Network Working Group N. Sullivan
Internet-Draft Cloudflare
Intended status: Standards Track H. Krawczyk
Expires: September 12, 2019 IBM Research
O. Friel
R. Barnes
Cisco
March 11, 2019
Usage of OPAQUE with TLS 1.3
draft-sullivan-tls-opaque-00
Abstract
This document describes two mechanisms for enabling the use of the
OPAQUE password-authenticated key exchange in TLS 1.3.
Status of This Memo
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Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 2
2. Conventions and Definitions . . . . . . . . . . . . . . . . . 3
3. OPAQUE . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
4. Password Registration . . . . . . . . . . . . . . . . . . . . 4
4.1. Implementing EnvU . . . . . . . . . . . . . . . . . . . . 5
5. TLS extensions . . . . . . . . . . . . . . . . . . . . . . . 6
6. Use of extensions in TLS handshake flows . . . . . . . . . . 8
6.1. OPAQUE-3DH, OPAQUE-HMQV . . . . . . . . . . . . . . . . . 8
6.2. OPAQUE-Sign . . . . . . . . . . . . . . . . . . . . . . . 10
7. Integration into Exported Authenticators . . . . . . . . . . 11
8. Summary of properties . . . . . . . . . . . . . . . . . . . . 11
9. Example OPRF . . . . . . . . . . . . . . . . . . . . . . . . 12
9.1. OPRF_1 . . . . . . . . . . . . . . . . . . . . . . . . . 13
9.2. OPRF_2 . . . . . . . . . . . . . . . . . . . . . . . . . 13
10. Privacy considerations . . . . . . . . . . . . . . . . . . . 13
11. Security Considerations . . . . . . . . . . . . . . . . . . . 14
12. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 14
13. References . . . . . . . . . . . . . . . . . . . . . . . . . 14
13.1. Normative References . . . . . . . . . . . . . . . . . . 14
13.2. Informative References . . . . . . . . . . . . . . . . . 15
Appendix A. Acknowledgments . . . . . . . . . . . . . . . . . . 16
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 16
1. Introduction
Note that this draft has not received significant security review and
should not be the basis for production systems.
OPAQUE [opaque-paper] is a mutual authentication method that enables
the establishment of an authenticated cryptographic key between a
client and server based on a user's memorized password, without ever
exposing the password to servers or other entities other than the
client machine and without relying on PKI. OPAQUE leverages a
primitive called a Strong Asymmetrical Password Authenticated Key
Exchange (Strong aPAKE) to provide desirable properties including
resistance to pre-computation attacks in the event of a server
compromise.
In some cases, it is desirable to combine password-based
authentication with traditional PKI-based authentication as a
defense-in-depth measure. For example, in the case of IoT devices,
it may be useful to validate that both parties were issued a
certificate from a certain manufacturer. Another desirable property
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for password-based authentication systems is the ability to hide the
client's identity from the network. This document describes the use
of OPAQUE in TLS 1.3 [TLS13] both as part of the TLS handshake and
post-handshake facilitated by Exported Authenticators
[I-D.ietf-tls-exported-authenticator], how the different approaches
satisfy the above properties and the trade-offs associated with each
design.
The in-handshake instantiations of OPAQUE can be used to authenticate
a TLS handshake with a password alone, or in conjunction with
certificate-based (mutual) authentication but does not provide
identity hiding for the client. The Exported Authenticators
instantiation of OPAQUE provides client identity hiding by default
and allows the application to do password authentication at any time
during the connection, but requires PKI authentication for the
initial handshake and application-layer semantics to be defined for
transporting authentication messages.
2. Conventions and Definitions
The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
"SHOULD", "SHOULD NOT", "RECOMMENDED", "NOT RECOMMENDED", "MAY", and
"OPTIONAL" in this document are to be interpreted as described in BCP
14 [RFC2119] [RFC8174] when, and only when, they appear in all
capitals, as shown here.
3. OPAQUE
In OPAQUE [opaque-paper], it is shown that a Strong Asymmetric
Password-Authenticated Key Exchange (Strong aPAKE) can be constructed
given an oblivious pseudo-random function (OPRF) and authenticated
key exchange protocol that is secure against reverse impersonation
(a.k.a. KCI). Unlike previous PAKE methods such as SRP [RFC2945]
and SPAKE-2 [I-D.irtf-cfrg-spake2], which require a public salt
value, a Strong aPAKE leverages the OPRF private key as salt, making
it resistant to pre-computation attacks on the password database
stored on the server.
TLS 1.3 provides a KCI-secure key agreement algorithm suitable for
use with OPAQUE. This document describes three instantiations of
OPAQUE in TLS 1.3: one based on digital signatures, one on Diffie-
Hellman key agreement, and one based on HMQV key exchange. Of the
three instantiations, the only one that has known IPR considerations
is HMQV.
OPAQUE consists of two distinct phases: password registration and
authentication. We will describe the mechanisms for password
registration in this document but it is assumed to have been done
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outside of TLS. During password registration, the client and server
establish a shared set of parameters for future authentication and
two private-public key pairs are generated, one for the client and
one for the server. The server keeps its private key and stores an
encapsulated copy of the client's key pair along with its own public
key in an "envelope" that is encrypted with the result of the OPRF
operation. Note that it is possible for the server to use the same
key for multiple clients. It may be necessary to permit multiple
simultaneous server keys in the even of a key rollover. The client
does not store any state nor any PKI information.
We call the first instantiation OPAQUE-Sign. In OPAQUE-Sign, the key
pairs generated at password registration time are digital signature
keys. These signature keys are used in place of certificate keys for
both server and client authentication in a TLS handshake. Client
authentication is technically optional, but in practice is almost
universally required. OPAQUE-Sign cannot be used alongside
certificate-based handshake authentication. This instantiation can
also be leveraged to do part of a post-handshake authentication using
Exported Authenticators [I-D.ietf-tls-exported-authenticator] given
an established TLS connection protected with certificate-based
authentication.
The second and third instantiations are called OPAQUE-3DH and OPAQUE-
HMQV. In these instantiations, the key pairs are Diffie-Hellman keys
and are used to establish a shared secret that is fed into the key
schedule for the handshake. The handshake continues to use
Certificate-based authentication. The two methods for establishing
the shared key are Diffie-Hellman and HMQV. These instantiations are
best suited to use cases in which both password and certificate-based
authentication are needed during the initial handshake, which is
useful in some scenarios. There is no unilateral authentication in
this context, mutual authentication is demonstrated explicitly
through the finished messages.
4. Password Registration
Password registration is run between a user U and a server S. It is
assumed that the user can authenticate the server during this
registration phase (this is the only part in OPAQUE that requires
some form of authenticated channel, either physical, out-of-band,
PKI-based, etc.)
A set of parameters is chosen. This includes an AuthEnc function for
key encapsulation, a group setting for the OPRF (chosen as a cipher
defined in Oblivious Pseudorandom Functions (OPRFs) using Prime-Order
Groups [I-D.sullivan-cfrg-voprf]), an instantiation (either OPAQUE-
Sign, OPAQUE-3DH or OPAQUE-HMQV), and a key type (either a TLS
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Signature Scheme [TLS13] for OPAQUE-Sign or a TLS Supported Group
[TLS13] for OPAQUE-3DH and OPAQUE-HMQV).
o U chooses password PwdU and a pair of private-public keys PrivU
and PubU of the chosen key type.
o S chooses OPRF key kU (random and independent for each user U) and
sets vU = g^kU; it also chooses its own pair of private-public
keys PrivS and PubS (the server can use the same pair of keys with
multiple users), and sends PubS to U.
o U and S run OPRF(kU;PwdU) as defined in with only U learning the
result, denoted RwdU (mnemonics for "Randomized PwdU").
o U generates an "envelope" EnvU defined as
EnvU = AuthEnc(RwdU; PrivU, PubU, PubS)
where AuthEnc is an authenticated encryption function with the "key
committing" property and is specified below in section. In EnvU, all
values require authentication and PrivU also requires encryption.
PubU can be omitted from EnvU if it can be reconstructed from PrivU
but while it will save bits on the wire it will come at some
computational cost during client authentication.
o U sends EnvU and PubU to S and erases PwdU, RwdU and all keys. S
stores (EnvU, PubS, PrivS, PubU, kU, vU) in a user-specific
record. If PrivS and PubS are used for multiple users, S can
store these values separately and omit them from the user's
record.
Note (salt). We note that in OPAQUE the OPRF key acts as the secret
salt value that ensures the infeasibility of pre-computation attacks.
No extra salt value is needed.
4.1. Implementing EnvU
The encryption for EnvU is required to be a key-committing
authenticated encryption algorithm. This, unfortunately, eliminates
both AES-GCM and AES-GCM-SIV as wrapping functions. It is possible
to create a key-committing authenticated encryption using AES-CBC
[RFC3602] or AES-CTR [RFC5930] with HMAC [RFC4868] as long as the
keys for encryption and authentication are derived separately with a
key domain separation mechanism such as HKDF [RFC5869].
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5. TLS extensions
We define several TLS extensions to signal support for OPAQUE and
transport the parameters. The extensions used here have a similar
structure to those described in Usage of PAKE with TLS 1.3
[I-D.barnes-tls-pake]. The permitted messages that these extensions
are allowed and the expected protocol flows are described below.
This document defines the following extension code points.
enum {
...
opaque_client_auth(TBD),
opaque_server_auth(TBD),
(65535)
} ExtensionType;
The opaque_client_auth extension contains a PAKEClientAuthExtension
struct and can only be included in the CertificateRequest and
Certificate messages. The opaque_client_auth extension contains a
PAKEServerAuthExtension struct and can only be included in the
ClientHello, EncryptedExtensions, CertificateRequest and Certificate
messages, depending on the type.
The structures contained in this extension are defined as:
struct {
opaque identity<0..2^16-1>;
opaque OPRF_1<1..2^16-1>;
} PAKEShareClient;
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struct {
opaque identity<0..2^16-1>;
opaque OPRF_2<1..2^16-1>;
opaque vU<1..2^16-1>;
opaque EnvU<1..2^16-1>;
} PAKEShareServer;
struct {
select (Handshake.msg_type) {
ClientHello:
PAKEShareClient client_shares<0..2^16-1>;
OPAQUEType types<0..2^16-1>;
EncryptedExtensions, Certificate:
PAKEShareServer server_share;
OPAQUEType type;
}
} PAKEServerAuthExtension;
struct {
opaque identity<0..2^16-1>;
} PAKEClientAuthExtension;
This document also defines the following set of types;
enum {
OPAQUE-Sign(1),
OPAQUE-3DH(2),
OPAQUE-3DH-Cert(3),
OPAQUE-HMQV(4),
OPAQUE-HMQV-Cert(5),
} OPAQUEType;
The "identity" field is the unique user id used to index the user's
record on the server. The types field indicates the set of supported
auth types by the client. The OPRF_1 message is as defined in
Oblivious Pseudorandom Functions (OPRFs) using Prime-Order Groups
[I-D.sullivan-cfrg-voprf]. The content of OPRF_1 is typically the
result of the password hashed into a group element and blinded by an
element known to the client. OPRF_2 is the OPRF_1 value operated on
by the OPRF private key kU. vU is the public component of kU and EnvU
is the envelope containing PrivU, PubS, and PubU. (Note that for
groups, it may be more space efficient to only include PrivU and have
the client derive PubU from PrivU). See Section 9 for details.
This document also describes a new CertificateEntry structure that
corresponds to an authentication via a signature derived using
OPAQUE. This structure serves as a placeholder for the
PAKEServerAuthExtension extension.
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struct {
select (certificate_type) {
case OPAQUESign:
/* Defined in this document */
opaque null<0>
case RawPublicKey:
/* From RFC 7250 ASN.1_subjectPublicKeyInfo */
opaque ASN1_subjectPublicKeyInfo<1..2^24-1>;
case X509:
opaque cert_data<1..2^24-1>;
};
Extension extensions<0..2^16-1>;
} CertificateEntry;
We request that IANA add an additional type to the "TLS Certificate
Types" registry for this OPAQUESign.
Support for the OPAQUESign Certificate type for server authentication
can be negotiated using the server_certificate_type [RFC7250] and the
Certificate type for client authentication can be negotiated using
the client_certificate_type extension [RFC7250].
Note that there needs to be a change to the client_certificate_type
row in the IANA TLS ExtensionType Values table to allow
client_certificate_type extension to be used as an extension to the
CertificateRequest message.
6. Use of extensions in TLS handshake flows
6.1. OPAQUE-3DH, OPAQUE-HMQV
In these two modes of operation, the OPAQUE private keys are used for
key agreement algorithm and the result is fed into the TLS key
schedule. Password validation is confirmed by the validation of the
finished message. These modes can be used in conjunction with
optional Certificate-based authentication.
It should be noted that since the identity of the client it is not
encrypted as it is sent as an extension to the ClientHello. This may
present a privacy problem unless a mechanism like ESNI
[I-D.ietf-tls-esni] is created to protect it.
Upon receiving a PAKEServerAuth extension, the server checks to see
if it has a matching record for this identity. If the record does
not exist, the handshake is aborted with a TBD error message. If the
record does exist, but the key type of the record does not match any
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of the supported_groups sent in the key_share extension of the
ClientHello, an HRR is sent containing the set of valid key types
that it found records for.
Given a matching key_share and an identity with a matching
supported_group, the server returns its PAKEServerAuth as an
extension to its EncryptedExtensions. Both parties then derive a
shared OPAQUE key using
HMQV
C computes K = (g^y * PubS^e)^{x + d*PrivU)
S computes K = (g^x * PubU^d)^{y + e*PrivS
where d = H(g^x, IdS) and e = H(g^y, IdU), and IdU, IdS represent the
identities of user (sent as identity in PAKEShareClient) and server
(EncryptedExtension or Certificate message). TODO: be more explicit
about content of IdS.
3DH
C computes K = H(g^y ^ PrivU || PubU ^ x || PubS ^ PrivU || IdU || IdS )
S computes K = H(g^x ^ PrivS || PubS ^ y || PubU ^ PrivS || IdU || IdS )
IdU, IdS represent the identities of user (sent as identity in
PAKEShareClient) and server (Certificate message).
H is the HKDF function agreed upon in the TLS handshake.
The result, K, is then added as an input to the Master Secret in
place of the 0 value defined in TLS 1.3:
0 -> HKDF-Extract = Master Secret
becomes
K -> HKDF-Extract = Master Secret
In this construction, the finished messages cannot be validated
unless the OPAQUE computation was done correctly on both sides,
authenticating both client and server.
For the certificate version of OPAQUE (OPAQUE-3DH-Cert, OPAQUE-HMQV-
Cert), the server's first flight contains the standard set of
messages: ServerHello, EncryptedExtension,
(optional)CertificateRequest, Certificate, CertificateVerify,
Finished. In the non-certificate cases (OPAQUE-3DH-Cert, OPAQUE-
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HMQV-Cert), the Certificate and CertificateVerify messages are
omitted, similar to the PSK mode in TLS 1.3.
6.2. OPAQUE-Sign
In this modes of operation, the OPAQUE private keys are used for
digital signatures and are used to define a new Certificate type and
CertificateVerify algorithm. Like the 3DH and HKDF instantiations
above, the identity of the client is sent in the clear in the
client's first flight unless a mechanism like ESNI
[I-D.ietf-tls-esni] is created to protect it.
Upon receiving a PAKEServerAuth extension, the server checks to see
if it has a matching record for this identity. If the record does
not exist, the handshake is aborted with a TBD error message. If the
record does exist, but the key type of the record does not match any
of the supported_signatures sent in the the ClientHello, the
handshake must be aborted with a TBD error.
We define a new Certificate message type for an OPAQUE-Sign
authenticated handshake.
enum {
X509(0),
RawPublicKey(2),
OPAQUE-Sign(3),
(255)
} CertificateType;
Certificates of this type have CertificateEntry structs of the form:
struct {
Extension extensions<0..2^16-1>;
} CertificateEntry;
Given a matching signature_scheme and an identity with a matching key
type, the server returns a certificate message with type OPAQUE-Sign
with PAKEServerAuth as an extension. The private key used in the
CertificateVerify message is set to PrivS, and the client verifies it
using PubS.
It is RECOMMENDED that the server includes a CertificateRequest
message with a PAKEClientAuth and the identity originally sent in the
PAKEServerAuth extension from the client hello. On receiving a
CertificateRequest message with a PAKEClientAuth extension, the
client returns a CertificateVerify message signed by PrivC which is
validated by the server using PubC.
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7. Integration into Exported Authenticators
Neither of the above mechanisms provides privacy for the user during
the authentication phase, as the user id is sent in the clear. It is
possible to create an encryption mechanism like ESNI
[I-D.ietf-tls-esni] to protect these values, but this is not in scope
for this document. Additionally, OPAQUE-Sign has the drawback that
it cannot be used in conjunction with certificate-based
authentication.
It is possible to address both the privacy concerns and the
requirement for certificate-based authentication by using OPAQUE-Sign
in Exported Authenticator [I-D.ietf-tls-exported-authenticator] flow,
since exported authenticators are sent over a secure channel that is
typically established with certificate-based authentication. Using
Exported Authenticators for OPAQUE has the additional benefit that it
can be triggered at any time after a TLS session has been
established, which better fits modern web-based authentication
mechanism.
The client hello contains PAKEServerAuth, PAKEClientAuth with empty
identity values to indicate support for these mechanisms.
1. Client creates Authenticator Request with CR extension
PAKEServerAuth (identity, OPRF_1)
2. Server creates Exported Authenticator with OPAQUE-Sign
(PAKEServerAuth) and CertificateVerify (signed with PrivS)
If the server would like to then establish mutual authentication, it
can do the following: 1. Server creates Authenticator Request with
CH extension PAKEClientAuth (identity) 2. Client creates Exported
Authenticator with OPAQUE-Sign Certificate and CertificateVerify
(signed with PrivU)
Support for Exported Authenticators is negotiated at the application
layer. For example, OPAQUE-Sign in EAs could be defined as an
extension to Secondary Certificates in HTTP/2
[I-D.ietf-httpbis-http2-secondary-certs].
8. Summary of properties
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+-------------+-------+------------+----------+------------+--------+
| Variant \ | Ident | Certificat | Server- | Post- | Minimu |
| Property | ity H | e Authenti | only | handshake | m |
| | iding | cation | Auth | auth | round |
| | | | | | trips |
+-------------+-------+------------+----------+------------+--------+
| OPAQUE- | yes | yes | yes | yes | 2-RTT |
| Sign-EA | | | | | |
| | | | | | |
| OPAQUE-Sign | no | no | yes | no | 1-RTT |
| | | | | | |
| OPAQUE-3DH | no | no | no | no | 1-RTT |
| | | | | | |
| OPAQUE-3DH- | no | yes | no | no | 1-RTT |
| Cert | | | | | |
| | | | | | |
| OPAQUE-HMQV | no | no | no | no | 1-RTT |
| | | | | | |
| OPAQUE- | no | yes | no | no | 1-RTT |
| HMQV-Cert | | | | | |
+-------------+-------+------------+----------+------------+--------+
9. Example OPRF
This is an example OPRF instantiation based on the ECOPRF-P256-HKDF-
SHA256-SSWU ciphersuite in [I-D.sullivan-cfrg-voprf]. We use
additive group notation in this description because we specifically
target the elliptic curve case. All operations can be replaced with
their multiplicative group counterparts.
The example ECOPRF-P256-HKDF-SHA256-SSWU instantiation uses the
following parameters:
o Curve: SECP256K1 curve
o H_1: H2C-P256-SHA256-SSWU- [I-D.sullivan-cfrg-voprf]
o label: voprf_h2c
o H_2: SHA256
See [I-D.sullivan-cfrg-voprf] for more details about how each of the
above components are used. In the following we will use the
functions OPRF_Blind, OPRF_Sign, OPRF_Unblind, OPRF_Finalize that are
defined in the same document.
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9.1. OPRF_1
Let p be the prime order of the base field of the curve that is used
(e.g. 2^256 - 2^224 + 2^192 + 2^96 - 1 for P-256). Let I2OSP, OS2IP
be functions as defined in [RFC8017]. Then OPRF_1 is computed using
the OPRF_Blind function on the password P follows:
1. r <-$ GF(p)
2. M := rH_1(P)
3. Output (r, M)
H_1 = hash-to-curve(P) = 1. t1 = H("h2c" || label || I2OSP(len(x),
4) || P) 2. t2 = OS2IP(t1) 3. y = t^2 mod p 4. H_1(P) =
map2curve_simple_swu(y) 5. M = rH_1(P)
The client keeps the blind r, and sends the OPRF_1 value M as an
EllipticCurve point [TLS13].
9.2. OPRF_2
The server now computes OPRF_2 by applying OPRF_Sign on the received
message M: 1. Z := kM 2. Output Z Note that the server should
multiply M by the cofactor of the given curve before it outputs Z.
In the case of P-256, this cofactor is equal to 1 and so it is not
necessary.
The output Z of OPRF_2 is sent as an EllipticCurve point "[]" back to
the client.
When the client receives the output of OPRF_2, it derives the
envelope decryption key using OPRF_Unblind followed by OPRF_Finalize.
1. N := (1/r)Z (OPRF_Unblind)
2. y := H_2(P, N) (OPRF_Finalize). Here, we require that N is
serialized before it is input to H_2. The client can now stores
(P, y) for future usage.
10. Privacy considerations
TBD
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11. Security Considerations
TODO: protecting against user enumeration
12. IANA Considerations
o Existing IANA references have not been updated yet to point to
this document.
IANA is asked to register a new value in the "TLS Certificate
Types" registry of Transport Layer Security (TLS) Extensions (TLS-
Certificate-Types-Registry), as follows:
o Value: 4 Description: OPAQUE Authentication Reference: This RFC
Correction request: The client_certificate_type row in the IANA TLS
ExtensionType Values table to allow client_certificate_type extension
to be used as an extension to the CertificateRequest message.
13. References
13.1. Normative References
[I-D.ietf-httpbis-http2-secondary-certs]
Bishop, M., Sullivan, N., and M. Thomson, "Secondary
Certificate Authentication in HTTP/2", draft-ietf-httpbis-
http2-secondary-certs-03 (work in progress), October 2018.
[I-D.ietf-tls-exported-authenticator]
Sullivan, N., "Exported Authenticators in TLS", draft-
ietf-tls-exported-authenticator-08 (work in progress),
October 2018.
[RFC2119] Bradner, S., "Key words for use in RFCs to Indicate
Requirement Levels", BCP 14, RFC 2119,
DOI 10.17487/RFC2119, March 1997, <https://www.rfc-
editor.org/info/rfc2119>.
[RFC3602] Frankel, S., Glenn, R., and S. Kelly, "The AES-CBC Cipher
Algorithm and Its Use with IPsec", RFC 3602,
DOI 10.17487/RFC3602, September 2003, <https://www.rfc-
editor.org/info/rfc3602>.
[RFC4868] Kelly, S. and S. Frankel, "Using HMAC-SHA-256, HMAC-SHA-
384, and HMAC-SHA-512 with IPsec", RFC 4868,
DOI 10.17487/RFC4868, May 2007, <https://www.rfc-
editor.org/info/rfc4868>.
Sullivan, et al. Expires September 12, 2019 [Page 14]
Internet-Draft TLS 1.3 OPAQUE March 2019
[RFC7250] Wouters, P., Ed., Tschofenig, H., Ed., Gilmore, J.,
Weiler, S., and T. Kivinen, "Using Raw Public Keys in
Transport Layer Security (TLS) and Datagram Transport
Layer Security (DTLS)", RFC 7250, DOI 10.17487/RFC7250,
June 2014, <https://www.rfc-editor.org/info/rfc7250>.
[RFC8174] Leiba, B., "Ambiguity of Uppercase vs Lowercase in RFC
2119 Key Words", BCP 14, RFC 8174, DOI 10.17487/RFC8174,
May 2017, <https://www.rfc-editor.org/info/rfc8174>.
[TLS13] Rescorla, E., "The Transport Layer Security (TLS) Protocol
Version 1.3", RFC 8446, DOI 10.17487/RFC8446, August 2018,
<https://www.rfc-editor.org/info/rfc8446>.
13.2. Informative References
[I-D.barnes-tls-pake]
Barnes, R. and O. Friel, "Usage of PAKE with TLS 1.3",
draft-barnes-tls-pake-04 (work in progress), July 2018.
[I-D.ietf-tls-esni]
Rescorla, E., Oku, K., Sullivan, N., and C. Wood,
"Encrypted Server Name Indication for TLS 1.3", draft-
ietf-tls-esni-03 (work in progress), March 2019.
[I-D.irtf-cfrg-spake2]
Ladd, W. and B. Kaduk, "SPAKE2, a PAKE", draft-irtf-cfrg-
spake2-08 (work in progress), March 2019.
[I-D.sullivan-cfrg-voprf]
Davidson, A., Sullivan, N., and C. Wood, "Oblivious
Pseudorandom Functions (OPRFs) using Prime-Order Groups",
draft-sullivan-cfrg-voprf-03 (work in progress), March
2019.
[opaque-paper]
Xu, J., "OPAQUE: An Asymmetric PAKE Protocol Secure
Against Pre-Computation Attacks", 2018.
[RFC2945] Wu, T., "The SRP Authentication and Key Exchange System",
RFC 2945, DOI 10.17487/RFC2945, September 2000,
<https://www.rfc-editor.org/info/rfc2945>.
[RFC5869] Krawczyk, H. and P. Eronen, "HMAC-based Extract-and-Expand
Key Derivation Function (HKDF)", RFC 5869,
DOI 10.17487/RFC5869, May 2010, <https://www.rfc-
editor.org/info/rfc5869>.
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Internet-Draft TLS 1.3 OPAQUE March 2019
[RFC5930] Shen, S., Mao, Y., and NSS. Murthy, "Using Advanced
Encryption Standard Counter Mode (AES-CTR) with the
Internet Key Exchange version 02 (IKEv2) Protocol",
RFC 5930, DOI 10.17487/RFC5930, July 2010,
<https://www.rfc-editor.org/info/rfc5930>.
[RFC8017] Moriarty, K., Ed., Kaliski, B., Jonsson, J., and A. Rusch,
"PKCS #1: RSA Cryptography Specifications Version 2.2",
RFC 8017, DOI 10.17487/RFC8017, November 2016,
<https://www.rfc-editor.org/info/rfc8017>.
Appendix A. Acknowledgments
Authors' Addresses
Nick Sullivan
Cloudflare
Email: nick@cloudflare.com
Hugo Krawczyk
IBM Research
Email: hugo@ee.technion.ac.il
Owen Friel
Cisco
Email: ofriel@cisco.com
Richard Barnes
Cisco
Email: rlb@ipv.sx
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