Re: [MLS] Adapting Hierarchical Key Derivation for Ephemeral Signatures in MLS

[Brendan McMillion <[e-mail]>]

There is the base scheme which has the following properties:
Constant-size public key, private key and signature of size approx 2*log(T).
Stateless verification.
Not post-compromise secure; can handle minor state regression.

You can make these modifications to it:
Require verifiers to verify signatures strictly one-after-the-other and update their understanding of the public key.
Require signers to certify the signing key for epoch N with the signing key from epoch N-1, regardless of the tree structure.
to get a construction with these properties:
Public key and private key of size approx 2*log(T), constant-size signature.
Stateful verification.
Post-compromise secure; state regression will lock the user out.

> On Nov 5, 2018, at 2:48 AM, Nick Sullivan <nick=[e-mail]> wrote:
> 
> Brendan,
> 
> Does verifying these derived keys that are deeper down the tree require knowledge of the public keys up the tree? Are these keys included in the messages (implying a log(depth) increase in message size) or can they be compressed somehow or are they distributed in some other manner?
> 
> Nick
> 
> On Tue, Oct 16, 2018 at 7:03 AM Brendan McMillion <brendan=[e-mail] <mailto:[e-mail]..org>> wrote:
> > We'd need to know the number of epochs we're allowing for this MLS session in advance.
> 
> I’d link the paper if I could find it, but there’s a tree construction that allows an unbounded number of intervals and fast setup. The root key would sign only two children: a left child which is the root of a tree of height 1 whose leaf(s) are used for signing data, and a right child. Once the left child is used up, the right child signs two children in the same way the root key did, but now the left child is the root of a tree of height 2. Every time you have to use the right-most node, the left child gets twice as large. Here’s a diagram, if the description isn’t clear: https://i.imgur.com/DosZ3Sf.png <https://i.imgur.com/DosZ3Sf.png>
> 
> So the signer’s private key and signatures are proportional to log(T), the current epoch count.
> > We're simply trying to limit the impact of device compromise. We're able to do this more easily for encryption keys, but signatures are more tricky.
> 
> I agree it's valuable that if participant A is offline for a long time and B’s key is compromised at epoch n, then when A comes back online she can still trust everything signed by B in previous epochs. I think you can also get something similar to post-compromise security with the above construction: Once B is no longer compromised, he would continue walking the tree and generating new keypairs where the attacker doesn’t know the private keys. So to sign a message, the attacker would need to certify their own keypairs. This can be prevented by all the group participants refusing to accept more than one distinct public key per node in the tree.
> 
> On Fri, Oct 12, 2018 at 10:45 PM Nadim Kobeissi <[e-mail]> wrote:
> Dear Brendan,
> Your proposed scheme could work, too. The disadvantages it presents, it seems to me, aren't severe:
> Your proposed scheme seems to have a larger performance overhead: each leaf keypair/epoch tuple would have to be generated and signed in advance.
> We'd need to know the number of epochs we're allowing for this MLS session in advance.
> We may not be able to parametrize the choice of upcoming signature keys based on a dynamically generated epoch identifier with the same degree of freedom that HKD would give us.
> > Also, since I didn’t go to the interim, what problem do forward-signature signature schemes solve for MLS?
> 
> We're simply trying to limit the impact of device compromise. We're able to do this more easily for encryption keys, but signatures are more tricky.
> 
> Nadim Kobeissi
> Symbolic Software • https://symbolic.software <https://symbolic..software/>
> Sent from office
> 
> 
> On Sat, Oct 13, 2018 at 2:43 AM Brendan McMillion <[e-mail] <mailto:[e-mail]>> wrote:
> Hey Nadim
> 
> I believe the typical way to build a forward-secure signature scheme is with a certification tree. You’d:
> 
> 1. Generate a root keypair.
> 2. Generate N leaf keypairs.
> 3. Sign each leaf keypair and the epoch it is meant to be used in, with the root keypair.
> 4. Delete the root private key.
> 
> Your root public key is what’s distributed to everybody. A signature at a given epoch is the tuple: (leaf public key, sig over leaf key from root key, sig over data from leaf key).
> 
> Could you talk about why a scheme like the above is not suitable here? Also, since I didn’t go to the interim, what problem do forward-signature signature schemes solve for MLS?
> 
>> On Oct 12, 2018, at 1:22 PM, Nadim Kobeissi <[e-mail] <mailto:[e-mail]>> wrote:
>> 
>> Dear Ted,
>> Thanks for your quick read-through!
>> 
>> You seem to be referring to [1], not to [2] as you wrote. In [1], the concept of "hardened" keys is defined and is also ported by [2] into Ed25519.
>> 
>> > What I think that means is that if an attacker ever gets access to both an extended public key and any extended private key, we have lost forward secrecy for all the MLS communications covered by any keys derived from any of the epoch pairs.  Is that correct?
>> 
>> This is correct in the sense that it allows you to rewind the key derivation chain. However, this does not apply to hardened keys. This is precisely why I'm trying to understand how epoch identifiers are agreed upon, in order to see whether we can use them to restrict the HKD logic to use only "hardened" keys in MLS. Since hardened keys in [2] cannot themselves have children, it becomes important to understand whether we can select enough of them for an HKD design in MLS to have a meaningful impact, and how this selection/potential caching of hardened keys would work.
>> 
>> > [...] means that Alice must refrain from ever using the parent extended public key has a signing key, but must instantiate signing keys from the n + 0 epoch.  
>> 
>> This could also be a solution, I suppose, but it sounds like it would result in weaker "signing forward secrecy" (or whatever we're calling this property) than focusing on hardened keys, although I'm frankly not sure off the top of my head.
>> 
>> Nadim Kobeissi
>> Symbolic Software • https://symbolic.software <https://symbolic.software/>
>> Sent from office
>> 
>> 
>> On Fri, Oct 12, 2018 at 10:03 PM Ted Hardie <[e-mail] <mailto:[e-mail]>> wrote:
>> Hi Nadim,
>> 
>> I suspect I'm missing something simple here in your proposal.  According to your reference 2, one of the issues with the derivation of this type of hierarchical key is:
>> 
>>  that knowledge of a parent extended public key plus any non-hardened private key descending from it is equivalent to knowing the parent extended private key (and thus every private and public key descending from it). This means that extended public keys must be treated more carefully than regular public keys. It is also the reason for the existence of hardened keys, and why they are used for the account level in the tree. This way, a leak of account-specific (or below) private key never risks compromising the master or other accounts.
>> 
>> What I think that means is that if an attacker ever gets access to both an extended public key and any extended private key, we have lost forward secrecy for all the MLS communications covered by any keys derived from any of the epoch pairs.  Is that correct?
>> 
>> This appears to make handling required of the parent extended public key roughly equivalent to the handling of a private key, so that your step:
>> 
>> Alice sends a public signing key to Bob during epoch n.
>> 
>> means that Alice must refrain from ever using the parent extended public key has a signing key, but must instantiate signing keys from the n + 0 epoch.  
>> 
>> Is that a correct understanding?
>> 
>> Thanks,
>> 
>> Ted
>> 
>> 
>> On Fri, Oct 12, 2018 at 12:47 PM Nadim Kobeissi <[e-mail] <mailto:[e-mail]>> wrote:
>> Hello everyone,
>> 
>> I've been working on adapting Hierarchical Key Derivation (HKD) in order to obtain some kind of ephemeral signatures that may be useful in MLS. I've arrived at a point where I'm optimistic that this is a direction worth pursuing and might indeed be a solution to this problem.
>> 
>> HKD was at some point a candidate for how signature keys are managed per epoch in the Tor Hidden Service design [0]. HKD logic has also been implemented in Bitcoin wallets for a while now [1]. HKD constructions can be also derived from existing popular fast signature algorithms such as Ed25519 with minimal changes [2], making them an easy fit for MLS. Very simply, the functionality that HKD signature schemes bring to MLS is the following:
>> Alice sends a public signing key to Bob during epoch n.
>> At the onset of epoch n+1, Bob is able to immediately calculate Alice's public signing key for epoch n+1 based purely on his knowledge of Alice's public signing key for epoch 0. Alice doesn't need to send new signing key information to Bob.
>> At this point, Bob can delete Alice's public signing key for epoch n.
>> More importantly, Alice herself can delete Alice's private signing key for epoch n, keeping only her private signing key for epoch n+1.
>> The way that this could work in MLS would be heavily based on HDKeys-Ed25519 [2]. I'll resist paraphrasing the paper, and instead will point out the relevant sections (which are short, well-written and worth reading:)
>> Section 2 describes the original concept as used for Bitcoin wallet derivation.
>> Section 4 describes the modifications to Ed25519 to enable HKD constructions.
>> Section 5 describes how private and public child keys are generated (Fig. 1 is also helpful.)
>> My questions:
>> How are we deriving epoch identifiers? Are they simply counters, or each epoch identified by a nonce that's communicated confidentially? If you read [2], you'll see why this can be important.
>> Performance impact seems to be negligible for Montgomery-based signing primitives, but I'm interested in more insight on this.
>> Is anyone else interested in having a standard HDKeys-Ed25519 implementation? I've been working on one in JavaScript and plan to eventually also write one in Go. Perhaps Richard would like to help with a C++ version?
>> I'm also interested in hearing your thoughts on this generally.
>> During the interim meeting (as well as before it), it was frequently discussed how ephemeral signatures may be useful for MLS. This also appears to be slated as a discussion topic for IETF 103, so it would be great if we could continue the discussion there as well. 
>> 
>> References:
>> [0] https://gitweb.torproject.org/torspec.git/tree/proposals/224-rend-spec-ng.txt#n1979 <https://gitweb.torproject.org/torspec.git/tree/proposals/224-rend-spec-ng.txt#n1979>
>> [1] https://github.com/bitcoin/bips/blob/master/bip-0032.mediawiki <https://github.com/bitcoin/bips/blob/master/bip-0032.mediawiki>
>> [2] https://cardanolaunch.com/assets/Ed25519_BIP.pdf <https://cardanolaunch.com/assets/Ed25519_BIP.pdf>
>> 
>> Nadim Kobeissi
>> Symbolic Software • https://symbolic.software <https://symbolic.software/>
>> Sent from office
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