Mon, Oct 1, 2018 at 10:34 PM Dave Cridland <dave@cridland.net> wrote:

>
>
> On Mon, 1 Oct 2018 at 19:06, Richard Barnes <rlb@ipv.sx> wrote:
>
>> Hey all,
>>
>> At the interim last week, there was agreement to remove the discussion of
>> ART from the protocol draft and focus on TreeKEM.  I have implemented that
>> change in the following pull request:
>>
>> https://github.com/mlswg/mls-protocol/pull/66
>>
>>
> I'm not objecting to the change - I lack sufficient cryptographic
> knowledge to express an opinion - but it'd be very useful to read a
> synopsis of the reasoning behind it, and a summary of the discussion. I
> imagine future participants would find it useful too, and of course, all
> decisions need to go by the list anyway.
>

To recap the discussions at the interim, I think the reasons are basically
as follows, in descending order of importance:

1. ART requires each recipient of a message to do O(log N) DH operations,
where as TreeKEM only requires O(1).  This is a significant difference for
large groups / small devices.
2. TreeKEM offers the possibility of doing Add/Remove without double join
3. TreeKEM offers the possibility of being able to merge Update messages

While I don't think anyone has proved that (2) and (3) aren't possible with
ART, the fact that it's contributive makes them more difficult.

> I reviewed the PR for clarity/typos.
>
>
>> If a couple of folks could give a quick review, it would be appreciated.
>> I also put together a PR describing how to do the "partial tree" approach
>> described at the interim and in my earlier message today.
>>
>> https://github.com/mlswg/mls-protocol/pull/67
>>
>
> Also reviewed for clarity/typos. I admit I'm mildly confused as to why
> adding a node needs to blank the direct path, but at the same time I'm not
> sure it makes any difference. (That is, here:
> https://github.com/mlswg/mls-protocol/pull/67/commits/7a7cd37aec0ceff773600564b5c9619c3d06a115#diff-a87cc9081154f564150420544170f1c9R1113
> ). That's probably just my lack of understanding somewhere.
>

The reason is symmetric for Add and Remove.

Recall that the invariant property the tree is supposed to have is that a
node's secret value and private key are only known to the holders of leaves
below that node in the tree.  For both Add and Remove, you need to change
the intermediate nodes above the target leaf, either to make it so that the
removed member doesn't know them or so that the added member does.  The
question is what relationship those intermediate nodes have to the sender
of the Add/Remove -- does the sender know the secret / private key or not?

On the one hand, if the sender does know the private key, then you have a
"double join" situation, where the sender knows something he's not supposed
to.  The phrase "double join" arises from the Add case, since the relevant
intermediate node secrets are known both to the new member and to the
sender of the Add.  Effectively, they both occupy the new member's leaf,
which complicates things quite a bit.  For example, if you now want to
evict the sender of the Add, you have to also evict the newly added leaf,
etc.  In the Remove case, the main impact of the double-join is that you
don't have a true Remove operation, you only have a Take-over operation.
That makes it difficult to imagine how you would ever compact the tree.

On the other hand, if the sender doesn't know the private key, then the
node has to be blank.  In the Add case, there's no way (AFAIK) to set the
intermediate node values to something that is known to (a) the existing
members under those nodes and (b) the new member, without it also being
known to the sender of the add.  So the values that get decrypted to
intermediate nodes during the Add are only for the purpose of computing the
new root secret; the intermediate nodes can't have a non-blank value
without violating the tree invariant.

It may be possible to avoid blanks in the Remove case, but we would have to
modify TreeKEM.  You could still do the "hash to the root" trick to
generate the fresh shared entropy for the epoch, but you couldn't just
overwrite the values of the intermediate nodes (as is done now).  You would
have to fold in some entropy only known to the existing members.  This is
probably worth some thought.

Anyway, hope that helps,
--Richard

>
>
>>
>> Feedback welcome!
>>
>> Thanks,
>> --Richard
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>