Re: [MLS] Key Schedule: Replace DPRF with multi-input PRF (NPRF)

[Chris Brzuska <[e-mail]>]

I see, thanks for clarifying. Obviously, with these requirements, pull 
request #336 does not work as is. I think that the conceptual issue of 
how to best combine two, three keys and more keys, remains, now with an 
additional requirement to combine two keys separately first.

Will think about it, thanks for clarifying the requirements!

Chris

On 24/07/2020 21:47, Richard Barnes wrote:
> Your confusion is understandable -- the document is wrong right now!  
> You are correct that the current design prohibits new joiners from 
> participating in the PSK proof, but that's a bug, not a feature.  The 
> epoch secret should verify that *all members of the current epoch* 
> know the PSK, not just the ones inherited from the last epoch.
>
> That's why #362 rearranges the key schedule as follows:
>
> init_secret_[n-1] (or 0)
>                         |
>                         V
>    commit_secret -> HKDF-Extract = joiner_secret
>                         |
>                         +--> Derive-Secret(., "welcome")
>                         |    = welcome_secret
>                         |
>                         V
>       PSK (or 0) -> HKDF-Extract = member_secret
>                         |
>                         V
> GroupContext_[n] -> HKDF-Extract = epoch_secret
>
> (I also promoted the GroupContext to the main key schedule.)  That's 
> the context for my earlier comments.  With that picture, the only 
> thing you're coalescing with nPRF would be the latter two HKDF-Extract 
> calls.
>
> Hope that helps,
> --Richard
>
>
>
> On Fri, Jul 24, 2020 at 2:32 PM Chris Brzuska <[e-mail] 
> <mailto:[e-mail]>> wrote:
>
>     Hey Richard,
>
>     thank you for looking into this. I think, I need more explanation
>     to understand the following point:
>
>     >>>  You can't add the commit secret and PSKs in the same
>     operation, because you want new joiners to put in the PSK, but you
>     don't want them to have to know the commit secret.
>
>     The current draft sais the following about the PSK:
>     "Groups which already have an out-of-band mechanism to generate
>     *shared* group secrets can inject those in the MLS key schedule to
>     seed the MLS group secrets computations by this external entropy.
>     At any epoch, including the initial state, an application can
>     decide to synchronize the injection of a PSK into the MLS key
>     schedule. This mechanism can be used to improve security in the
>     cases where having a full run of updates across members is too
>     expensive or in the case where the external group key
>     establishment mechanism provides stronger security against
>     classical or quantum adversaries."
>
>     As I understand this paragraph, the PSK is known by all group
>     members and not related to new joiners. Maybe, the requirements
>     and/or design changed in the meanwhile, and I am not aware of it.
>     I interpreted the paragraph this way, since the current
>     construction (posted below for convenience) also requires to know
>     the commit_secret to derive the epoch_secret (from which the
>     welcome_secret is derived). Where did I go wrong?
>
>     Thanks!
>
>     Chris
>
>                     init_secret_[n-1] (or 0)
>                           |
>                           V
>          PSK (or 0) -> HKDF-Extract = early_secret
>                           |
>                     Derive-Secret(., "derived", "")
>                           |
>                           V
>     commit_secret -> HKDF-Extract = epoch_secret
>
>
>     On 24/07/2020 20:53, Richard Barnes wrote:
>>     Hey Chris,
>>
>>     I was looking again at the key schedule as I was drafting #362
>>     [1].  A couple of things occurred to me:
>>
>>     1. You can't add the commit secret and PSKs in the same
>>     operation, because you want new joiners to put in the PSK, but
>>     you don't want them to have to know the commit secret.
>>
>>     2. The nPRF construction you propose has the same number of HMAC
>>     invocations as the chained-HKDF-Extract stuff that's in the
>>     current draft / 362.
>>
>>     Given those observations, I wonder how much an nPRF is really
>>     buying us.  It's not saving us any HMAC calls, and relative to
>>     #362, it would only coalesce two DPRF calls into one nPRF call.
>>
>>     Maybe there's some benefit if there are multiple PSKs?  But even
>>     then, it seems like you could add a layer, computing a synthetic
>>     PSK from the multiple ones, and keeping the main key schedule simple.
>>
>>     At this point, given the above and the novelty of the nPRF
>>     construction, I'm inclined to just stick with HKDF and merge #362
>>     instead of #336.
>>
>>     --Richard
>>
>>
>>     [1] https://github.com/mlswg/mls-protocol/pull/362
>>
>>     On Tue, Jul 7, 2020 at 5:30 AM Chris Brzuska
>>     <[e-mail] <mailto:[e-mail]>> wrote:
>>
>>         Thank you for the pointer to Carter-Wegman MACs.
>>
>>         >>> This style of combing hash outputs does affect collision
>>         resistance [4], and some discussion on relation to that would
>>         be nice to see.
>>
>>         That's an excellent point. In addition to pseudorandomness,
>>         we prove the collision-resistance of our construction. I.e.,
>>         assuming that no unique value is used twice and assuming that
>>         HMAC is collision-resistance, then the final Expand operation
>>         guarantees unique outputs. I.e., by including the unique
>>         value into the final Expand operation after the xor, the
>>         construction recovers from any collisions incurred by the xor.
>>
>>         Chris
>>
>>         On 07/07/2020 05:41, Hale, Britta (CIV) wrote:
>>>
>>>         This is an interesting proposal. It is closely related at a
>>>         high level to Carter-Wegman MACs (i.e. for random seed r,
>>>         MAC((k1, k2), m) =  PRF(k1, r) XOR MAC(k2, m)). Quite a few
>>>         MACs fall into this category in practice. Considering the
>>>         use of a MAC-based KDF and the proofs of [3] on DPRFs, there
>>>         is an overlap between NPRFs and extrapolation of the above
>>>         (based on iteration of the PRF guarantees).
>>>
>>>         This is worth noting from an assurance standpoint: there was
>>>         discussion at the virtual interims with respect to the
>>>         current formulation of MLS key derivation, which has a “TLS
>>>         precedence”, yet this proposal is not without precedence
>>>         itself. Ergo, such a change should not necessarily be
>>>         concerning based on differing from current practice.
>>>
>>>         This style of combing hash outputs does affect collision
>>>         resistance [4], and some discussion on relation to that
>>>         would be nice to see.
>>>
>>>         Britta
>>>
>>>         [1] Carter, Wegman. Universal classes of hash functions.
>>>
>>>         [2] Carter, Wegman. New hash functions and their use in
>>>         authentication and set equality.
>>>
>>>         [3] Bellare and Lysyanskaya. Symmetric and Dual PRFs from
>>>         Standard Assumptions: A Generic Validation of an HMAC
>>>         Assumption.
>>>
>>>         [4] Bernstein. What output size resists collisions in a xor
>>>         of independent expansions?
>>>
>>>         *From: *MLS <[e-mail]>
>>>         <mailto:[e-mail]> on behalf of Chris Brzuska
>>>         <[e-mail]> <mailto:[e-mail]>
>>>         *Date: *Tuesday, June 9, 2020 at 10:32 AM
>>>         *To: *"[e-mail]" <mailto:[e-mail]> <[e-mail]>
>>>         <mailto:[e-mail]>
>>>         *Subject: *[MLS] Key Schedule: Replace DPRF with multi-input
>>>         PRF (NPRF)
>>>
>>>         Hi all,
>>>
>>>         I would like to open a discussion on a suggestion for a
>>>         change in the key schedule. In the current draft, we use the
>>>         Extract function twice as a dual pseudorandom function
>>>         (DPRF) when combining 3 keys (*) and interleave them with an
>>>         Expand call.
>>>
>>>         The suggestion [1] is to replace these 3 calls by a
>>>         multi-input PRF (NPRF) which is especially designed to
>>>         return a pseudorandom key when at least one of the input
>>>         keys is pseudorandom. The new suggestion relies on standard
>>>         PRF security rather than DPRF-security of Extract.
>>>
>>>         You can find the accompanying paper with pictures,
>>>         discussion and security reduction for the design principle
>>>         here [2]. I include a summary of the main points in the end
>>>         of this eMail.
>>>
>>>         Please comment/share your opinion. Thanks!
>>>
>>>         Chris
>>>
>>>         (*) commit_secret, PSK and init_secret
>>>
>>>         [1] Pull
>>>         Request:https://github.com/mlswg/mls-protocol/pull/337
>>>         <https://github.com/mlswg/mls-protocol/pull/337>
>>>
>>>         [2] Paper: http://chrisbrzuska.de/2020-NPRF.html
>>>
>>>         *--------------------------------------------------------------------------------------------------------------------*
>>>
>>>         *Summary of main points:*
>>>
>>>         The current key schedule
>>>         - uses Extract as a dual pseudorandom function and assumes
>>>         that HMAC is a dual pseudorandom function
>>>         - applies Extract after Expand, i.e., after applying a
>>>         function which generates a pseudorandom value
>>>         - iterates Extract-then-Expand sequentially to combine more
>>>         than 2 keys
>>>
>>>         The pull request suggests to
>>>         - replace the ad-hoc assumption that Extract is a dual
>>>         pseudorandom function
>>>         - remove Extract steps when applied after Expand
>>>         - use a provably secure NPRF construction which allows to
>>>         combine more than 2 keys and is based on a standard PRF
>>>         assumption and statistical properties of xor.
>>>
>>>         Efficiency:
>>>         - The suggested construction has higher parallel efficiency.
>>>         It increases the overall number of HMAC evaluations by 1.
>>>
>>>         Assumptions:
>>>         - HMAC is a standard PRF.
>>>         - Relies on a unique value, the group_context was suggested.
>>>
>>>         Construction:
>>>         (1) Use unique value to expand each key and xor the result
>>>         (2) expand resulting key, including unique value into the
>>>         context again
>>>
>>>         Security argument:
>>>         - Pseudorandomness: unique value ensures that each outcome
>>>         of Expand in (1) is used only once in a xor combination,
>>>         thus allowing on one-time pad argument of xor.
>>>         - Uniqueness of resulting keys: (2) ensures that if HMAC is
>>>         collision-resistent, then the result is collision-resistent.
>>>
>>>         Variants:
>>>         - It is possible to use an NPRF variant called NameNPRF [2]
>>>         which has 3 HMAC evaluations more and relies less on the
>>>         unique value. I.e., NameNPRF is secure in the same scenarios
>>>         as DPRF: Keys only repeat if the input keys repeat *and* the
>>>         group context repeats.
>>>
>>>         Questions/Comments that came up:
>>>         - Barnes, MacMillion suggested group_context as unique value
>>>         - MacMillion wondered about removal of Extract: One can add
>>>         an extract operation for the psk. For other input keys, it
>>>         does not seem needed, since they were returned from Expand.
>>>         - Wood: Can we replace HMAC by arbitrary PRF? Yes. For
>>>         uniqueness of output keys, the PRF needs to be
>>>         collision-resistant, too.
>>>
>>>
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