Re: [MLS] KDF instead of hashing up the tree
Konrad Kohbrok <konrad.kohbrok@datashrine.de> Wed, 06 February 2019 10:07 UTC
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From: Konrad Kohbrok <konrad.kohbrok@datashrine.de>
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Subject: Re: [MLS] KDF instead of hashing up the tree
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A question I ran into while working on the PR: Currently, there is the notion of "Derive-Key-Pair" function that produces a key pair from an octet string. Do we want to keep that function for modularity/composability purposes at the possible price of an additional KDF expand operation per key derivation? This is probably just a formal detail, but I wasn't quite sure what the best way forward would be. The options as I see them are as follows: Consider a node A that wants to update its secret. Option 1, derive the private KEM key directly, no Derive-Key-Pair function. Instead a Derive-Public-Key function: x_a <-$- {0,1}^n // This is A's new secret octet string a <-- KDF(x_a,"kem_key") // This is A's private KEM-key A <-- Derive-Public-Key(a) // This is A's public KEM-key x_b <-- KDF(x_a,"parent_secret") // This is B's new secret octet string b <-- KDF(x_b,"kem_key") // This is B's new private KEM-key B <-- Derive-Public-Key(b) // This is B's public KEM-key Option 2, stick with a Derive-Key-Pair function, but add additional KDF expand to ensure key separation: x_a <-$- {0,1}^n // This is B's new seed octet string x_a' <-- KDF(x_a,"secret_seed") // This is A's new secret octet string (a,A) <-- Derive-Key-Pair(x_a') // This is A's new private/public key pair x_b <-- KDF(x_a,"parent_secret") // This is B's new seed octet string x_b' <-- KDF(x_b,"secret_seed") // This is B's new secret octet string (b,A) <-- Derive-Key-Pair(x_b) // This is B's new private/public key pair Option 3, use Derive-Key-Pair function directly on seed. This would add the requirement to the Derive-Key-Pair notion, that it (internally) uses a KDF to derive the private key. x_a <-$- {0,1}^n (a,A) <-- Derive-Key-Pair(x_a) // This is A's new private/public key pair x_b <-- KDF(x_a,"parent_secret") // This is B's new secret octet string (b,B) <-- Derive-Key-Pair(x_b) // This is B's new private/public key pair My guess is that in most cases the Derive-Key-Pair function will in the end call a KDF to get the private key anyway, which means that we have one superfluous KDF expand operation. Konrad On 23/01/2019 17:47, Richard Barnes wrote: > Ah, ok, I get it. I misunderstood "new secret" as "fresh entropy". > > In that case, this falls into the "sure, if it makes the analysis better" > bucket. We've been treating hashes/HKDF invocations as basically free. At some > point we might need to worry about that, but I suspect that today is not that day. > > Want to make a PR? > > --Richard > > > On Wed, Jan 23, 2019 at 10:19 AM Konrad Kohbrok <konrad.kohbrok@datashrine.de > <mailto:konrad.kohbrok@datashrine.de>> wrote: > > Exactly, thanks Karthik! > > Say we have the same tree as in the example in 5.4: > > G > / \ > / \ > E _ > / \ / \ > A B C D > > Then A generates a fresh secret X_1secret and derives the following new secrets: > X_1kemkey=HKDF(X_1secret,"kemkey") > X_2secret=HKDF(X_1secret,"parent") > > X_2kemkey=HKDF(X_2secret,"kemkey") > X_3secret=HKDF(X_2secret,"parent") > > X_3kemkey=HKDF(X_3secret,"kemkey") > > A then sends E(pk(B), X_2secret) to B, E(pk(C),X_3secret) to C and > E(pk(D),X_3secret) to D. > > Hopefully that makes the idea a little clearer. Sorry for the terrible notation. > > Konrad > > On 23/01/2019 16:59, Karthikeyan Bhargavan wrote: > > If I understand correctly, Chris and Konrad are not suggesting changing > the secrets. > > Instead, they are suggesting that H(.) be implemented as something like: > > > > H(x) = HKDF(x,label=”parent”) > > > > where x is the tree secret for the current node. > > > > Similarly, when generating the KEM private key for a node, we use > > > > KGEN(x) = HKDF(x,label=“kem key”) > > > > This would be a good way of making sure that each key in the protocol is > > independent, but at no additional cost. > > Am I understanding this correctly, Konrad? > > > >> On 23 Jan 2019, at 15:29, Richard Barnes <rlb@ipv.sx <mailto:rlb@ipv.sx > <mailto:rlb@ipv.sx>>> wrote: > >> > >> Note this is a little bit expensive in terms of message size; it changes the > >> size of an update from log(N) to log(N)^2. It does not change the number of > >> DH operations > >> > >> This is because you have to send the fresh secret for each intermediate node > >> in the tree to all its descendants. Comparing the secrets you generate in > >> each case, from leaf to root, along a path of depth 3 with S0 at the leaf: > >> > >> Current: S0, S1 = H(S0), S2 = H^2(S0), S3 = H^3(S0) > >> Proposed: S0, S1 = KDF(T0, S0), S2 = KDF(T1, S1), S3 = KDF(T2, S2) > >> > >> Where T* are the fresh secrets called for here. This doesn't change to whom > >> you encrypt things, but changes what you encrypt to each copath node: > >> > >> Current -> Proposed > >> S1 -> S1, T1, T2 > >> S2 -> S2, T2 > >> S3 -> S3 > >> > >> (This is of course because you need to enable each recipient to compute > up the > >> tree.) So there's your log->log^2. > >> > >> This discussion is not to say that I'm opposed to this idea. It just looks > >> like it has some non-negligible cost, so we should make sure we know what > >> we're getting for that cost. > >> > >> --Ricahrd > >> > >> > >> > >> On Wed, Jan 23, 2019 at 8:58 AM Konrad Kohbrok <konrad.kohbrok@datashrine..de > >> <mailto:konrad.kohbrok@datashrine.de > <mailto:konrad.kohbrok@datashrine.de>>> wrote: > >> > >> Hey everyone, > >> > >> I just discussed the current draft with my advisor Chris Brzuska and he > >> came up > >> with a suggestion that I thought I'd just quickly relay here. As I > have only > >> started following the discussion recently, I apologize if this was > already > >> brought up in the past. > >> > >> In terms of key separation, wouldn't it make for a cleaner design, if we > >> used a > >> KDF instead of a hash function? Instead of generating a new > leaf-node secret > >> and then hashing it to compute the new secret for the parent node, it > would be > >> better to generate a new secret and then from that secret > independently (i.e. > >> with different labels) compute the new leaf secret and the new secret > for the > >> parent node. This key independence would also make the proof easier. In > >> terms of > >> overhead, this would mean two KDF operations instead of one hashing > operation. > >> > >> Cheers, > >> Konrad > >> > >> _______________________________________________ > >> MLS mailing list > >> MLS@ietf.org <mailto:MLS@ietf.org> <mailto:MLS@ietf.org > <mailto:MLS@ietf.org>> > >> https://www.ietf.org/mailman/listinfo/mls > >> > >> _______________________________________________ > >> MLS mailing list > >> MLS@ietf.org <mailto:MLS@ietf.org> <mailto: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] KDF instead of hashing up the tree Konrad Kohbrok
- Re: [MLS] KDF instead of hashing up the tree Richard Barnes
- Re: [MLS] KDF instead of hashing up the tree Karthikeyan Bhargavan
- Re: [MLS] KDF instead of hashing up the tree Konrad Kohbrok
- Re: [MLS] KDF instead of hashing up the tree Richard Barnes
- Re: [MLS] KDF instead of hashing up the tree Konrad Kohbrok
- Re: [MLS] KDF instead of hashing up the tree Konrad Kohbrok
- Re: [MLS] KDF instead of hashing up the tree Benjamin Beurdouche
- Re: [MLS] KDF instead of hashing up the tree Konrad Kohbrok
- Re: [MLS] KDF instead of hashing up the tree Konrad Kohbrok
- Re: [MLS] KDF instead of hashing up the tree Benjamin Beurdouche