Re: [MLS] Re-randomized TreeKEM

Benjamin Beurdouche <> Tue, 22 October 2019 22:10 UTC

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From: Benjamin Beurdouche <>
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Date: Wed, 23 Oct 2019 00:10:38 +0200
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Cc: Karthikeyan Bhargavan <>, Messaging Layer Security WG <>, Joel Alwen <>, Yevgeniy Dodis <>
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To: Richard Barnes <>
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Subject: Re: [MLS] Re-randomized TreeKEM
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That’s my opinion as well... :)

> On Oct 22, 2019, at 11:34 PM, Richard Barnes <> wrote:
> Since it appears I haven't chimed in on this thread -- I am generally OK with this change, if folks think it would improve the FS properties of the protocol, and assuming that Joël's / Mike's solution to the X25519 problem works out.  
> On the one hand, if we have to shove X25519 overboard, my bias would probably be against making this change, barring some really strong security rationale.  
> On the other hand, if we can get confidence that the X25519 solution works (or that the failures are rare and tolerable), then this seems like a pretty minor burden from an engineering POV (a little more code, 2x the DH operations on Update/Commit), so if there's security benefit, great.
>> On Tue, Oct 22, 2019 at 5:26 PM Karthikeyan Bhargavan <> wrote:
>> Indeed!
>> Like I said, it would be a ridiculous design for MLS.
>> I was simply trying to understand the guarantees.
>> -Karthik
>>> On 22 Oct 2019, at 23:20, Richard Barnes <> wrote:
>>> Just so we're clear, I would be *strongly* opposed to putting anything like this naïve UPKE scheme into MLS..  For the simple reason that it expands the size of Welcome message by a factor of K.  RTreeKEM or nothing :)
>>> --Richard
>>>> On Mon, Oct 21, 2019 at 6:53 PM Yevgeniy Dodis <> wrote:
>>>> Great summary, Karthik!
>>>> As I put in the other thread, comparison with the "naive" UPKE (for K=100 or less) might be a good idea.
>>>> Pros of Naive Scheme: 
>>>> - more general, uses any PKE
>>>> - using stream ciphers to generate K key pairs as needed makes the efficiency hit noticeably less than a factor of K,
>>>> and perhaps closer to a factor of 2 (see below), but unclear a-priori.
>>>> - for K>1, offers non-trivial (but still sub-optimal) security enhancement over basic TreeKEM (K=1)
>>>> Cons (pros of RTreeKEM):
>>>> - Public key storage increases by at least factor of K
>>>> - While the naive use increases secret storage and computation by a factor of K, using stream cipher, after i uses one can only store the 
>>>> current seed to generate last (K-i) keys. However, K public keys should be published right away, so we must 
>>>> lose at least factor of 2 compared to TreeKEM to generate all keys twice (but possibly factor of K if people update too frequently, so all but 
>>>> 1 of the K keys gets used). So overall efficiency hit between 2 and K, which might already be comparable or worse than RTreeKEM.
>>>> - Still much worse security than RTreeKEM, but possibly more expensive too, already for small K!
>>>> Please let us know if you think this should be explored further.
>>>> Yevgeniy
>>>>> On Mon, Oct 21, 2019 at 8:03 AM Karthikeyan Bhargavan <> wrote:
>>>>> I see. So, here’s how I read the improvements proposed in RTreeKEM.
>>>>> Currently, in TreeKEM (like in ART before it) we rely on each member to regularly *send* updates in order to get both PCS and FS for the group secrets.
>>>>> The informal secrecy guarantees we get are that:
>>>>> - (FS) if member A sends an update in epoch N (moving the epoch to N+1), and if A gets compromised in epoch N+1, the messages sent in epoch N remain secret
>>>>> - (PCS) if member A sends an update in epoch N (moving the epoch to N+1), and if A was (passively) compromised in epoch N, the messages sent in epoch N+1 remain secret
>>>>> In other words, each member who sends an update gets local protection against compromise, encouraging vulnerable members to keep sending updates...
>>>>> However, as Joel, Sandro, Yevgeniy, and Yiannis note in their paper, we could do better, at least for FS, if we use one-time decryption keys.
>>>>> If each recipient deletes the old decryption key after processing an update, then even just by *processing* an update, we get an additional  guarantee:
>>>>> - (FS’) if member A processes an update in epoch N (moving the epoch to N+1), and if A gets compromised in epoch N+1, the messages sent in epoch N remain secret
>>>>> It is also worth remembering that Signal also has a notion of one-time prekeys that work similarly for new messaging sessions.
>>>>> Although the following would be a bit ridiculous to use in large dynamic groups, here  is a sketch to achieve the receiver FS guarantee without the need for new crypto.
>>>>> - Every time a member A sends an update, it generates fresh node secrets for nodes on the path from A to the root
>>>>> - From each node secret, A generates a large number K (= 100) private-public encryption keypairs and sends the public keys with the update..
>>>>> - On receiving the update, each member B stores all K public keys for each node in its co-path
>>>>> - Each of these public keys can be used only once for sending an update, after which the private key is deleted from all recipients.
>>>>> - The last public key at each node is not deleted; it can only be replaced when one of the members under that node sends a new update (with a fresh batch of public keys)..
>>>>> As far as I understand, the above scheme can be seen as an (inefficient) implementation of UPKE, right?
>>>>> Of course, it increases the size of each update by K, and only provides FS for K updates, after which some member has to send an update.
>>>>> Conversely, it does not require any new crypto algorithm. Is this a good baseline to compare UPKE schemes against?
>>>>> If I am mis-reading something, do let me know!
>>>>> -Karthik
>>>>>> On 17 Oct 2019, at 17:18, Joel Alwen <> wrote:
>>>>>> I think the challenge with the hash-forward approach is how to do that
>>>>>> homomorphically. I.e. what we need are two algorithms; one to refresh
>>>>>> the PK without knowing the SK (but possibly knowing a secret
>>>>>> rerandomizer delta if needed) and one to update SK (again possibly using
>>>>>> delta). So to use a hash-forward approach their must be:
>>>>>> 1) a way to evolve PK forward to PK' and
>>>>>> 2) a *one-way* method to evolve SK forward to SK' compatible PK'.
>>>>>> One-wayness is what gives us Forward Secrecy and "compatibility" between
>>>>>> the two key evolution methods is what allows for asynchronous (i.e. 1
>>>>>> packet) updates.
>>>>>> Currently we use a secret re-randomizer delta to ensure the SK update
>>>>>> method is one-way. That is, without the delta you cant "undo" the
>>>>>> update. But that would break if we (at least naively) used some public
>>>>>> delta, say hash(ciphertext). So I think this is the challenge that we'd
>>>>>> have to overcome.. Basically, make sure we SK evolution is one-way but
>>>>>> also compatible the public evolution of PK.
>>>>>> Now one way sweet way to get all this (and more) would be to use a HIBE.
>>>>>> Initial, PK for a ratchet tree node (i.e. its "identity" since this is a
>>>>>> HIBE now) is simply the empty vector PK := () while the secret key is
>>>>>> the master public key for a fresh HIBE instance SK := MSK. We also
>>>>>> include, as a second component of the nodes PK, the master public key
>>>>>> PK_0 = MPK. To "hash forward" / "re-randomize" when sending a ciphertext
>>>>>> C to that node we can do:
>>>>>> PK' := (PK, hash(C)).
>>>>>> SK' := DeriveHIBEKey(PK, SK).
>>>>>> So simply append hash(C) to the identity for that node and derive the
>>>>>> corresponding HIBE key.
>>>>>> Ignoring the problems with using HIBE for a second, this is a very cool
>>>>>> solution. We don't need to send out the updated PK since everyone in the
>>>>>> group (and even the adversary) can compute it for themselves. We also
>>>>>> dont need a re-randomize delta as part of the plaintext because we're
>>>>>> using delta := hash(ciphertext) so the plaintext is shorter again.
>>>>>> Moreover, HIBE security means that learning SK' doesn't tell you
>>>>>> anything interesting about SK. In particular, we have forward security.
>>>>>> (In fact, FS will hold even if hash(C) were chosen *completely*
>>>>>> adversarially, say, as part of a malicious update in an insider attack!)
>>>>>> Of course, the problem with this solution is that we're using HIBE.
>>>>>> Worse, with unbounded depth because each new ciphertext sent to a node
>>>>>> results in going one depth further into the hierarchy. AFAIK all HIBE
>>>>>> constructions have pretty horrible (read exponential) efficiency as a
>>>>>> function of their depth. (And I won't mention the state of
>>>>>> standardization and open implementations for HIBE.)
>>>>>> Now there could be a totally different approach that entirly avoids
>>>>>> HIBE. But even with this approach there's at least some glimer of hope
>>>>>> to improve on it because, if we don't wory about insider attacks we can
>>>>>> assume C is honestly generated which means hash(C) really has a ton of
>>>>>> entropy. So we dont seem to need the full expresivity HIBE identities
>>>>>> allow us. Rather we only need HIBE for "random" identities. Still, that
>>>>>> seems like a pretty slim hope for major efficiency improvement. It also
>>>>>> doesn't do anything to address the lack of implementations and standards.
>>>>>> - Joël
>>>>>>> On 17/10/2019 16:37, Karthik Bhargavan wrote:
>>>>>>> Thanks Yevgeniy,
>>>>>>> This helps a lot.
>>>>>>> To further my understanding, another question:
>>>>>>>>  Intuitively, the sender will not only encrypt the message, but also a
>>>>>>>> random Delta value. It will change public key using homomorthism by
>>>>>>>> multiplying with g^Delta (in specific DH based scheme), while the
>>>>>>>> recipient will decrypt Delta (using old secret key), and add it to the
>>>>>>>> old secret key to get there new one. So now corrupting (old sk plus
>>>>>>>> Delta) will not help decrypting the ciphertext just decepted, emailing
>>>>>>>> forward secrecy. 
>>>>>>> I see that in the DH-based scheme, this Delta needs to be private,
>>>>>>> otherwise the adversary can compute sk once it knows sk+Delta.
>>>>>>> But, in general, is it possible to conceive of a UPKE scheme where the
>>>>>>> recipient effectively “hashes forward” its symmetric key,
>>>>>>> where this one way hash-forward function does not have to rely on an
>>>>>>> externally chosen secret value?
>>>>>>> Best,
>>>>>>> Karthik
>>>>>>>> This is the high level, hope it makes sense.
>>>>>>>> Thanks for your question,
>>>>>>>> Yevgeniy
>>>>>>>> On Thu, Oct 17, 2019, 1:43 AM Karthik Bhargavan
>>>>>>>> <
>>>>>>>> <>> wrote:
>>>>>>>>    Hi Joel,
>>>>>>>>    This looks very interesting. It is new to me since I was not at
>>>>>>>>    the interim.
>>>>>>>>    After reading the paper and the slides, I am still a bit fuzzy
>>>>>>>>    about what the recipient of an update needs to do.
>>>>>>>>    For example, for the running example in your slide deck, it would
>>>>>>>>    help if I could see:
>>>>>>>>    - what secret keys does each leaf need to keep
>>>>>>>>    - how do these secrets change when an update from some other node
>>>>>>>>    is received.
>>>>>>>>    Just working this out for one update is enough.
>>>>>>>>    I know that this is made precise in the eprint, but it would be
>>>>>>>>    faster if you could help us understand it :)
>>>>>>>>    Best,
>>>>>>>>    Karthik
>>>>>>>>>> On 16 Oct 2019, at 23:51, Joel Alwen <
>>>>>>>>>    <>> wrote:
>>>>>>>>> <FS-TreeKEM.pdf>
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