Re: [MLS] TreeKEM: An alternative to ART
Peter Saint-Andre <stpeter@mozilla.com> Wed, 30 May 2018 14:45 UTC
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Cc: mls@ietf.org, Nick Sullivan <nick@cloudflare.com>, Sean Turner <sean@sn3rd.com>
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From: Peter Saint-Andre <stpeter@mozilla.com>
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Subject: Re: [MLS] TreeKEM: An alternative to ART
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Yet this is no longer true... > Fortunately, we're not a WG yet, so we're not bound by the rules for > virtual interims :) The tutorial would be beneficial, though! Peter On 5/30/18 7:43 AM, Richard Barnes wrote: > Sorry, I dropped the ball on this, and now we're in the midst of these > dates. Based on the responses, I propose we do tomorrow at 11:00 ET == > 15:00 UTC. > > https://www.timeanddate.com/worldclock/fixedtime.html?msg=TreeKEM+overview+%2F+discussion&iso=20180531T11&p1=263&ah=1 > > The below Webex details should work: > > Join from a video conferencing system or application > Dial https://cisco.webex.com/meet/richbarn > Join by Phone > Toll free: +1-866-432-9903 Toll: +1-408-525-6800 Access code: 201006237 > > > > On Thu, May 10, 2018 at 3:05 PM Richard Barnes <rlb@ipv.sx> wrote: > > Fortunately, we're not a WG yet, so we're not bound by the rules for > virtual interims :) Here's a Doodle to see if there's a time that > looks good to folks: > > https://doodle.com/poll/u84kpg2i4vfvnmsz > > On Thu, May 10, 2018 at 2:01 PM Russ Housley <housley@vigilsec..com > <mailto:housley@vigilsec.com>> wrote: > > I think that a virtual interim to go through a tutorial of > TreeKEM would be very useful. > > Russ > > >> On May 3, 2018, at 10:36 AM, Richard Barnes <rlb@ipv.sx >> <mailto:rlb@ipv.sx>> wrote: >> >> Just for context: Note that TreeKEM, like ART, is an "inner >> loop" / "subroutine" for MLS. It handles the establishment of >> a key that's confidential to the group members. There's still >> a need for more mechanism to provide authentication. >> >> Speaking of protocol, in protocol terms, TreeKEM, while we >> haven't elaborated a precise protocol, if you look at the very >> basic sketch that's in the repo EKR linked, the protocol looks >> very similar to what we have for ART now. Basically, where >> ART sends public keys, TreeKEM needs to send (public key, PKE >> ciphertext) pairs. So there's a bit of additional >> communications overhead, but not a dramatic reworking of the >> messages. >> >> Having spent some time with this approach, I appreciate that >> it can be kind of hard to digest; it has a few more moving >> parts than ART. I would be happy to set up a call sometime if >> people wanted to talk this through. >> >> --Richard >> >> On Thu, May 3, 2018 at 10:33 AM Eric Rescorla <ekr@rtfm.com >> <mailto:ekr@rtfm.com>> wrote: >> >> Oops. I forgot to attach the paper. >> >> >> On Thu, May 3, 2018 at 7:26 AM, Eric Rescorla >> <ekr@rtfm.com <mailto:ekr@rtfm.com>> wrote: >> >> Hi folks, >> >> Several of us (Karthik, Richard, and I) have been >> working on an >> alternative to ART which we call TreeKEM. TreeKEM >> parallels ART in >> many ways, but is more cryptographically efficient and >> is much better >> at handling concurrent changes. The most common >> behaviors (updating >> ones own key) can be executed completely concurrently, >> merging all the >> requested changes. >> >> We've attached a draft technical paper describing the >> details, and >> some slides, but here's a brief overview of TreeKEM. >> >> Code: https://github.com/bifurcation/treekem, >> https://github.com/bifurcation/treekem >> Explainer slides: >> https://docs.google.com/presentation/d/1myiQ22ddxHAcF8uCJBXk9cdJMvAQfAw9nmKiqE5seJc/edit?usp=sharing >> >> As with ART, TreeKEM addresses the scaling problem by >> arranging nodes >> in a binary tree. In the steady state, each node i has >> a key pair but >> instead of having two siblings do DH to determine >> their shared key, we >> derive the shared key by hashing the key of the last >> node to update. >> As before, each node knows all the keys to its parents. >> >> Imagine we have the four node tree a, b, c, d which >> was constructed >> in that order. The private keys at each vertex are >> shown below. >> >> H^2(d) >> / \ >> H(b) H(d) >> / \ / \ >> a b c d >> >> >> UPDATES >> Now say that b wants to update its key to b', giving >> us the tree: >> >> H^2(b') >> / \ >> H(b') H(d) >> / \ / \ >> a b' c d >> >> This requires providing >> >> - a with H(b') -- note that a can compute H^2(b') >> for itself. >> - c and d with H^2(b') >> >> Recall that you can encrypt to any subset of the tree >> by just >> encrypting to the appropriate set of parent nodes. So, >> we can >> do this by sending: >> >> - E(pubkey(a), H(b')) >> - E(pubkey(H^2(d)), H^2(b')) >> >> Where pubkey(k) gives the public key derived from >> private key k. >> >> As with ART, you then mix the new tree root (H^2(b')) >> into the current >> operational keys and use the result to derive the >> actual working keys. >> >> >> CONCURRENT UPDATES >> The big win in TreeKEM is that you can handle an >> arbitrary number >> of concurrent updates, just by applying them in order. >> Again, >> consider our starting tree, but assume that b and c >> both try to >> update at once. a thus receives two updates >> >> - E(pubkey(a), H(b')) [b's update] >> - E(pubkey(H(b)), H^2(c')) [c's update] >> >> If we apply these in order b, c we get the tree: >> >> H^2(c') >> / \ >> H(b') H(c') >> / \ / \ >> a b' c d >> >> a can easily compute this. >> >> In order to make this work, we need two things: >> >> 1. a needs to keep a copy of its current tree around >> until it has >> received all updates based on that tree >> 2. there needs to be an unambiguous ordering of updates >> >> The way to handle (1) is probably to have some defined >> "window" >> of time during which an update can be received. The >> node needs >> to hold onto its old key until that window has passed. >> (2) can >> be handled by having the messaging system provide a >> consistent >> order and then agreeing to apply updates >> consecutively. If we >> want to concurrently apply other changes, we may need >> to sort >> based on change type within the window. >> >> >> ADDS >> In order to add itself to the group (USERADD), a node >> merely puts >> itself at the right position in the tree and, >> generates a random key, >> and then sends the appropriate keying material to >> everyone in its path >> to the root. >> >> In order to add another node to the group (GROUPADD), >> the adding >> node does exactly the same thing as with a USERADD, >> but also sends >> a copy of the new key to the node being added.. Note >> that this creates >> a double-join, which we will cover later. >> >> >> REMOVAL >> In order to remove another node from the tree, the >> removing node >> sends the same message that the evicted node would >> have sent if >> it had sent an update, but with a new key not known to >> the evicted >> node (note that this naturally omits the evicted node, >> because you >> encrypt to the co-path). This also creates a >> double-join, where the >> removing node knows the dummy key. >> >> >> >> STATE >> In order to receive messages, a node need only keep >> its secret keys, >> which range between 1 key (if it was the last to >> update) and log(N) >> keys (in the worst case). >> >> In the best case, in order to update, a node needs to >> also know >> the public keys for everyone on its co-path. However. >> >> In order to be able to do deletes, a node also needs >> to be able >> to get the public key for any node in the tree (leaf >> or internal). >> It's easy to see this by realizing that to delete a >> node you need >> to encrypt a new key to its sibling, and so to delete >> any node, >> you need to be able to access every node's public key. >> However, >> a node need not store this information, but can >> retrieve it >> on demand when it needs to delete another node. >> >> >> EFFICIENCY >> The paper contains more details. but generally TreeKEM >> is somewhat >> more efficient in terms of asymmetric crypto >> operations than ART. >> >> >> DOUBLE JOINS >> Like ART, TreeKEM has double-join problems whenever >> one group member >> provides a service (or a disservice, in the case of >> remove) for another >> group member. In the case of GROUPADD, the double join >> will resolve itself >> as soon as the added node updates its key. However in >> the case of >> REMOVE, this cannot happen, and so double join needs to be >> dealt with in some other way. >> >> One option is to have selective updates: each node >> keeps track of >> extra tree state and uses it to control its updates. >> For instance, >> if we never send updates to deleted nodes, than as >> soon as a deleted >> node's sibling sends an update, the double-join will >> be resolved. >> In a more sophisticated -- but also more expensive to >> implement -- >> version, we track which nodes control the keys of >> other nodes and >> REMOVE all affected nodes when we do a delete. >> >> -Ekr >> >> >> _______________________________________________ >> MLS mailing list >> MLS@ietf.org <mailto:MLS@ietf.org> >> https://www.ietf.org/mailman/listinfo/mls > > _______________________________________________ > MLS mailing list > MLS@ietf.org <mailto:MLS@ietf.org> > https://www.ietf.org/mailman/listinfo/mls > > > > _______________________________________________ > MLS mailing list > MLS@ietf.org > https://www.ietf.org/mailman/listinfo/mls >
- [MLS] TreeKEM: An alternative to ART Eric Rescorla
- Re: [MLS] TreeKEM: An alternative to ART Eric Rescorla
- Re: [MLS] TreeKEM: An alternative to ART Richard Barnes
- Re: [MLS] TreeKEM: An alternative to ART =JeffH
- Re: [MLS] TreeKEM: An alternative to ART Eric Rescorla
- Re: [MLS] TreeKEM: An alternative to ART Katriel Cohn-Gordon
- Re: [MLS] TreeKEM: An alternative to ART Richard Barnes
- Re: [MLS] TreeKEM: An alternative to ART Eric Rescorla
- Re: [MLS] TreeKEM: An alternative to ART Daniel Van Geest
- Re: [MLS] TreeKEM: An alternative to ART Karthikeyan Bhargavan
- Re: [MLS] TreeKEM: An alternative to ART Cas Cremers
- Re: [MLS] TreeKEM: An alternative to ART Karthikeyan Bhargavan
- Re: [MLS] TreeKEM: An alternative to ART Alexey Ermishkin
- Re: [MLS] TreeKEM: An alternative to ART Richard Barnes
- Re: [MLS] TreeKEM: An alternative to ART Russ Housley
- Re: [MLS] TreeKEM: An alternative to ART Richard Barnes
- Re: [MLS] TreeKEM: An alternative to ART Stephen Farrell
- Re: [MLS] TreeKEM: An alternative to ART Benjamin Kaduk
- Re: [MLS] TreeKEM: An alternative to ART Benjamin Beurdouche
- Re: [MLS] TreeKEM: An alternative to ART Eric Rescorla
- Re: [MLS] TreeKEM: An alternative to ART Richard Barnes
- Re: [MLS] TreeKEM: An alternative to ART Peter Saint-Andre
- Re: [MLS] TreeKEM: An alternative to ART Richard Barnes
- Re: [MLS] TreeKEM: An alternative to ART Peter Saint-Andre