Re: [TLS] OPTLS: Signature-less TLS 1.3

Hugo Krawczyk <> Sun, 02 November 2014 22:05 UTC

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From: Hugo Krawczyk <>
Date: Mon, 03 Nov 2014 00:05:02 +0200
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To: Eric Rescorla <>
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Subject: Re: [TLS] OPTLS: Signature-less TLS 1.3
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These are good questions as they point to some of the choices we need to
consider before defining the actual key derivation mechanisms in the
Below are some responses.

On Sat, Nov 1, 2014 at 3:44 AM, Eric Rescorla <> wrote:

> Hugo,
> Thanks for writing this up. I'm still digesting this, but I had a few
> questions.
> 1. In the interim, I believe you suggested MAC of the transcript under
> g^{xs} to authenticate g^y. This is fairly analogous to CertificateVerify,
> except using a MAC rather than a signature. In the current design, you
> instead generate a combined key from g^{xs] and g^{xy}. Are there
> advantages to this design or is it just a matter of style?

​Your understanding of the MAC (in the Finished message) as replacing the
functionality of the signature in CertificateVerify is correct. Also
correct is
that we could use g^{xs} for such authentication and derive the session
directly from g^{xy}. On the other hand, deriving the key from both g^{xs}
g^{xy} has the advantage that an attacker that learns the ephemeral
exponent y
cannot compute the session key; for that it needs to find both y and s.
It also has the property that you get (implicit) authentication even
without the
ServerFinished message but this is not too significant in our case given
that we
mandate the Finished message.

One additional consideration in chosing the key derivation is the number of
exponentiations it requires. One could actually combine g^{xs] and g^{xy}
without requiring two exponentiations by using a HMQV-like key derivation.
However, this does not apply to our case where you either need to explicitly
compute g^{xs} (for encrypting ClientData in the 0-RTT case) or explicitly
compute g^{xy} (for encrypting ServerCertificate in the 1-RTT case).

> 2. I'm thinking about how to adapt this to PSK+PFS modes (i.e.,
> where you want the PSK for authentication but you want to do
> a DHE exchange for PFS). In the design you propose, it seems
> like the analogous thing to do would be to treat the PSK like
> g^{xy}? Does this interact at all with whether to mix the keys
> or use a MAC?

​Indeed, this is one of the conceptual advantages of this design.
You can replace g^{xs} (not g^{xy}) with the PSK shared between client and
server. It is not hard to define the authentication and key derivation
mechanisms so that they apply equally to the non-PSK and PSK settings.

> 3. WRT client auth, I think we've generally decided that the client's
> certificate ought to be encrypted. Given that, I wonder if it would be
> easier
> for the client to just do a digital signature over the transcript and/or
> an authenticator derived from the secret. Generally, the additional
> cost of the RSA signature isn't a huge problem for most clients and
> those which do should be able to quickly move to EC-based keys.
​I don't see the advantage of signatures in this case. It is possible to
design a
hybrid protocol with signature authentication at the client side and static
at the server but I wouldn't do that without a clear advantage over the more
uniform approach using static DH on both sides. In any case, doing static
DH at
the client should not be a problem, it is already doing it to authenticate
server and compute keys.


> Thanks,
> -Ekr
> On Fri, Oct 31, 2014 at 5:54 PM, Hugo Krawczyk <>
> wrote:
>> During the TLS interim meeting of last week (Oct 22 2014) I suggested
>> that TLS
>> 1.3 should abandon signature-based authentication (other than for
>> certificates)
>> and be based solely on a combination of ephemeral Diffie-Hellman for PFS
>> and
>> static Diffie-Hellman for authentication. This has multiple benefits
>> including
>> major performance gain (by replacing the per-handshake RSA signature by
>> the
>> server with a much cheaper elliptic curve exponentiation), compatibility
>> with
>> the mechanisms required for forward secrecy, natural accommodation of a
>> 0-RTT
>> option, and a simple extension without signatures for client
>> authentication.
>> Below I present a schematic representation of the proposed protocol
>> referred
>> to as OPTLS where OPT stands for OPTimized and/or for One-Point-Three.
>> The presentation is sketchy and omits the exact procedure for key
>> derivation.
>> The latter is a crucial component for the security of the protocol, but
>> before getting into these details we want to get a sense of whether the
>> WG is
>> interested in this approach. In the meantime, Hoeteck Wee and myself are
>> working on the details of the protocol and the security proof.
>> We describe a setting with optional 0-RTT and server-only authentication.
>> Client authentication can be added as a further option or as an extension
>> (similar to the current 1.3 proposal) - see below.
>> [K] symbols represent pointers to key material whose exact derivation is
>> not
>> included here except for specifying the basic DH values from which the
>> key is
>> derived (actual derivation will include further information similar to the
>> extended hash mechanisms or SessionHash proposal considered for 1.3).
>> Asterisks represent optional fields that the WG can decide to leave as
>> optional,
>> mandatory, or simply remove without changing the core cryptographic
>> security of
>> the protocol. All references to encryption mean "authenticated encryption"
>> using the encrypt-then-mac paradigm (or any other secure AEAD
>> mechanism).
>> KeyShare's represent ephemeral Diffie-Hellman values exchanged by the
>> parties.
>> All the public key and Diffie-Hellman operations are assumed to happen
>> over a
>> cyclic group with generator g of order q (typically implemented by an
>> elliptic
>> curve group). We use multiplicative notation where ^ denotes
>> exponentiation as
>> in g^x, g^{xy} (here xy denotes multiplication of the scalars x and y),
>> etc.
>> Omitted from the current high level description is a mechanism for
>> testing group
>> membership of DH values or cofactor exponentiation (the specific mechanism
>> depends on the group type and is typically very efficient for elliptic
>> curves).
>> The server has a long term private-public key pair denoted by (s,g^s)
>> where
>> s is uniform random in [0..q-1] (we refer to s and g^s as "static keys").
>> We assume that the server has a certificate that includes the server's
>> public
>> key g^s and a CA-signed binding of this key to the server's identity.
>> We discuss the implementation of such certificates below.
>> ClientHello
>> ClientKeyShare
>> ClientData* [K0]       -------->
>>                                            ServerHello
>>                                            ServerKeyShare
>>                                            ServerCertificate* [K1]
>>                                            ServerFinished [K2]
>>                        <--------           ServerData* [K2]
>> ClientFinished* [K2]   -------->
>>             Protected Application Data [K3]
>>                        <------->
>> 1-RTT CASE:
>> The basic 1-RTT case omits the ClientData* field. It includes a
>> ClientKeyShare
>> g^x and a ServerKeyShare g^y and an optional (encrypted) server
>> certificate.
>> If the certificate is sent (it can be omitted if the client has indicated
>> that
>> it knows the server key as in the case in the 0-RTT scenario) and is
>> encrypted,
>> the encryption key K1 is derived from g^{xy}.
>> Key K2 is an encryption key derived from both g^{xs} and g^{xy}. It is
>> used to
>> authenticate-encrypt the ServerFinished and ClientFinished messages (which
>> include a hash of the previous traffic) and to encrypt data from the
>> server if
>> such data is piggybacked to the second message.
>> Key K3 is the "application key" used to derive key material for
>> protection of
>> application data.  This key material will include (directional)
>> Authenticated
>> Encryption keys and, possibly, keys for derivation of further re-key
>> material.
>> K3 is computed from  both g^{xs} and g^{xy} similarly to K2, but its
>> derivation
>> will be different than K2, e.g., using a separating key expansion
>> technique.
>> The above protocol is compatible with a 0-RTT protocol such as QUIC. In
>> this
>> case, the client is assumed to have information about the server's public
>> key
>> and other security parameters. The server is assumed to have some
>> mechanism in
>> place for detecting replay (e.g., via timestamps, stored client nonces,
>> etc.).
>> The resulting protocol is as described above where the ClientData field
>> is sent
>> encrypted under key K0 derived from g^{xs}.
>> The rest of the protocol is identical to the above.
>> Note: In this case, ServerCertificate is not sent as the client had to
>> know
>> the server's public key before the first message (one can imagine a
>> setting
>> where the server may send a different certificate in the second message -
>> if
>> desired, this can be accommodated too as an option or extension).
>> Client authentication can be supported via an option or extension. It
>> would
>> include a client certificate for a static DH key g^c sent in the third
>> message
>> (the certificate can be encrypted under key K2 to provide client's
>> identity
>> protection). In this case, the key for computing the ClientFinished
>> message and
>> the application key K3 would be derived from a combination of the values
>> g^xy,
>> g^xs, g^yc (and possibly also g^{cs}).
>> Note on Finished messages: The above spec sets ServerFinished as
>> mandatory and
>> ClientFinished as optional. The latter option is needed for a 1-RTT
>> protocol.
>> In principle, both Finished messages could be omitted and still obtain
>> security
>> via implicit authentication (assuming the inputs to key derivation are
>> chosen
>> appropriately). But given the advantages of ServerFinished for providing
>> explicit authentication, key confirmation, and active forward secrecy (see
>> below), it seems advisable to always include it. Including ClientFinished
>> provides key confirmation from client and also explicit client
>> authentication
>> when client certificate is included. ClientFinished also provides
>> Universal
>> Composable (UC) security (this is a result of the Canetti-Krawczyk proof
>> that
>> CK security implies UC security when a client confirmation step is
>> included).
>> Note on certificates: Since in current practice servers hold certificates
>> for
>> RSA signature keys rather than for static DH keys, the certificate field
>> in the
>> above protocol will be implemented by a pair consisting of (i) the
>> server's RSA
>> signature certificate and (ii) the server's signature using this RSA key
>> on the
>> server's static public DH key g^s. The latter signature by the server is
>> performed only when a new static DH key is created (how often this
>> happens and
>> how many such keys are created is completely up to the server - it has the
>> advantage that these keys can be changed often to increase security
>> against
>> leaked keys). This use of RSA also enjoys the high efficiency of RSA
>> verification for the client.
>> The handling of Client certificates would be similar.
>> Note on forward security (a.k.a. as PFS for Perfect Forward Security):
>> PFS is provided by the (mandatory) use of ephemeral Diffie-Hellman keys.
>> The meaning of PFS is that an attacker that finds the (long-term) static
>> private keys of the parties cannot compromise past session keys. Without
>> the
>> ServerFinished message the above protocol ensures forward secrecy against
>> passive attackers (i.e., for sessions where the attacker did not choose
>> g^y).
>> With ServerFinished, PFS holds also against active attackers.  A similar
>> consideration applies to ClientFinished.
>> Client certificates in the first message: We note that in cases where
>> client
>> certificates can be sent in the clear in the first message of the
>> protocol, one
>> can provide PFS and mutual authentication in a 1-RTT at essentially the
>> same
>> cost of an unauthenticated DH exchange (i.e., a cost of little more than
>> two
>> exponentiations). In such a setting one can also obtain mutual
>> authentication in
>> a 0-RTT protocol (with forward secrecy with respect to the client's
>> key).
>> These options, however, require HMQV-like mechanisms and may raise IP
>> issues (this
>> can be investigated further if the WG is interested).
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