Internet DRAFT - draft-irtf-cfrg-opaque
draft-irtf-cfrg-opaque
Network Working Group D. Bourdrez
Internet-Draft
Intended status: Informational H. Krawczyk
Expires: 20 June 2024 AWS
K. Lewi
Meta
C. A. Wood
Cloudflare, Inc.
18 December 2023
The OPAQUE Asymmetric PAKE Protocol
draft-irtf-cfrg-opaque-13
Abstract
This document describes the OPAQUE protocol, a secure asymmetric
password-authenticated key exchange (aPAKE) that supports mutual
authentication in a client-server setting without reliance on PKI and
with security against pre-computation attacks upon server compromise.
In addition, the protocol provides forward secrecy and the ability to
hide the password from the server, even during password registration.
This document specifies the core OPAQUE protocol and one
instantiation based on 3DH.
Discussion Venues
This note is to be removed before publishing as an RFC.
Source for this draft and an issue tracker can be found at
https://github.com/cfrg/draft-irtf-cfrg-opaque.
Status of This Memo
This Internet-Draft is submitted in full conformance with the
provisions of BCP 78 and BCP 79.
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This Internet-Draft will expire on 20 June 2024.
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Copyright Notice
Copyright (c) 2023 IETF Trust and the persons identified as the
document authors. All rights reserved.
This document is subject to BCP 78 and the IETF Trust's Legal
Provisions Relating to IETF Documents (https://trustee.ietf.org/
license-info) in effect on the date of publication of this document.
Please review these documents carefully, as they describe your rights
and restrictions with respect to this document. Code Components
extracted from this document must include Revised BSD License text as
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provided without warranty as described in the Revised BSD License.
Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 4
1.1. Requirements Notation . . . . . . . . . . . . . . . . . . 5
1.2. Notation . . . . . . . . . . . . . . . . . . . . . . . . 5
2. Cryptographic Dependencies . . . . . . . . . . . . . . . . . 6
2.1. Oblivious Pseudorandom Function . . . . . . . . . . . . . 6
2.2. Key Derivation Function and Message Authentication
Code . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.3. Hash Functions . . . . . . . . . . . . . . . . . . . . . 8
3. Protocol Overview . . . . . . . . . . . . . . . . . . . . . . 8
3.1. Setup . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3.2. Offline Registration . . . . . . . . . . . . . . . . . . 9
3.3. Online Authenticated Key Exchange . . . . . . . . . . . . 10
4. Client Credential Storage and Key Recovery . . . . . . . . . 11
4.1. Key Recovery . . . . . . . . . . . . . . . . . . . . . . 13
4.1.1. Envelope Structure . . . . . . . . . . . . . . . . . 13
4.1.2. Envelope Creation . . . . . . . . . . . . . . . . . . 13
4.1.3. Envelope Recovery . . . . . . . . . . . . . . . . . . 14
5. Offline Registration . . . . . . . . . . . . . . . . . . . . 15
5.1. Registration Messages . . . . . . . . . . . . . . . . . . 17
5.2. Registration Functions . . . . . . . . . . . . . . . . . 17
5.2.1. CreateRegistrationRequest . . . . . . . . . . . . . . 18
5.2.2. CreateRegistrationResponse . . . . . . . . . . . . . 18
5.2.3. FinalizeRegistrationRequest . . . . . . . . . . . . . 19
6. Online Authenticated Key Exchange . . . . . . . . . . . . . . 20
6.1. AKE Messages . . . . . . . . . . . . . . . . . . . . . . 23
6.2. AKE Functions . . . . . . . . . . . . . . . . . . . . . . 24
6.2.1. GenerateKE1 . . . . . . . . . . . . . . . . . . . . . 24
6.2.2. GenerateKE2 . . . . . . . . . . . . . . . . . . . . . 25
6.2.3. GenerateKE3 . . . . . . . . . . . . . . . . . . . . . 25
6.2.4. ServerFinish . . . . . . . . . . . . . . . . . . . . 26
6.3. Credential Retrieval . . . . . . . . . . . . . . . . . . 27
6.3.1. Credential Retrieval Messages . . . . . . . . . . . . 27
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6.3.2. Credential Retrieval Functions . . . . . . . . . . . 27
6.4. 3DH Protocol . . . . . . . . . . . . . . . . . . . . . . 31
6.4.1. 3DH Key Exchange Functions . . . . . . . . . . . . . 32
6.4.2. Key Schedule Functions . . . . . . . . . . . . . . . 33
6.4.3. 3DH Client Functions . . . . . . . . . . . . . . . . 35
6.4.4. 3DH Server Functions . . . . . . . . . . . . . . . . 37
7. Configurations . . . . . . . . . . . . . . . . . . . . . . . 39
8. Application Considerations . . . . . . . . . . . . . . . . . 40
9. Implementation Considerations . . . . . . . . . . . . . . . . 42
9.1. Implementation Safeguards . . . . . . . . . . . . . . . . 42
9.2. Error Considerations . . . . . . . . . . . . . . . . . . 43
10. Security Considerations . . . . . . . . . . . . . . . . . . . 43
10.1. Notable Design Differences . . . . . . . . . . . . . . . 44
10.2. Security Analysis . . . . . . . . . . . . . . . . . . . 47
10.3. Related Protocols . . . . . . . . . . . . . . . . . . . 48
10.4. Identities . . . . . . . . . . . . . . . . . . . . . . . 48
10.5. Export Key Usage . . . . . . . . . . . . . . . . . . . . 50
10.6. Static Diffie-Hellman Oracles . . . . . . . . . . . . . 50
10.7. Random-Key Robust MACs . . . . . . . . . . . . . . . . . 50
10.8. Input Validation . . . . . . . . . . . . . . . . . . . . 50
10.9. OPRF Key Stretching . . . . . . . . . . . . . . . . . . 51
10.10. Client Enumeration . . . . . . . . . . . . . . . . . . . 51
10.11. Protecting the Registration Masking Key . . . . . . . . 52
10.12. Password Salt and Storage Implications . . . . . . . . . 52
10.13. AKE Private Key Storage . . . . . . . . . . . . . . . . 52
11. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 53
12. References . . . . . . . . . . . . . . . . . . . . . . . . . 53
12.1. Normative References . . . . . . . . . . . . . . . . . . 53
12.2. Informative References . . . . . . . . . . . . . . . . . 53
Appendix A. Acknowledgments . . . . . . . . . . . . . . . . . . 57
Appendix B. Alternate Key Recovery Mechanisms . . . . . . . . . 57
Appendix C. Alternate AKE Instantiations . . . . . . . . . . . . 58
C.1. HMQV Instantiation Sketch . . . . . . . . . . . . . . . . 58
C.2. SIGMA-I Instantiation Sketch . . . . . . . . . . . . . . 59
Appendix D. Test Vectors . . . . . . . . . . . . . . . . . . . . 59
D.1. Real Test Vectors . . . . . . . . . . . . . . . . . . . . 60
D.1.1. OPAQUE-3DH Real Test Vector 1 . . . . . . . . . . . . 60
D.1.2. OPAQUE-3DH Real Test Vector 2 . . . . . . . . . . . . 63
D.1.3. OPAQUE-3DH Real Test Vector 3 . . . . . . . . . . . . 66
D.1.4. OPAQUE-3DH Real Test Vector 4 . . . . . . . . . . . . 69
D.1.5. OPAQUE-3DH Real Test Vector 5 . . . . . . . . . . . . 72
D.1.6. OPAQUE-3DH Real Test Vector 6 . . . . . . . . . . . . 74
D.2. Fake Test Vectors . . . . . . . . . . . . . . . . . . . . 76
D.2.1. OPAQUE-3DH Fake Test Vector 1 . . . . . . . . . . . . 77
D.2.2. OPAQUE-3DH Fake Test Vector 2 . . . . . . . . . . . . 78
D.2.3. OPAQUE-3DH Fake Test Vector 3 . . . . . . . . . . . . 79
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 81
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1. Introduction
Password authentication is ubiquitous in many applications. In a
common implementation, a client authenticates to a server by sending
its client ID and password to the server over a secure connection.
This makes the password vulnerable to server mishandling, including
accidentally logging the password or storing it in plaintext in a
database. Server compromise resulting in access to these plaintext
passwords is not an uncommon security incident, even among security-
conscious organizations. Moreover, plaintext password authentication
over secure channels such as TLS is also vulnerable to cases where
TLS may fail, including PKI attacks, certificate mishandling,
termination outside the security perimeter, visibility to TLS-
terminating intermediaries, and more.
Asymmetric (or Augmented) Password Authenticated Key Exchange (aPAKE)
protocols are designed to provide password authentication and
mutually authenticated key exchange in a client-server setting
without relying on PKI (except during client registration) and
without disclosing passwords to servers or other entities other than
the client machine. A secure aPAKE should provide the best possible
security for a password protocol. Indeed, some attacks are
inevitable, such as online impersonation attempts with guessed client
passwords and offline dictionary attacks upon the compromise of a
server and leakage of its credential file. In the latter case, the
attacker learns a mapping of a client's password under a one-way
function and uses such a mapping to validate potential guesses for
the password. Crucially important is for the password protocol to
use an unpredictable one-way mapping. Otherwise, the attacker can
pre-compute a deterministic list of mapped passwords leading to
almost instantaneous leakage of passwords upon server compromise.
This document describes OPAQUE, an aPAKE that is secure against pre-
computation attacks (as defined in [JKX18]). OPAQUE provides forward
secrecy with respect to password leakage while also hiding the
password from the server, even during password registration. OPAQUE
allows applications to increase the difficulty of offline dictionary
attacks via iterated hashing or other key stretching schemes. OPAQUE
is also extensible, allowing clients to safely store and retrieve
arbitrary application data on servers using only their password.
OPAQUE is defined and proven as the composition of three
functionalities: an oblivious pseudorandom function (OPRF), a key
recovery mechanism, and an authenticated key exchange (AKE) protocol.
It can be seen as a "compiler" for transforming any suitable AKE
protocol into a secure aPAKE protocol. (See Section 10 for
requirements of the OPRF and AKE protocols.) This document specifies
one OPAQUE instantiation based on [TripleDH]. Other instantiations
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are possible, as discussed in Appendix C, but their details are out
of scope for this document. In general, the modularity of OPAQUE's
design makes it easy to integrate with additional AKE protocols,
e.g., TLS or HMQV, and with future ones such as those based on post-
quantum techniques.
OPAQUE consists of two stages: registration and authenticated key
exchange. In the first stage, a client registers its password with
the server and stores information used to recover authentication
credentials on the server. Recovering these credentials can only be
done with knowledge of the client password. In the second stage, a
client uses its password to recover those credentials and
subsequently uses them as input to an AKE protocol. This stage has
additional mechanisms to prevent an active attacker from interacting
with the server to guess or confirm clients registered via the first
phase. Servers can use this mechanism to safeguard registered
clients against this type of enumeration attack; see Section 10.10
for more discussion.
The name OPAQUE is a homonym of O-PAKE where O is for Oblivious. The
name OPAKE was taken.
This draft complies with the requirements for PAKE protocols set
forth in [RFC8125].
1.1. Requirements Notation
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.
1.2. Notation
The following functions are used throughout this document:
* I2OSP and OS2IP: Convert a byte string to and from a non-negative
integer as described in Section 4 of [RFC8017]. Note that these
functions operate on byte strings in big-endian byte order.
* concat(x0, ..., xN): Concatenate byte strings. For example,
concat(0x01, 0x0203, 0x040506) = 0x010203040506.
* random(n): Generate a cryptographically secure pseudorandom byte
string of length n bytes.
* zeroes(n): Generate a string of n bytes all equal to 0 (zero).
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* xor(a,b): Apply XOR to byte strings. For example, xor(0xF0F0,
0x1234) = 0xE2C4. It is an error to call this function with
arguments of unequal length.
* ct_equal(a, b): Return true if a is equal to b, and false
otherwise. The implementation of this function must be constant-
time in the length of a and b, which are assumed to be of equal
length, irrespective of the values a or b.
Except if said otherwise, random choices in this specification refer
to drawing with uniform distribution from a given set (i.e., "random"
is short for "uniformly random"). Random choices can be replaced
with fresh outputs from a cryptographically strong pseudorandom
generator, according to the requirements in [RFC4086], or
pseudorandom function. For convenience, we define nil as a lack of
value.
All protocol messages and structures defined in this document use the
syntax from [RFC8446], Section 3.
2. Cryptographic Dependencies
OPAQUE depends on the following cryptographic protocols and
primitives:
* Oblivious Pseudorandom Function (OPRF); Section 2.1
* Key Derivation Function (KDF); Section 2.2
* Message Authentication Code (MAC); Section 2.2
* Cryptographic Hash Function; Section 2.3
* Key Stretching Function (KSF); Section 2.3
This section describes these protocols and primitives in more detail.
Unless said otherwise, all random nonces and seeds used in these
dependencies and the rest of the OPAQUE protocol are of length Nn and
Nseed bytes, respectively, where Nn = Nseed = 32.
2.1. Oblivious Pseudorandom Function
An Oblivious Pseudorandom Function (OPRF) is a two-party protocol
between client and server for computing a PRF, where the PRF key is
held by the server and the input to the function is provided by the
client. The client does not learn anything about the PRF other than
the obtained output and the server learns nothing about the client's
input or the function output. This specification depends on the
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prime-order OPRF construction specified in [OPRF], draft version -21,
using the OPRF mode (0x00) from [OPRF], Section 3.1.
The following OPRF client APIs are used:
* Blind(element): Create and output (blind, blinded_element),
consisting of a blinded representation of input element, denoted
blinded_element, along with a value to revert the blinding
process, denoted blind.
* Finalize(element, blind, evaluated_element): Finalize the OPRF
evaluation using input element, random inverter blind, and
evaluation output evaluated_element, yielding output oprf_output.
Moreover, the following OPRF server APIs are used:
* BlindEvaluate(k, blinded_element): Evaluate blinded input element
blinded_element using input key k, yielding output element
evaluated_element. This is equivalent to the BlindEvaluate
function described in [OPRF], Section 3.3.1, where k is the
private key parameter.
* DeriveKeyPair(seed, info): Create and output (sk, pk), consisting
of a private and public key derived deterministically from a seed
and info parameter, as described in [OPRF], Section 3.2.
Finally, this specification makes use of the following shared APIs
and parameters:
* SerializeElement(element): Map input element to a fixed-length
byte array.
* DeserializeElement(buf): Attempt to map input byte array buf to an
OPRF group element. This function can raise a DeserializeError
upon failure; see [OPRF], Section 2.1 for more details.
* Noe: The size of a serialized OPRF group element output from
SerializeElement.
* Nok: The size of an OPRF private key as output from DeriveKeyPair.
2.2. Key Derivation Function and Message Authentication Code
A Key Derivation Function (KDF) is a function that takes some source
of initial keying material and uses it to derive one or more
cryptographically strong keys. This specification uses a KDF with
the following API and parameters:
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* Extract(salt, ikm): Extract a pseudorandom key of fixed length Nx
bytes from input keying material ikm and an optional byte string
salt.
* Expand(prk, info, L): Expand a pseudorandom key prk using the
optional string info into L bytes of output keying material.
* Nx: The output size of the Extract() function in bytes.
This specification also makes use of a random-key robust Message
Authentication Code (MAC). See Section 10.7 for more details on this
property. The API and parameters for the random-key robust MAC are
as follows:
* MAC(key, msg): Compute a message authentication code over input
msg with key key, producing a fixed-length output of Nm bytes.
* Nm: The output size of the MAC() function in bytes.
2.3. Hash Functions
This specification makes use of a collision-resistant hash function
with the following API and parameters:
* Hash(msg): Apply a cryptographic hash function to input msg,
producing a fixed-length digest of size Nh bytes.
* Nh: The output size of the Hash() function in bytes.
This specification makes use of a Key Stretching Function (KSF),
which is a slow and expensive cryptographic hash function with the
following API:
* Stretch(msg): Apply a key stretching function to stretch the input
msg and harden it against offline dictionary attacks. This
function also needs to satisfy collision resistance.
3. Protocol Overview
OPAQUE consists of two stages: registration and authenticated key
exchange (AKE). In the first stage, a client registers its password
with the server and stores its credential file on the server. In the
second stage (also called the "login" or "online" stage), the client
recovers its authentication material and uses it to perform a
mutually authenticated key exchange.
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3.1. Setup
Prior to both stages, the client and server agree on a configuration
that fully specifies the cryptographic algorithm dependencies
necessary to run the protocol; see Section 7 for details. The server
chooses a pair of keys (server_private_key and server_public_key) for
the AKE, and chooses a seed (oprf_seed) of Nh bytes for the OPRF.
The server can use server_private_key and server_public_key with
multiple clients. The server can also opt to use different seeds for
each client, so long as they are maintained across the registration
and online AKE stages, and kept consistent for each client (since an
inconsistent mapping of clients to seeds could leak information as
described in Section 10.10).
3.2. Offline Registration
Registration is the only stage in OPAQUE that requires a server-
authenticated channel with confidentiality and integrity: either
physical, out-of-band, PKI-based, etc.
The client inputs its credentials, which include its password and
user identifier, and the server inputs its parameters, which include
its private key and other information.
The client output of this stage is a single value export_key that the
client may use for application-specific purposes, e.g., as a
symmetric key used to encrypt additional information for storage on
the server. The server does not have access to this export_key.
The server output of this stage is a record corresponding to the
client's registration that it stores in a credential file alongside
other clients registrations as needed.
The registration flow is shown below:
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creds parameters
| |
v v
Client Server
------------------------------------------------
registration request
------------------------->
registration response
<-------------------------
record
------------------------->
------------------------------------------------
| |
v v
export_key record
These messages are named RegistrationRequest, RegistrationResponse,
and RegistrationRecord, respectively. Their contents and wire format
are defined in Section 5.1.
3.3. Online Authenticated Key Exchange
In this second stage, a client obtains credentials previously
registered with the server, recovers private key material using the
password, and subsequently uses them as input to the AKE protocol.
As in the registration phase, the client inputs its credentials,
including its password and user identifier, and the server inputs its
parameters and the credential file record corresponding to the
client. The client outputs two values, an export_key (matching that
from registration) and a session_key, the latter of which is the
primary AKE output. The server outputs a single value session_key
that matches that of the client. Upon completion, clients and
servers can use these values as needed.
The authenticated key exchange flow is shown below:
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creds (parameters, record)
| |
v v
Client Server
------------------------------------------------
AKE message 1
------------------------->
AKE message 2
<-------------------------
AKE message 3
------------------------->
------------------------------------------------
| |
v v
(export_key, session_key) session_key
These messages are named KE1, KE2, and KE3, respectively. They carry
the messages of the concurrent execution of the key recovery process
(OPRF) and the authenticated key exchange (AKE), and their
corresponding wire formats are specified in Section 6.1.
The rest of this document describes the specifics of these stages in
detail. Section 4 describes how client credential information is
generated, encoded, and stored on the server during registration, and
recovered during login. Section 5 describes the first registration
stage of the protocol, and Section 6 describes the second
authentication stage of the protocol. Section 7 describes how to
instantiate OPAQUE using different cryptographic dependencies and
parameters.
4. Client Credential Storage and Key Recovery
OPAQUE makes use of a structure called Envelope to manage client
credentials. The client creates its Envelope on registration and
sends it to the server for storage. On every login, the server sends
this Envelope to the client so it can recover its key material for
use in the AKE.
Applications may pin key material to identities if desired. If no
identity is given for a party, its value MUST default to its public
key. The following types of application credential information are
considered:
* client_private_key: The encoded client private key for the AKE
protocol.
* client_public_key: The encoded client public key for the AKE
protocol.
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* server_public_key: The encoded server public key for the AKE
protocol.
* client_identity: The client identity. This is an application-
specific value, e.g., an e-mail address or an account name. If
not specified, it defaults to the client's public key.
* server_identity: The server identity. This is typically a domain
name, e.g., example.com. If not specified, it defaults to the
server's public key. See Section 10.4 for information about this
identity.
A subset of these credential values are used in the
CleartextCredentials structure as follows:
struct {
uint8 server_public_key[Npk];
uint8 server_identity<1..2^16-1>;
uint8 client_identity<1..2^16-1>;
} CleartextCredentials;
The function CreateCleartextCredentials constructs a
CleartextCredentials structure given application credential
information.
CreateCleartextCredentials
Input:
- server_public_key, the encoded server public key for the AKE protocol.
- client_public_key, the encoded client public key for the AKE protocol.
- server_identity, the optional encoded server identity.
- client_identity, the optional encoded client identity.
Output:
- cleartext_credentials, a CleartextCredentials structure.
def CreateCleartextCredentials(server_public_key, client_public_key,
server_identity, client_identity):
# Set identities as public keys if no application-layer identity is provided
if server_identity == nil
server_identity = server_public_key
if client_identity == nil
client_identity = client_public_key
Create CleartextCredentials cleartext_credentials with
(server_public_key, server_identity, client_identity)
return cleartext_credentials
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4.1. Key Recovery
This specification defines a key recovery mechanism that uses the
stretched OPRF output as a seed to directly derive the private and
public keys using the DeriveDiffieHellmanKeyPair() function defined
in Section 6.4.1.
4.1.1. Envelope Structure
The key recovery mechanism defines its Envelope as follows:
struct {
uint8 nonce[Nn];
uint8 auth_tag[Nm];
} Envelope;
nonce: A randomly-sampled nonce of length Nn, used to protect this
Envelope.
auth_tag: An authentication tag protecting the contents of the
envelope, covering the envelope nonce and CleartextCredentials.
4.1.2. Envelope Creation
Clients create an Envelope at registration with the function Store
defined below. Note that DeriveDiffieHellmanKeyPair in this function
can fail with negligible probability. If this occurs, servers should
re-run the function, sampling a new envelope_nonce, to completion.
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Store
Input:
- randomized_password, a randomized password.
- server_public_key, the encoded server public key for
the AKE protocol.
- server_identity, the optional encoded server identity.
- client_identity, the optional encoded client identity.
Output:
- envelope, the client's Envelope structure.
- client_public_key, the client's AKE public key.
- masking_key, an encryption key used by the server with the sole purpose
of defending against client enumeration attacks.
- export_key, an additional client key.
def Store(randomized_password, server_public_key, server_identity, client_identity):
envelope_nonce = random(Nn)
masking_key = Expand(randomized_password, "MaskingKey", Nh)
auth_key = Expand(randomized_password, concat(envelope_nonce, "AuthKey"), Nh)
export_key = Expand(randomized_password, concat(envelope_nonce, "ExportKey"), Nh)
seed = Expand(randomized_password, concat(envelope_nonce, "PrivateKey"), Nseed)
(_, client_public_key) = DeriveDiffieHellmanKeyPair(seed)
cleartext_credentials =
CreateCleartextCredentials(server_public_key, client_public_key,
server_identity, client_identity)
auth_tag = MAC(auth_key, concat(envelope_nonce, cleartext_credentials))
Create Envelope envelope with (envelope_nonce, auth_tag)
return (envelope, client_public_key, masking_key, export_key)
4.1.3. Envelope Recovery
Clients recover their Envelope during login with the Recover function
defined below.
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Recover
Input:
- randomized_password, a randomized password.
- server_public_key, the encoded server public key for the AKE protocol.
- envelope, the client's Envelope structure.
- server_identity, the optional encoded server identity.
- client_identity, the optional encoded client identity.
Output:
- client_private_key, the encoded client private key for the AKE protocol.
- cleartext_credentials, a CleartextCredentials structure.
- export_key, an additional client key.
Exceptions:
- EnvelopeRecoveryError, the envelope fails to be recovered.
def Recover(randomized_password, server_public_key, envelope,
server_identity, client_identity):
auth_key = Expand(randomized_password, concat(envelope.nonce, "AuthKey"), Nh)
export_key = Expand(randomized_password, concat(envelope.nonce, "ExportKey"), Nh)
seed = Expand(randomized_password, concat(envelope.nonce, "PrivateKey"), Nseed)
(client_private_key, client_public_key) = DeriveDiffieHellmanKeyPair(seed)
cleartext_credentials = CreateCleartextCredentials(server_public_key,
client_public_key, server_identity, client_identity)
expected_tag = MAC(auth_key, concat(envelope.nonce, cleartext_credentials))
If !ct_equal(envelope.auth_tag, expected_tag)
raise EnvelopeRecoveryError
return (client_private_key, cleartext_credentials, export_key)
In the case of EnvelopeRecoveryError being raised, all previously-
computed intermediary values in this function MUST be deleted.
5. Offline Registration
The registration process proceeds as follows. The client inputs the
following values:
* password: The client's password.
* creds: The client credentials, as described in Section 4.
The server inputs the following values:
* server_public_key: The server public key for the AKE protocol.
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* credential_identifier: A unique identifier for the client's
credential, generated by the server.
* client_identity: The optional client identity as described in
Section 4.
* oprf_seed: A seed used to derive per-client OPRF keys.
The registration protocol then runs as shown below:
Client Server
------------------------------------------------------
(request, blind) = CreateRegistrationRequest(password)
request
------------------------->
response = CreateRegistrationResponse(request,
server_public_key,
credential_identifier,
oprf_seed)
response
<-------------------------
(record, export_key) = FinalizeRegistrationRequest(response,
server_identity,
client_identity)
record
------------------------->
Section 5.1 describes the formats for the above messages, and
Section 5.2 describes details of the functions and the corresponding
parameters referenced above.
At the end of this interaction, the server stores the record object
as the credential file for each client along with the associated
credential_identifier and client_identity (if different). Note that
the values oprf_seed and server_private_key from the server's setup
phase must also be persisted. The oprf_seed value SHOULD be used for
all clients; see Section 10.10. The server_private_key may be unique
for each client.
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Both client and server MUST validate the other party's public key
before use. See Section 10.8 for more details. Upon completion, the
server stores the client's credentials for later use. Moreover, the
client MAY use the output export_key for further application-specific
purposes; see Section 10.5.
5.1. Registration Messages
This section contains definitions of the RegistrationRequest,
RegistrationResponse, and RegistrationRecord messages exchanged
between client and server during registration.
struct {
uint8 blinded_message[Noe];
} RegistrationRequest;
blinded_message: A serialized OPRF group element.
struct {
uint8 evaluated_message[Noe];
uint8 server_public_key[Npk];
} RegistrationResponse;
evaluated_message: A serialized OPRF group element.
server_public_key: The server's encoded public key that will be used
for the online AKE stage.
struct {
uint8 client_public_key[Npk];
uint8 masking_key[Nh];
Envelope envelope;
} RegistrationRecord;
client_public_key: The client's encoded public key, corresponding to
the private key client_private_key.
masking_key: An encryption key used by the server with the sole
purpose of defending against client enumeration attacks.
envelope: The client's Envelope structure.
5.2. Registration Functions
This section contains definitions of the functions used by client and
server during registration, including CreateRegistrationRequest,
CreateRegistrationResponse, and FinalizeRegistrationRequest.
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5.2.1. CreateRegistrationRequest
To begin the registration flow, the client executes the following
function. This function can fail with an InvalidInputError error
with negligibile probability. A different input password is
necessary in the event of this error.
CreateRegistrationRequest
Input:
- password, an opaque byte string containing the client's password.
Output:
- request, a RegistrationRequest structure.
- blind, an OPRF scalar value.
Exceptions:
- InvalidInputError, when Blind fails
def CreateRegistrationRequest(password):
(blind, blinded_element) = Blind(password)
blinded_message = SerializeElement(blinded_element)
Create RegistrationRequest request with blinded_message
return (request, blind)
5.2.2. CreateRegistrationResponse
To process the client's registration request, the server executes the
following function. This function can fail with a DeriveKeyPairError
error with negligible probability. In this case, application can
choose a new credential_identifier for this registration record and
re-run this function.
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CreateRegistrationResponse
Input:
- request, a RegistrationRequest structure.
- server_public_key, the server's public key.
- credential_identifier, an identifier that uniquely represents the credential.
- oprf_seed, the seed of Nh bytes used by the server to generate an oprf_key.
Output:
- response, a RegistrationResponse structure.
Exceptions:
- DeserializeError, when OPRF element deserialization fails.
- DeriveKeyPairError, when OPRF key derivation fails.
def CreateRegistrationResponse(request, server_public_key,
credential_identifier, oprf_seed):
seed = Expand(oprf_seed, concat(credential_identifier, "OprfKey"), Nok)
(oprf_key, _) = DeriveKeyPair(seed, "OPAQUE-DeriveKeyPair")
blinded_element = DeserializeElement(request.blinded_message)
evaluated_element = BlindEvaluate(oprf_key, blinded_element)
evaluated_message = SerializeElement(evaluated_element)
Create RegistrationResponse response with (evaluated_message, server_public_key)
return response
5.2.3. FinalizeRegistrationRequest
To create the user record used for subsequent authentication and
complete the registration flow, the client executes the following
function.
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FinalizeRegistrationRequest
Input:
- password, an opaque byte string containing the client's password.
- blind, an OPRF scalar value.
- response, a RegistrationResponse structure.
- server_identity, the optional encoded server identity.
- client_identity, the optional encoded client identity.
Output:
- record, a RegistrationRecord structure.
- export_key, an additional client key.
Exceptions:
- DeserializeError, when OPRF element deserialization fails.
def FinalizeRegistrationRequest(password, blind, response, server_identity, client_identity):
evaluated_element = DeserializeElement(response.evaluated_message)
oprf_output = Finalize(password, blind, evaluated_element)
stretched_oprf_output = Stretch(oprf_output)
randomized_password = Extract("", concat(oprf_output, stretched_oprf_output))
(envelope, client_public_key, masking_key, export_key) =
Store(randomized_password, response.server_public_key,
server_identity, client_identity)
Create RegistrationRecord record with (client_public_key, masking_key, envelope)
return (record, export_key)
See Section 6 for details about the output export_key usage.
6. Online Authenticated Key Exchange
The generic outline of OPAQUE with a 3-message AKE protocol includes
three messages: KE1, KE2, and KE3, where KE1 and KE2 include key
exchange shares, e.g., DH values, sent by the client and server,
respectively, and KE3 provides explicit client authentication and
full forward security (without it, forward secrecy is only achieved
against eavesdroppers, which is insufficient for OPAQUE security).
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This section describes the online authenticated key exchange protocol
flow, message encoding, and helper functions. This stage is composed
of a concurrent OPRF and key exchange flow. The key exchange
protocol is authenticated using the client and server credentials
established during registration; see Section 5. In the end, the
client proves its knowledge of the password, and both client and
server agree on (1) a mutually authenticated shared secret key and
(2) any optional application information exchange during the
handshake.
In this stage, the client inputs the following values:
* password: The client's password.
* client_identity: The client identity, as described in Section 4.
The server inputs the following values:
* server_private_key: The server's private key for the AKE protocol.
* server_public_key: The server's public key for the AKE protocol.
* server_identity: The server identity, as described in Section 4.
* record: The RegistrationRecord object corresponding to the
client's registration.
* credential_identifier: An identifier that uniquely represents the
credential.
* oprf_seed: The seed used to derive per-client OPRF keys.
The client receives two outputs: a session secret and an export key.
The export key is only available to the client and may be used for
additional application-specific purposes, as outlined in
Section 10.5. Clients and servers MUST NOT use the output export_key
before authenticating the peer in the authenticated key exchange
protocol. See Appendix B for more details about this requirement.
The server receives a single output: a session secret matching the
client's.
The protocol runs as shown below:
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Client Server
------------------------------------------------------
ke1 = GenerateKE1(password)
ke1
------------------------->
ke2 = GenerateKE2(server_identity, server_private_key,
server_public_key, record,
credential_identifier, oprf_seed, ke1)
ke2
<-------------------------
(ke3,
session_key,
export_key) = GenerateKE3(client_identity,
server_identity, ke2)
ke3
------------------------->
session_key = ServerFinish(ke3)
Both client and server may use implicit internal state objects to
keep necessary material for the OPRF and AKE, client_state and
server_state, respectively.
The client state ClientState may have the following fields:
* password: The client's password.
* blind: The random blinding inverter returned by Blind().
* client_ake_state: The ClientAkeState defined in Section 6.4.
The server state ServerState may have the following fields:
* server_ake_state: The ServerAkeState defined in Section 6.4.
Both of these states are ephemeral and should be erased after the
protocol completes.
The rest of this section describes these authenticated key exchange
messages and their parameters in more detail. Section 6.1 defines
the structure of the messages passed between client and server in the
above setup. Section 6.2 describes details of the functions and
corresponding parameters mentioned above. Section 6.3 discusses
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internal functions used for retrieving client credentials, and
Section 6.4 discusses how these functions are used to execute the
authenticated key exchange protocol.
6.1. AKE Messages
In this section, we define the KE1, KE2, and KE3 structs that make up
the AKE messages used in the protocol. KE1 is composed of a
CredentialRequest and AuthRequest, and KE2 is composed of a
CredentialResponse and AuthResponse.
struct {
uint8 client_nonce[Nn];
uint8 client_public_keyshare[Npk];
} AuthRequest;
client_nonce: A fresh randomly generated nonce of length Nn.
client_public_keyshare: A serialized client ephemeral public key of
fixed size Npk.
struct {
CredentialRequest credential_request;
AuthRequest auth_request;
} KE1;
credential_request: A CredentialRequest structure.
auth_request: An AuthRequest structure.
struct {
uint8 server_nonce[Nn];
uint8 server_public_keyshare[Npk];
uint8 server_mac[Nm];
} AuthResponse;
server_nonce: A fresh randomly generated nonce of length Nn.
server_public_keyshare: A server ephemeral public key of fixed size
Npk, where Npk depends on the corresponding prime order group.
server_mac: An authentication tag computed over the handshake
transcript computed using Km2, defined below.
struct {
CredentialResponse credential_response;
AuthResponse auth_response;
} KE2;
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credential_response: A CredentialResponse structure.
auth_response: An AuthResponse structure.
struct {
uint8 client_mac[Nm];
} KE3;
client_mac: An authentication tag computed over the handshake
transcript of fixed size Nm, computed using Km2, defined below.
6.2. AKE Functions
In this section, we define the main functions used to produce the AKE
messages in the protocol. Note that this section relies on
definitions of subroutines defined in later sections:
* CreateCredentialRequest, CreateCredentialResponse,
RecoverCredentials defined in Section 6.3
* AuthClientStart, AuthServerRespond, AuthClientFinalize, and
AuthServerFinalize defined in Section 6.4.3 and Section 6.4.4
6.2.1. GenerateKE1
The GenerateKE1 function begins the AKE protocol and produces the
client's KE1 output for the server.
GenerateKE1
State:
- state, a ClientState structure.
Input:
- password, an opaque byte string containing the client's password.
Output:
- ke1, a KE1 message structure.
def GenerateKE1(password):
request, blind = CreateCredentialRequest(password)
state.password = password
state.blind = blind
ke1 = AuthClientStart(request)
return ke1
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6.2.2. GenerateKE2
The GenerateKE2 function continues the AKE protocol by processing the
client's KE1 message and producing the server's KE2 output.
GenerateKE2
State:
- state, a ServerState structure.
Input:
- server_identity, the optional encoded server identity, which is set to
server_public_key if not specified.
- server_private_key, the server's private key.
- server_public_key, the server's public key.
- record, the client's RegistrationRecord structure.
- credential_identifier, an identifier that uniquely represents the credential.
- oprf_seed, the server-side seed of Nh bytes used to generate an oprf_key.
- ke1, a KE1 message structure.
- client_identity, the optional encoded client identity, which is set to
client_public_key if not specified.
Output:
- ke2, a KE2 structure.
def GenerateKE2(server_identity, server_private_key, server_public_key,
record, credential_identifier, oprf_seed, ke1, client_identity):
credential_response = CreateCredentialResponse(ke1.credential_request, server_public_key, record,
credential_identifier, oprf_seed)
cleartext_credentials = CreateCleartextCredentials(server_public_key,
record.client_public_key, server_identity, client_identity)
auth_response = AuthServerRespond(cleartext_credentials, server_private_key,
record.client_public_key, ke1, credential_response)
Create KE2 ke2 with (credential_response, auth_response)
return ke2
6.2.3. GenerateKE3
The GenerateKE3 function completes the AKE protocol for the client
and produces the client's KE3 output for the server, as well as the
session_key and export_key outputs from the AKE.
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GenerateKE3
State:
- state, a ClientState structure.
Input:
- client_identity, the optional encoded client identity, which is set
to client_public_key if not specified.
- server_identity, the optional encoded server identity, which is set
to server_public_key if not specified.
- ke2, a KE2 message structure.
Output:
- ke3, a KE3 message structure.
- session_key, the session's shared secret.
- export_key, an additional client key.
def GenerateKE3(client_identity, server_identity, ke2):
(client_private_key, cleartext_credentials, export_key) =
RecoverCredentials(state.password, state.blind, ke2.credential_response,
server_identity, client_identity)
(ke3, session_key) =
AuthClientFinalize(cleartext_credentials, client_private_key, ke2)
return (ke3, session_key, export_key)
6.2.4. ServerFinish
The ServerFinish function completes the AKE protocol for the server,
yielding the session_key. Since the OPRF is a two-message protocol,
KE3 has no element of the OPRF, and it, therefore, invokes the AKE's
AuthServerFinalize directly. The AuthServerFinalize function takes
KE3 as input and MUST verify the client authentication material it
contains before the session_key value can be used. This verification
is necessary to ensure forward secrecy against active attackers.
ServerFinish
State:
- state, a ServerState structure.
Input:
- ke3, a KE3 structure.
Output:
- session_key, the shared session secret if and only if ke3 is valid.
def ServerFinish(ke3):
return AuthServerFinalize(ke3)
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This function MUST NOT return the session_key value if the client
authentication material is invalid, and may instead return an
appropriate error message such as ClientAuthenticationError, invoked
from AuthServerFinalize.
6.3. Credential Retrieval
This section describes the sub-protocol run during authentication to
retrieve and recover the client credentials.
6.3.1. Credential Retrieval Messages
This section describes the CredentialRequest and CredentialResponse
messages exchanged between client and server to perform credential
retrieval.
struct {
uint8 blinded_message[Noe];
} CredentialRequest;
blinded_message: A serialized OPRF group element.
struct {
uint8 evaluated_message[Noe];
uint8 masking_nonce[Nn];
uint8 masked_response[Npk + Nn + Nm];
} CredentialResponse;
evaluated_message: A serialized OPRF group element.
masking_nonce: A nonce used for the confidentiality of the
masked_response field.
masked_response: An encrypted form of the server's public key and the
client's Envelope structure.
6.3.2. Credential Retrieval Functions
This section describes the CreateCredentialRequest,
CreateCredentialResponse, and RecoverCredentials functions used for
credential retrieval.
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6.3.2.1. CreateCredentialRequest
The CreateCredentialRequest is used by the client to initiate the
credential retrieval process, and it produces a CredentialRequest
message and OPRF state. Like CreateRegistrationRequest, this
function can fail with an InvalidInputError error with negligibile
probability. However, this should not occur since registration (via
CreateRegistrationRequest) will fail when provided the same password
input.
CreateCredentialRequest
Input:
- password, an opaque byte string containing the client's password.
Output:
- request, a CredentialRequest structure.
- blind, an OPRF scalar value.
Exceptions:
- InvalidInputError, when Blind fails
def CreateCredentialRequest(password):
(blind, blinded_element) = Blind(password)
blinded_message = SerializeElement(blinded_element)
Create CredentialRequest request with blinded_message
return (request, blind)
6.3.2.2. CreateCredentialResponse
The CreateCredentialResponse function is used by the server to
process the client's CredentialRequest message and complete the
credential retrieval process, producing a CredentialResponse.
There are two scenarios to handle for the construction of a
CredentialResponse object: either the record for the client exists
(corresponding to a properly registered client), or it was never
created (corresponding to an unregistered client identity, possibly
the result of an enumeration attack attempt).
In the case of an existing record with the corresponding identifier
credential_identifier, the server invokes the following function to
produce a CredentialResponse:
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CreateCredentialResponse
Input:
- request, a CredentialRequest structure.
- server_public_key, the public key of the server.
- record, an instance of RegistrationRecord which is the server's
output from registration.
- credential_identifier, an identifier that uniquely represents the credential.
- oprf_seed, the server-side seed of Nh bytes used to generate an oprf_key.
Output:
- response, a CredentialResponse structure.
Exceptions:
- DeserializeError, when OPRF element deserialization fails.
def CreateCredentialResponse(request, server_public_key, record,
credential_identifier, oprf_seed):
seed = Expand(oprf_seed, concat(credential_identifier, "OprfKey"), Nok)
(oprf_key, _) = DeriveKeyPair(seed, "OPAQUE-DeriveKeyPair")
blinded_element = DeserializeElement(request.blinded_message)
evaluated_element = BlindEvaluate(oprf_key, blinded_element)
evaluated_message = SerializeElement(evaluated_element)
masking_nonce = random(Nn)
credential_response_pad = Expand(record.masking_key,
concat(masking_nonce, "CredentialResponsePad"),
Npk + Nn + Nm)
masked_response = xor(credential_response_pad,
concat(server_public_key, record.envelope))
Create CredentialResponse response with (evaluated_message, masking_nonce, masked_response)
return response
In the case of a record that does not exist and if client enumeration
prevention is desired, the server MUST respond to the credential
request to fake the existence of the record. The server SHOULD
invoke the CreateCredentialResponse function with a fake client
record argument that is configured so that:
* record.client_public_key is set to a randomly generated public key
of length Npk
* record.masking_key is set to a random byte string of length Nh
* record.envelope is set to the byte string consisting only of zeros
of length Nn + Nm
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It is RECOMMENDED that a fake client record is created once (e.g. as
the first user record of the application) and stored alongside
legitimate client records. This allows servers to retrieve the
record in a time comparable to that of a legitimate client record.
Note that the responses output by either scenario are
indistinguishable to an adversary that is unable to guess the
registered password for the client corresponding to
credential_identifier.
6.3.2.3. RecoverCredentials
The RecoverCredentials function is used by the client to process the
server's CredentialResponse message and produce the client's private
key, server public key, and the export_key.
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RecoverCredentials
Input:
- password, an opaque byte string containing the client's password.
- blind, an OPRF scalar value.
- response, a CredentialResponse structure.
- server_identity, The optional encoded server identity.
- client_identity, The encoded client identity.
Output:
- client_private_key, the encoded client private key for the AKE protocol.
- cleartext_credentials, a CleartextCredentials structure.
- export_key, an additional client key.
Exceptions:
- DeserializeError, when OPRF element deserialization fails.
def RecoverCredentials(password, blind, response,
server_identity, client_identity):
evaluated_element = DeserializeElement(response.evaluated_message)
oprf_output = Finalize(password, blind, evaluated_element)
stretched_oprf_output = Stretch(oprf_output)
randomized_password = Extract("", concat(oprf_output, stretched_oprf_output))
masking_key = Expand(randomized_password, "MaskingKey", Nh)
credential_response_pad = Expand(masking_key,
concat(response.masking_nonce, "CredentialResponsePad"),
Npk + Nn + Nm)
concat(server_public_key, envelope) = xor(credential_response_pad,
response.masked_response)
(client_private_key, cleartext_credentials, export_key) =
Recover(randomized_password, server_public_key, envelope,
server_identity, client_identity)
return (client_private_key, cleartext_credentials, export_key)
6.4. 3DH Protocol
This section describes the authenticated key exchange protocol for
OPAQUE using 3DH, a 3-message AKE which satisfies the forward secrecy
and KCI properties discussed in Section 10.
The client AKE state ClientAkeState mentioned in Section 6 has the
following fields:
* client_secret: An opaque byte string of length Nsk.
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* ke1: A value of type KE1.
The server AKE state ServerAkeState mentioned in Section 6 has the
following fields:
* expected_client_mac: An opaque byte string of length Nm.
* session_key: An opaque byte string of length Nx.
Section 6.4.3 and Section 6.4.4 specify the inner workings of client
and server functions, respectively.
6.4.1. 3DH Key Exchange Functions
We assume the following functions to exist for all Diffie-Hellman key
exchange variants:
* DeriveDiffieHellmanKeyPair(seed): Derive a private and public
Diffie-Hellman key pair deterministically from the input seed.
The type of the private key depends on the implementation, whereas
the type of the public key is a byte string of Npk bytes.
* DiffieHellman(k, B): A function that performs the Diffie-Hellman
operation between the private input k and public input B. The
output of this function is a unique, fixed-length byte string.
It is RECOMMENDED to use Elliptic Curve Diffie-Hellman for this key
exchange protocol. Implementations for recommended groups in
Section 7, as well as groups covered by test vectors in Appendix D,
are described in the following sections.
6.4.1.1. 3DH ristretto255
This section describes the implementation of the Diffie-Hellman key
exchange functions based on ristretto255, as defined in [RISTRETTO].
* DeriveDiffieHellmanKeyPair(seed): This function is implemented as
DeriveKeyPair(seed, "OPAQUE-DeriveDiffieHellmanKeyPair"), where
DeriveKeyPair is as specified in [OPRF], Section 3.2. The public
value from DeriveKeyPair is encoded using SerializeElement from
Section 2.1 of [OPRF].
* DiffieHellman(k, B): Implemented as scalar multiplication as
described in Section 4 of [RISTRETTO] after decoding B from its
encoded input using the Decode function in Section 4.3.1 of
[RISTRETTO]. The output is then encoded using the
SerializeElement function of the OPRF group described in [OPRF],
Section 2.1.
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6.4.1.2. 3DH P-256
This section describes the implementation of the Diffie-Hellman key
exchange functions based on NIST P-256, as defined in [NISTCurves].
* DeriveDiffieHellmanKeyPair(seed): This function is implemented as
DeriveKeyPair(seed, "OPAQUE-DeriveDiffieHellmanKeyPair"), where
DeriveKeyPair is as specified in [OPRF], Section 3.2. The public
value from DeriveKeyPair is encoded using SerializeElement from
Section 2.1 of [OPRF].
* DiffieHellman(k, B): Implemented as scalar multiplication as
described in [NISTCurves], after decoding B from its encoded input
using the compressed Octet-String-to-Elliptic-Curve-Point method
according to [NISTCurves]. The output is then encoded using the
SerializeElement function of the OPRF group described in [OPRF],
Section 2.1.
6.4.1.3. 3DH Curve25519
This section describes the implementation of the Diffie-Hellman key
exchange functions based on Curve25519, as defined in [Curve25519].
* DeriveDiffieHellmanKeyPair(seed): This function is implemented by
returning the private key k based on seed (of length Nseed = 32
bytes), as described in Section 5 of [Curve25519], as well as the
result of DiffieHellman(k, B), where B is the base point of
Curve25519.
* DiffieHellman(k, B): Implemented using the X25519 function in
Section 5 of [Curve25519]. The output is then used raw, with no
processing.
6.4.2. Key Schedule Functions
This section contains functions used for the AKE key schedule.
6.4.2.1. Transcript Functions
The OPAQUE-3DH key derivation procedures make use of the functions
below, re-purposed from TLS 1.3 [RFC8446].
Expand-Label(Secret, Label, Context, Length) =
Expand(Secret, CustomLabel, Length)
Where CustomLabel is specified as:
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struct {
uint16 length = Length;
opaque label<8..255> = "OPAQUE-" + Label;
uint8 context<0..255> = Context;
} CustomLabel;
Derive-Secret(Secret, Label, Transcript-Hash) =
Expand-Label(Secret, Label, Transcript-Hash, Nx)
Note that the Label parameter is not a NULL-terminated string.
OPAQUE-3DH can optionally include application-specific, shared
context information in the transcript, such as configuration
parameters or application-specific info, e.g. "appXYZ-v1.2.3".
The OPAQUE-3DH key schedule requires a preamble, which is computed as
follows.
Preamble
Parameters:
- context, optional shared context information.
Input:
- client_identity, the optional encoded client identity, which is set
to client_public_key if not specified.
- ke1, a KE1 message structure.
- server_identity, the optional encoded server identity, which is set
to server_public_key if not specified.
- credential_response, the corresponding field on the KE2 structure.
- server_nonce, the corresponding field on the AuthResponse structure.
- server_public_keyshare, the corresponding field on the AuthResponse structure.
Output:
- preamble, the protocol transcript with identities and messages.
def Preamble(client_identity, ke1, server_identity, credential_response,
server_nonce, server_public_keyshare):
preamble = concat("OPAQUEv1-",
I2OSP(len(context), 2), context,
I2OSP(len(client_identity), 2), client_identity,
ke1,
I2OSP(len(server_identity), 2), server_identity,
credential_response,
server_nonce,
server_public_keyshare)
return preamble
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6.4.2.2. Shared Secret Derivation
The OPAQUE-3DH shared secret derived during the key exchange protocol
is computed using the following helper function.
DeriveKeys
Input:
- ikm, input key material.
- preamble, the protocol transcript with identities and messages.
Output:
- Km2, a MAC authentication key.
- Km3, a MAC authentication key.
- session_key, the shared session secret.
def DeriveKeys(ikm, preamble):
prk = Extract("", ikm)
handshake_secret = Derive-Secret(prk, "HandshakeSecret", Hash(preamble))
session_key = Derive-Secret(prk, "SessionKey", Hash(preamble))
Km2 = Derive-Secret(handshake_secret, "ServerMAC", "")
Km3 = Derive-Secret(handshake_secret, "ClientMAC", "")
return (Km2, Km3, session_key)
6.4.3. 3DH Client Functions
The AuthClientStart function is used by the client to create a KE1
structure.
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AuthClientStart
Parameters:
- Nn, the nonce length.
State:
- state, a ClientAkeState structure.
Input:
- credential_request, a CredentialRequest structure.
Output:
- ke1, a KE1 structure.
def AuthClientStart(credential_request):
client_nonce = random(Nn)
client_keyshare_seed = random(Nseed)
(client_secret, client_public_keyshare) = DeriveDiffieHellmanKeyPair(client_keyshare_seed)
Create AuthRequest auth_request with (client_nonce, client_public_keyshare)
Create KE1 ke1 with (credential_request, auth_request)
state.client_secret = client_secret
state.ke1 = ke1
return ke1
The AuthClientFinalize function is used by the client to create a KE3
message and output session_key using the server's KE2 message and
recovered credential information.
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AuthClientFinalize
State:
- state, a ClientAkeState structure.
Input:
- cleartext_credentials, a CleartextCredentials structure.
- client_private_key, the client's private key.
- ke2, a KE2 message structure.
Output:
- ke3, a KE3 structure.
- session_key, the shared session secret.
Exceptions:
- ServerAuthenticationError, the handshake fails.
def AuthClientFinalize(cleartext_credentials, client_private_key, ke2):
dh1 = DiffieHellman(state.client_secret, ke2.auth_response.server_public_keyshare)
dh2 = DiffieHellman(state.client_secret, cleartext_credentials.server_public_key)
dh3 = DiffieHellman(client_private_key, ke2.auth_response.server_public_keyshare)
ikm = concat(dh1, dh2, dh3)
preamble = Preamble(cleartext_credentials.client_identity,
state.ke1,
cleartext_credentials.server_identity,
ke2.credential_response,
ke2.auth_response.server_nonce,
ke2.auth_response.server_public_keyshare)
Km2, Km3, session_key = DeriveKeys(ikm, preamble)
expected_server_mac = MAC(Km2, Hash(preamble))
if !ct_equal(ke2.auth_response.server_mac, expected_server_mac),
raise ServerAuthenticationError
client_mac = MAC(Km3, Hash(concat(preamble, expected_server_mac)))
Create KE3 ke3 with client_mac
return (ke3, session_key)
6.4.4. 3DH Server Functions
The AuthServerRespond function is used by the server to process the
client's KE1 message and public credential information to create a
KE2 message.
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AuthServerRespond
Parameters:
- Nn, the nonce length.
State:
- state, a ServerAkeState structure.
Input:
- cleartext_credentials, a CleartextCredentials structure.
- server_private_key, the server's private key.
- client_public_key, the client's public key.
- ke1, a KE1 message structure.
Output:
- auth_response, an AuthResponse structure.
def AuthServerRespond(cleartext_credentials, server_private_key, client_public_key, ke1, credential_response):
server_nonce = random(Nn)
server_keyshare_seed = random(Nseed)
(server_private_keyshare, server_public_keyshare) = DeriveDiffieHellmanKeyPair(server_keyshare_seed)
preamble = Preamble(cleartext_credentials.client_identity,
ke1,
cleartext_credentials.server_identity,
credential_response,
server_nonce,
server_public_keyshare)
dh1 = DiffieHellman(server_private_keyshare, ke1.auth_request.client_public_keyshare)
dh2 = DiffieHellman(server_private_key, ke1.auth_request.client_public_keyshare)
dh3 = DiffieHellman(server_private_keyshare, client_public_key)
ikm = concat(dh1, dh2, dh3)
Km2, Km3, session_key = DeriveKeys(ikm, preamble)
server_mac = MAC(Km2, Hash(preamble))
state.expected_client_mac = MAC(Km3, Hash(concat(preamble, server_mac)))
state.session_key = session_key
Create AuthResponse auth_response with (server_nonce, server_public_keyshare, server_mac)
return auth_response
The AuthServerFinalize function is used by the server to process the
client's KE3 message and output the final session_key.
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AuthServerFinalize
State:
- state, a ServerAkeState structure.
Input:
- ke3, a KE3 structure.
Output:
- session_key, the shared session secret if and only if ke3 is valid.
Exceptions:
- ClientAuthenticationError, the handshake fails.
def AuthServerFinalize(ke3):
if !ct_equal(ke3.client_mac, state.expected_client_mac):
raise ClientAuthenticationError
return state.session_key
7. Configurations
An OPAQUE-3DH configuration is a tuple (OPRF, KDF, MAC, Hash, KSF,
Group, Context) such that the following conditions are met:
* The OPRF protocol uses the "base mode" variant of [OPRF] and
implements the interface in Section 2. Examples include
ristretto255-SHA512 and P256-SHA256.
* The KDF, MAC, and Hash functions implement the interfaces in
Section 2. Examples include HKDF [RFC5869] for the KDF, HMAC
[RFC2104] for the MAC, and SHA-256 and SHA-512 for the Hash
functions. If an extensible output function such as SHAKE128
[FIPS202] is used then the output length Nh MUST be chosen to
align with the target security level of the OPAQUE configuration.
For example, if the target security parameter for the
configuration is 128 bits, then Nh SHOULD be at least 32 bytes.
* The KSF is determined by the application and implements the
interface in Section 2. As noted, collision resistance is
required. Examples for KSF include Argon2id [ARGON2], scrypt
[SCRYPT], and PBKDF2 [PBKDF2] with fixed parameter choices. See
Section 8 for more information about this choice of function.
* The Group mode identifies the group used in the OPAQUE-3DH AKE.
This SHOULD match that of the OPRF. For example, if the OPRF is
ristretto255-SHA512, then Group SHOULD be ristretto255.
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Context is the shared parameter used to construct the preamble in
Section 6.4.2.1. This parameter SHOULD include any application-
specific configuration information or parameters that are needed to
prevent cross-protocol or downgrade attacks.
Absent an application-specific profile, the following configurations
are RECOMMENDED:
* ristretto255-SHA512, HKDF-SHA-512, HMAC-SHA-512, SHA-512,
Argon2id(S = zeroes(16), p = 4, T = Nh, m = 2^21, t = 1, v = 0x13,
K = nil, X = nil, y = 2), ristretto255
* P256-SHA256, HKDF-SHA-256, HMAC-SHA-256, SHA-256, Argon2id(S =
zeroes(16), p = 4, T = Nh, m = 2^21, t = 1, v = 0x13, K = nil, X =
nil, y = 2), P-256
* P256-SHA256, HKDF-SHA-256, HMAC-SHA-256, SHA-256, scrypt(N =
32768, r = 8, p = 1), P-256
The above recommended configurations target 128-bit security.
Future configurations may specify different combinations of dependent
algorithms, with the following considerations:
1. The size of AKE public and private keys -- Npk and Nsk,
respectively -- must adhere to the output length limitations of
the KDF Expand function. If HKDF is used, this means Npk, Nsk <=
255 * Nx, where Nx is the output size of the underlying hash
function. See [RFC5869] for details.
2. The output size of the Hash function SHOULD be long enough to
produce a key for MAC of suitable length. For example, if MAC is
HMAC-SHA256, then Nh could be 32 bytes.
8. Application Considerations
Beyond choosing an appropriate configuration, there are several
parameters which applications can use to control OPAQUE:
* Credential identifier: As described in Section 5, this is a unique
handle to the client's credential being stored. In applications
where there are alternate client identities that accompany an
account, such as a username or email address, this identifier can
be set to those alternate values. For simplicity, applications
may choose to set credential_identifier to be equal to
client_identity. Applications MUST NOT use the same credential
identifier for multiple clients.
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* Context information: As described in Section 7, applications may
include a shared context string that is authenticated as part of
the handshake. This parameter SHOULD include any configuration
information or parameters that are needed to prevent cross-
protocol or downgrade attacks. This context information is not
sent over the wire in any key exchange messages. However,
applications may choose to send it alongside key exchange messages
if needed for their use case.
* Client and server identities: As described in Section 4, clients
and servers are identified with their public keys by default.
However, applications may choose alternate identities that are
pinned to these public keys. For example, servers may use a
domain name instead of a public key as their identifier. Absent
alternate notions of identity, applications SHOULD set these
identities to nil and rely solely on public key information.
* Configuration and envelope updates: Applications may wish to
update or change their configuration or other parameters which
affect the client's RegistrationRecord over time. Some reasons
for changing these are to use different cryptographic algorithms,
e.g., a different KSF with improved parameters, or to update key
material that is cryptographically bound to the
RegistrationRecord, such as the server's public key
(server_public_key). Any such change will require users to re-
register to create a new RegistrationRecord. Supporting these
types of updates can be helpful for applications which anticipate
such changes in their deployment setting.
* Password hardening parameters: Key stretching is done to help
prevent password disclosure in the event of server compromise; see
Section 10.9. There is no ideal or default set of parameters,
though relevant specifications for KSFs give some reasonable
defaults.
* Enumeration prevention: As described in Section 6.3.2.2, if
servers receive a credential request for a non-existent client,
they SHOULD respond with a "fake" response to prevent active
client enumeration attacks. Servers that implement this
mitigation SHOULD use the same configuration information (such as
the oprf_seed) for all clients; see Section 10.10. In settings
where this attack is not a concern, servers may choose to not
support this functionality.
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* Handling password changes: In the event of a password change, the
client and server can run the offline registration phase using the
new password as a fresh instance (ensuring to resample all random
values). The resulting registration record can then replace the
previous record corresponding to the client's old password
registration.
9. Implementation Considerations
This section documents considerations for OPAQUE implementations.
This includes implementation safeguards and error handling
considerations.
9.1. Implementation Safeguards
Certain information created, exchanged, and processed in OPAQUE is
sensitive. Specifically, all private key material and intermediate
values, along with the outputs of the key exchange phase, are all
secret. Implementations should not retain these values in memory
when no longer needed. Moreover, all operations, particularly the
cryptographic and group arithmetic operations, should be constant-
time and independent of the bits of any secrets. This includes any
conditional branching during the creation of the credential response,
as needed to mitigate client enumeration attacks.
As specified in Section 5 and Section 6, OPAQUE only requires the
client password as input to the OPRF for registration and
authentication. However, if client_identity can be bound to the
client's registration record (in that the identity will not change
during the lifetime of the record), then an implementation SHOULD
incorporate client_identity alongside the password as input to the
OPRF. Furthermore, it is RECOMMENDED to incorporate server_identity
alongside the password as input to the OPRF. These additions provide
domain separation for clients and servers; see Section 10.2.
Finally, note that online guessing attacks (against any aPAKE) can be
done from both the client side and the server side. In particular, a
malicious server can attempt to simulate honest responses to learn
the client's password. While this constitutes an exhaustive online
attack, hence as expensive as an online guessing attack from the
client side, it can be mitigated when the channel between client and
server is authenticated, e.g., using server-authenticated TLS. In
such cases, these online attacks are limited to clients and the
authenticated server itself. Moreover, such a channel provides
privacy of user information, including identity and envelope values.
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9.2. Error Considerations
Some functions included in this specification are fallible. For
example, the authenticated key exchange protocol may fail because the
client's password was incorrect or the authentication check failed,
yielding an error. The explicit errors generated throughout this
specification, along with conditions that lead to each error, are as
follows:
* EnvelopeRecoveryError: The envelope Recover function failed to
produce any authentication key material; Section 4.1.3.
* ServerAuthenticationError: The client failed to complete the
authenticated key exchange protocol with the server;
Section 6.4.3.
* ClientAuthenticationError: The server failed to complete the
authenticated key exchange protocol with the client;
Section 6.4.4.
Beyond these explicit errors, OPAQUE implementations can produce
implicit errors. For example, if protocol messages sent between
client and server do not match their expected size, an implementation
should produce an error. More generally, if any protocol message
received from the peer is invalid, perhaps because the message
contains an invalid public key (indicated by the AKE
DeserializeElement function failing) or an invalid OPRF element
(indicated by the OPRF DeserializeElement), then an implementation
should produce an error.
The errors in this document are meant as a guide for implementors.
They are not an exhaustive list of all the errors an implementation
might emit. For example, an implementation might run out of memory.
10. Security Considerations
OPAQUE is defined as the composition of two functionalities: an OPRF
and an AKE protocol. It can be seen as a "compiler" for transforming
any AKE protocol (with KCI security and forward secrecy; see below)
into a secure aPAKE protocol. In OPAQUE, the client derives a
private key during password registration and retrieves this key each
time it needs to authenticate to the server. The OPRF security
properties ensure that only the correct password can unlock the
private key while at the same time avoiding potential offline
guessing attacks. This general composability property provides great
flexibility and enables a variety of OPAQUE instantiations, from
optimized performance to integration with existing authenticated key
exchange protocols such as TLS.
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10.1. Notable Design Differences
The specification as written here differs from the original
cryptographic design in [JKX18] and the corresponding CFRG document
[I-D.krawczyk-cfrg-opaque-03], both of which were used as input to
the CFRG PAKE competition. This section describes these differences,
including their motivation and explanation as to why they preserve
the provable security of OPAQUE based on [JKX18].
The following list enumerates important functional differences that
were made as part of the protocol specification process to address
application or implementation considerations.
* Clients construct envelope contents without revealing the password
to the server, as described in Section 5, whereas the servers
construct envelopes in [JKX18]. This change adds to the security
of the protocol. [JKX18] considered the case where the envelope
was constructed by the server for reasons of compatibility with
previous UC modeling. [HJKW23] analyzes the registration phase as
specified in this document. This change was made to support
registration flows where the client chooses the password and
wishes to keep it secret from the server, and it is compatible
with the variant in [JKX18] that was originally analyzed.
* Envelopes do not contain encrypted credentials. Instead,
envelopes contain information used to derive client private key
material for the AKE. This change improves the assumption behind
the protocol by getting rid of equivocality and random key
robustness for the encryption function. The random-key robustness
property defined in Section 2.2 is only needed for the MAC
function. This change was made for two reasons. First, it
reduces the number of bytes stored in envelopes, which is a
helpful improvement for large applications of OPAQUE with many
registered users. Second, it removes the need for client
applications to generate private keys during registration.
Instead, this responsibility is handled by OPAQUE, thereby
simplifying the client interface to the protocol.
* Envelopes are masked with a per-user masking key as a way of
preventing client enumeration attacks. See Section 10.10 for more
details. This extension is not needed for the security of OPAQUE
as an aPAKE but only used to provide a defense against enumeration
attacks. In the analysis, the masking key can be simulated as a
(pseudo) random key. This change was made to support real-world
use cases where client or user enumeration is a security (or
privacy) risk.
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* Per-user OPRF keys are derived from a client identity and cross-
user PRF seed as a mitigation against client enumeration attacks.
See Section 10.10 for more details. The analysis of OPAQUE
assumes OPRF keys of different users are independently random or
pseudorandom. Deriving these keys via a single PRF (i.e., with a
single cross-user key) applied to users' identities satisfies this
assumption. This change was made to support real-world use cases
where client or user enumeration is a security (or privacy) risk.
* The protocol outputs an export key for the client in addition to a
shared session key that can be used for application-specific
purposes. This key is a pseudorandom value derived from the
client password (among other values) and has no influence on the
security analysis (it can be simulated with a random output).
This change was made to support more application use cases for
OPAQUE, such as the use of OPAQUE for end-to-end encrypted
backups; see [WhatsAppE2E].
* The protocol admits optional application-layer client and server
identities. In the absence of these identities, the client and
server are authenticated against their public keys. Binding
authentication to identities is part of the AKE part of OPAQUE.
The type of identities and their semantics are application
dependent and independent of the protocol analysis. This change
was made to simplify client and server interfaces to the protocol
by removing the need to specify additional identities alongside
their corresponding public authentication keys when not needed.
* The protocol admits application-specific context information
configured out-of-band in the AKE transcript. This allows domain
separation between different application uses of OPAQUE. This is
a mechanism for the AKE component and is best practice for domain
separation between different applications of the protocol. This
change was made to allow different applications to use OPAQUE
without the risk of cross-protocol attacks.
* Servers use a separate identifier for computing OPRF evaluations
and indexing into the registration record storage, called the
credential_identifier. This allows clients to change their
application-layer identity (client_identity) without inducing
server-side changes, e.g., by changing an email address associated
with a given account. This mechanism is part of the derivation of
OPRF keys via a single PRF. As long as the derivation of
different OPRF keys from a single PRF has different PRF inputs,
the protocol is secure. The choice of such inputs is up to the
application.
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* [JKX18] comments on a defense against offline dictionary attacks
upon server compromise or honest-but-curious servers. The authors
suggest implementing the OPRF phase as a threshold OPRF [TOPPSS],
effectively forcing an attacker to act online or to control at
least t key shares (among the total n), where t is the threshold
number of shares necessary to recombine the secret OPRF key, and
only then be able to run an offline dictionary attack. This
implementation only affects the server and changes nothing for the
client. Furthermore, if the threshold OPRF servers holding these
keys are separate from the authentication server, then recovering
all n shares would still not suffice to run an offline dictionnary
attack without access to the client record database. However,
this mechanism is out of scope for this document.
The following list enumerates notable differences and refinements
from the original cryptographic design in [JKX18] and the
corresponding CFRG document [I-D.krawczyk-cfrg-opaque-03] that were
made to make this specification suitable for interoperable
implementations.
* [JKX18] used a generic prime-order group for the DH-OPRF and HMQV
operations, and includes necessary prime-order subgroup checks
when receiving attacker-controlled values over the wire. This
specification instantiates the prime-order group used for 3DH
using prime-order groups based on elliptic curves, as described in
[I-D.irtf-cfrg-voprf], Section 2.1. This specification also
delegates OPRF group choice and operations to
[I-D.irtf-cfrg-voprf]. As such, the prime-order group as used in
the OPRF and 3DH as specified in this document both adhere to the
requirements as [JKX18].
* [JKX18] specified DH-OPRF (see Appendix B) to instantiate the OPRF
functionality in the protocol. A critical part of DH-OPRF is the
hash-to-group operation, which was not instantiated in the
original analysis. However, the requirements for this operation
were included. This specification instantiates the OPRF
functionality based on the [I-D.irtf-cfrg-voprf], which is
identical to the DH-OPRF functionality in [JKX18] and, concretely,
uses the hash-to-curve functions in [I-D.irtf-cfrg-hash-to-curve].
All hash-to-curve methods in [I-D.irtf-cfrg-hash-to-curve] are
compliant with the requirement in [JKX18], namely, that the output
be a member of the prime-order group.
* [JKX18] and [I-D.krawczyk-cfrg-opaque-03] both used HMQV as the
AKE for the protocol. However, this document fully specifies 3DH
instead of HMQV (though a sketch for how to instantiate OPAQUE
using HMQV is included in Appendix C.1). Since 3DH satisfies the
essential requirements for the AKE as described in [JKX18] and
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[I-D.krawczyk-cfrg-opaque-03], as recalled in Section 10.2, this
change preserves the overall security of the protocol. 3DH was
chosen for its simplicity and ease of implementation.
* The DH-OPRF and HMQV instantiation of OPAQUE in [JKX18], Figure 12
uses a different transcript than that which is described in this
specification. In particular, the key exchange transcript
specified in Section 6.4 is a superset of the transcript as
defined in [JKX18]. This was done to align with best practices,
such as is done for key exchange protocols like TLS 1.3 [RFC8446].
* Neither [JKX18] nor [I-D.krawczyk-cfrg-opaque-03] included wire
format details for the protocol, which is essential for
interoperability. This specification fills this gap by including
such wire format details and corresponding test vectors; see
Appendix D.
10.2. Security Analysis
Jarecki et al. [JKX18] proved the security of OPAQUE (modulo the
design differences outlined in Section 10.1) in a strong aPAKE model
that ensures security against pre-computation attacks and is
formulated in the Universal Composability (UC) framework [Canetti01]
under the random oracle model. This assumes security of the OPRF
function and the underlying key exchange protocol.
OPAQUE's design builds on a line of work initiated in the seminal
paper of Ford and Kaliski [FK00] and is based on the HPAKE protocol
of Xavier Boyen [Boyen09] and the (1,1)-PPSS protocol from Jarecki et
al. [JKKX16]. None of these papers considered security against pre-
computation attacks or presented a proof of aPAKE security (not even
in a weak model).
The KCI property required from AKE protocols for use with OPAQUE
states that knowledge of a party's private key does not allow an
attacker to impersonate others to that party. This is an important
security property achieved by most public-key based AKE protocols,
including protocols that use signatures or public key encryption for
authentication. It is also a property of many implicitly
authenticated protocols, e.g., HMQV, but not all of them. We also
note that key exchange protocols based on shared keys do not satisfy
the KCI requirement, hence they are not considered in the OPAQUE
setting. We note that KCI is needed to ensure a crucial property of
OPAQUE: even upon compromise of the server, the attacker cannot
impersonate the client to the server without first running an
exhaustive dictionary attack. Another essential requirement from AKE
protocols for use in OPAQUE is to provide forward secrecy (against
active attackers).
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In [JKX18], security is proven for one instance (i.e., one key) of
the OPAQUE protocol, and without batching. There is currently no
security analysis available for the OPAQUE protocol described in this
document in a setting with multiple server keys or batching.
As stated in Section 9.1, incorporating client_identity adds domain
separation, in particular against servers that choose the same OPRF
key for multiple clients. The client_identity as input to the OPRF
also acts as a key identifier that would be required for a proof of
the protocol in the multi-key setting; the OPAQUE analysis in [JKX18]
assumes single server-key instances. Adding server_identityto the
OPRF input provides domain separation for clients that reuse the
sameclient_identity` across different server instantiations.
10.3. Related Protocols
Despite the existence of multiple designs for (PKI-free) aPAKE
protocols, none of these protocols are secure against pre-computation
attacks. This includes protocols that have recent analyses in the UC
model such as AuCPace [AuCPace] and SPAKE2+ [SPAKE2plus]. In
particular, none of these protocols can use the standard technique
against pre-computation that combines secret random values ("salt")
into the one-way password mappings. Either these protocols do not
use a salt at all or, if they do, they transmit the salt from server
to client in the clear, hence losing the secrecy of the salt and its
defense against pre-computation.
We note that as shown in [JKX18], these protocols, and any aPAKE in
the model from [GMR06], can be converted into an aPAKE secure against
pre-computation attacks at the expense of an additional OPRF
execution.
Beyond AuCPace and SPAKE2+, the most widely deployed PKI-free aPAKE
is SRP [RFC2945], which is vulnerable to pre-computation attacks,
lacks proof of security, and is less efficient than OPAQUE.
Moreover, SRP requires a ring as it mixes addition and multiplication
operations, and thus does not work over standard elliptic curves.
OPAQUE is therefore a suitable replacement for applications that use
SRP.
10.4. Identities
AKE protocols generate keys that need to be uniquely and verifiably
bound to a pair of identities. In the case of OPAQUE, those
identities correspond to client_identity and server_identity. Thus,
it is essential for the parties to agree on such identities,
including an agreed bit representation of these identities as needed.
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Note that the method of transmission of client_identity from client
to server is outside the scope of this protocol, and it is up to an
application to choose how this identity should be delivered (for
instance, alongside the first OPAQUE message, or perhaps agreed upon
before the OPAQUE protocol begins).
Applications may have different policies about how and when
identities are determined. A natural approach is to tie
client_identity to the identity the server uses to fetch the envelope
(hence determined during password registration) and to tie
server_identity to the server identity used by the client to initiate
an offline password registration or online authenticated key exchange
session. server_identity and client_identity can also be part of the
envelope or be tied to the parties' public keys. In principle,
identities may change across different sessions as long as there is a
policy that can establish if the identity is acceptable or not to the
peer. However, we note that the public keys of both the server and
the client must always be those defined at the time of password
registration.
The client identity (client_identity) and server identity
(server_identity) are optional parameters that are left to the
application to designate as aliases for the client and server. If
the application layer does not supply values for these parameters,
then they will be omitted from the creation of the envelope during
the registration stage. Furthermore, they will be substituted with
client_identity = client_public_key and server_identity =
server_public_key during the authenticated key exchange stage.
The advantage of supplying a custom client_identity and
server_identity (instead of simply relying on a fallback to
client_public_key and server_public_key) is that the client can then
ensure that any mappings between client_identity and
client_public_key (and server_identity and server_public_key) are
protected by the authentication from the envelope. Then, the client
can verify that the client_identity and server_identity contained in
its envelope match the client_identity and server_identity supplied
by the server.
However, if this extra layer of verification is unnecessary for the
application, then simply leaving client_identity and server_identity
unspecified (and using client_public_key and server_public_key
instead) is acceptable.
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10.5. Export Key Usage
The export key can be used (separately from the OPAQUE protocol) to
provide confidentiality and integrity to other data which only the
client should be able to process. For instance, if the client wishes
to store secrets with a third party, then this export key can be used
by the client to encrypt these secrets so that they remain hidden
from a passive adversary that does not have access to the server's
secret keys or the client's password.
10.6. Static Diffie-Hellman Oracles
While one can expect the practical security of the OPRF function
(namely, the hardness of computing the function without knowing the
key) to be in the order of computing discrete logarithms or solving
Diffie-Hellman, Brown and Gallant [BG04] and Cheon [Cheon06] show an
attack that slightly improves on generic attacks. For typical
curves, the attack requires an infeasible number of calls to the OPRF
or results in insignificant security loss; see [OPRF] for more
information. For OPAQUE, these attacks are particularly impractical
as they translate into an infeasible number of failed authentication
attempts directed at individual users.
10.7. Random-Key Robust MACs
The random-key robustness property for a MAC states that, given two
random keys k1 and k2, it is infeasible to find a message m such that
MAC(k1, m) = MAC(k2, m). Note that in general, not every MAC
function is key-robust. In particular, GMAC (which underlies GCM)
does not satisfy key-robustness, whereas HMAC with a collision-
resistant hash function does satisfy key-robustness.
An application can choose to use a non-key-robust MAC within the AKE
portion of the protocol described in Section 6.4, but it MUST use a
key-robust MAC for the creation of the auth_tag parameter in
Section 4.1.2.
10.8. Input Validation
Both client and server MUST validate the other party's public key(s)
used for the execution of OPAQUE. This includes the keys shared
during the offline registration phase, as well as any keys shared
during the online key agreement phase. The validation procedure
varies depending on the type of key. For example, for OPAQUE
instantiations using 3DH with P-256, P-384, or P-521 as the
underlying group, validation is as specified in Section 5.6.2.3.4 of
[keyagreement]. This includes checking that the coordinates are in
the correct range, that the point is on the curve, and that the point
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is not the point at infinity. Additionally, validation MUST ensure
the Diffie-Hellman shared secret is not the point at infinity.
10.9. OPRF Key Stretching
Applying a key stretching function to the output of the OPRF greatly
increases the cost of an offline attack upon the compromise of the
credential file at the server. Applications SHOULD select parameters
for the KSF that balance cost and complexity across different client
implementations and deployments. Note that in OPAQUE, the key
stretching function is executed by the client, as opposed to the
server in traditional password hashing scenarios. This means that
applications must consider a tradeoff between the performance of the
protocol on clients (specifically low-end devices) and protection
against offline attacks after a server compromise.
10.10. Client Enumeration
Client enumeration refers to attacks where the attacker tries to
learn whether a given user identity is registered with a server or
whether a re-registration or change of password was performed for
that user. OPAQUE counters these attacks by requiring servers to act
with unregistered client identities in a way that is
indistinguishable from their behavior with existing registered
clients. Servers do this by simulating a fake CredentialResponse as
specified in Section 6.3.2.2 for unregistered users, and also
encrypting CredentialResponse using a masking key. In this way, real
and fake CredentialResponse messages are indistinguishable from one
another. Implementations must also take care to avoid side-channel
leakage (e.g., timing attacks) from helping differentiate these
operations from a regular server response. Note that this may
introduce possible abuse vectors since the server's cost of
generating a CredentialResponse is less than that of the client's
cost of generating a CredentialRequest. Server implementations may
choose to forego the construction of a simulated credential response
message for an unregistered client if these client enumeration
attacks can be mitigated through other application-specific means or
are otherwise not applicable for their threat model.
OPAQUE does not prevent against this type of attack during the
registration flow. Servers necessarily react differently during the
registration flow between registered and unregistered clients. This
allows an attacker to use the server's response during registration
as an oracle for whether a given client identity is registered.
Applications should mitigate against this type of attack by rate
limiting or otherwise restricting the registration flow.
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10.11. Protecting the Registration Masking Key
The user enumeration prevention method described in this document
uses a symmetric encryption key, masking_key, generated and sent to
the server by the client during registration. This requires a
confidential channel between client and server during registration,
e.g., using TLS [RFC8446]. If the channel is only authenticated
(this is a requirement for correct identification of the parties), a
confidential channel can be established using public-key encryption,
e.g., with HPKE [RFC9180]. However, the details of this mechanism
are out of scope of this document.
10.12. Password Salt and Storage Implications
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. Also, clients never disclose their passwords to the server,
even during registration. Note that a corrupted server can run an
exhaustive offline dictionary attack to validate guesses for the
client's password; this is inevitable in any (single-server) aPAKE
protocol. It can be avoided in the case of OPAQUE by resorting to a
multi-server threshold OPRF implementation, e.g., [TOPPSS].
Furthermore, if the server does not sample the PRF seed with
sufficiently high entropy, or if it is not kept hidden from an
adversary, then any derivatives from the client's password may also
be susceptible to an offline dictionary attack to recover the
original password.
Some applications may require learning the client's password for
enforcing password rules. Doing so invalidates this important
security property of OPAQUE and is NOT RECOMMENDED, unless it is not
possible for applications to move such checks to the client. Note
that limited checks at the server are possible to implement, e.g.,
detecting repeated passwords upon re-registrations or password
change.
In general, passwords should be selected with sufficient entropy to
avoid being susceptible to recovery through dictionary attacks, both
online and offline.
10.13. AKE Private Key Storage
Server implementations of OPAQUE do not need access to the raw AKE
private key. They only require the ability to compute shared secrets
as specified in Section 6.4.2. Thus, applications may store the
server AKE private key in a Hardware Security Module (HSM) or
similar. Upon compromise of the OPRF seed and client envelopes, this
would prevent an attacker from using this data to mount a server
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spoofing attack. Supporting implementations need to consider
allowing separate AKE and OPRF algorithms in cases where the HSM is
incompatible with the OPRF algorithm.
11. IANA Considerations
This document makes no IANA requests.
12. References
12.1. Normative References
[I-D.irtf-cfrg-voprf]
Davidson, A., Faz-Hernandez, A., Sullivan, N., and C. A.
Wood, "Oblivious Pseudorandom Functions (OPRFs) using
Prime-Order Groups", Work in Progress, Internet-Draft,
draft-irtf-cfrg-voprf-21, 21 February 2023,
<https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-
voprf-21>.
[OPRF] Davidson, A., Faz-Hernandez, A., Sullivan, N., and C. A.
Wood, "Oblivious Pseudorandom Functions (OPRFs) using
Prime-Order Groups", Work in Progress, Internet-Draft,
draft-irtf-cfrg-voprf-21, 21 February 2023,
<https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-
voprf-21>.
[RFC2104] Krawczyk, H., Bellare, M., and R. Canetti, "HMAC: Keyed-
Hashing for Message Authentication", RFC 2104,
DOI 10.17487/RFC2104, February 1997,
<https://www.rfc-editor.org/rfc/rfc2104>.
[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/rfc/rfc2119>.
[RFC4086] Eastlake 3rd, D., Schiller, J., and S. Crocker,
"Randomness Requirements for Security", BCP 106, RFC 4086,
DOI 10.17487/RFC4086, June 2005,
<https://www.rfc-editor.org/rfc/rfc4086>.
[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/rfc/rfc8174>.
12.2. Informative References
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[ARGON2] Biryukov, A., Dinu, D., Khovratovich, D., and S.
Josefsson, "Argon2 Memory-Hard Function for Password
Hashing and Proof-of-Work Applications", RFC 9106,
DOI 10.17487/RFC9106, September 2021,
<https://www.rfc-editor.org/rfc/rfc9106>.
[AuCPace] Haase, B. and B. Labrique, "AuCPace: Efficient verifier-
based PAKE protocol tailored for the IIoT",
http://eprint.iacr.org/2018/286 , 2018.
[BG04] Brown, D. and R. Galant, "The static Diffie-Hellman
problem", http://eprint.iacr.org/2004/306 , 2004.
[Boyen09] Boyen, X., "HPAKE: Password Authentication Secure against
Cross-Site User Impersonation", Cryptology and Network
Security (CANS) , 2009.
[Canetti01]
Canetti, R., "Universally composable security: A new
paradigm for cryptographic protocols", IEEE Symposium on
Foundations of Computer Science (FOCS) , 2001.
[Cheon06] Cheon, J. H., "Security analysis of the strong Diffie-
Hellman problem", Eurocrypt , 2006.
[Curve25519]
Langley, A., Hamburg, M., and S. Turner, "Elliptic Curves
for Security", RFC 7748, DOI 10.17487/RFC7748, January
2016, <https://www.rfc-editor.org/rfc/rfc7748>.
[FIPS202] National Institute of Standards and Technology (NIST),
"SHA-3 Standard: Permutation-Based Hash and Extendable-
Output Functions", August 2015,
<https://nvlpubs.nist.gov/nistpubs/FIPS/
NIST.FIPS.202.pdf>.
[FK00] Ford, W. and B. S. Kaliski, Jr, "Server-assisted
generation of a strong secret from a password", WETICE ,
2000.
[GMR06] Gentry, C., MacKenzie, P., and Z, Ramzan, "A method for
making password-based key exchange resilient to server
compromise", CRYPTO , 2006.
[HJKW23] Hesse, J., Jarecki, S., Krawczyk, H., and C. Wood,
"Password-Authenticated TLS via OPAQUE and Post-Handshake
Authentication", EUROCRYPT , 2023.
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[HMQV] Krawczyk, H., "HMQV: A high-performance secure Diffie-
Hellman protocol", CRYPTO , 2005.
[I-D.irtf-cfrg-hash-to-curve]
Faz-Hernandez, A., Scott, S., Sullivan, N., Wahby, R. S.,
and C. A. Wood, "Hashing to Elliptic Curves", Work in
Progress, Internet-Draft, draft-irtf-cfrg-hash-to-curve-
16, 15 June 2022, <https://datatracker.ietf.org/doc/html/
draft-irtf-cfrg-hash-to-curve-16>.
[I-D.krawczyk-cfrg-opaque-03]
"The OPAQUE Asymmetric PAKE Protocol", n.d.,
<https://datatracker.ietf.org/doc/html/draft-krawczyk-
cfrg-opaque-03>.
[JKKX16] Jarecki, S., Kiayias, A., Krawczyk, H., and J. Xu,
"Highly-efficient and composable password-protected secret
sharing (or: how to protect your bitcoin wallet online)",
IEEE European Symposium on Security and Privacy , 2016.
[JKX18] Jarecki, S., Krawczyk, H., and J. Xu, "OPAQUE: An
Asymmetric PAKE Protocol Secure Against Pre-Computation
Attacks", Eurocrypt , 2018.
[keyagreement]
Barker, E., Chen, L., Roginsky, A., Vassilev, A., and R.
Davis, "Recommendation for pair-wise key-establishment
schemes using discrete logarithm cryptography", National
Institute of Standards and Technology,
DOI 10.6028/nist.sp.800-56ar3, April 2018,
<https://doi.org/10.6028/nist.sp.800-56ar3>.
[LGR20] Len, J., Grubbs, P., and T. Ristenpart, "Partitioning
Oracle Attacks", n.d.,
<https://eprint.iacr.org/2020/1491.pdf>.
[NISTCurves]
"Digital Signature Standard (DSS)", National Institute of
Standards and Technology, DOI 10.6028/nist.fips.186-4,
July 2013, <https://doi.org/10.6028/nist.fips.186-4>.
[PAKE-Selection]
"CFRG PAKE selection process repository", n.d.,
<https://github.com/cfrg/pake-selection>.
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[PBKDF2] Kaliski, B., "PKCS #5: Password-Based Cryptography
Specification Version 2.0", RFC 2898,
DOI 10.17487/RFC2898, September 2000,
<https://www.rfc-editor.org/rfc/rfc2898>.
[RFC2945] Wu, T., "The SRP Authentication and Key Exchange System",
RFC 2945, DOI 10.17487/RFC2945, September 2000,
<https://www.rfc-editor.org/rfc/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/rfc/rfc5869>.
[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/rfc/rfc8017>.
[RFC8125] Schmidt, J., "Requirements for Password-Authenticated Key
Agreement (PAKE) Schemes", RFC 8125, DOI 10.17487/RFC8125,
April 2017, <https://www.rfc-editor.org/rfc/rfc8125>.
[RFC8446] Rescorla, E., "The Transport Layer Security (TLS) Protocol
Version 1.3", RFC 8446, DOI 10.17487/RFC8446, August 2018,
<https://www.rfc-editor.org/rfc/rfc8446>.
[RFC9180] Barnes, R., Bhargavan, K., Lipp, B., and C. Wood, "Hybrid
Public Key Encryption", RFC 9180, DOI 10.17487/RFC9180,
February 2022, <https://www.rfc-editor.org/rfc/rfc9180>.
[RISTRETTO]
de Valence, H., Grigg, J., Hamburg, M., Lovecruft, I.,
Tankersley, G., and F. Valsorda, "The ristretto255 and
decaf448 Groups", Work in Progress, Internet-Draft, draft-
irtf-cfrg-ristretto255-decaf448-08, 5 September 2023,
<https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-
ristretto255-decaf448-08>.
[SCRYPT] Percival, C. and S. Josefsson, "The scrypt Password-Based
Key Derivation Function", RFC 7914, DOI 10.17487/RFC7914,
August 2016, <https://www.rfc-editor.org/rfc/rfc7914>.
[SIGMA-I] Krawczyk, H., "SIGMA: The ‘SIGn-and-MAc’ Approach to
Authenticated Diffie-Hellman and its Use in the IKE
Protocols", https://www.iacr.org/cryptodb/archive/2003/
CRYPTO/1495/1495.pdf , 2003.
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[SPAKE2plus]
Shoup, V., "Security Analysis of SPAKE2+",
http://eprint.iacr.org/2020/313 , 2020.
[TOPPSS] Jarecki, S., Kiayias, A., Krawczyk, H., and J. Xu,
"TOPPSS: Cost-minimal Password-Protected Secret Sharing
based on Threshold OPRF", Applied Cryptology and Network
Security – ACNS 2017 , 2017.
[TripleDH] "Simplifying OTR deniability",
https://signal.org/blog/simplifying-otr-deniability ,
2016.
[WhatsAppE2E]
WhatsApp, "Security of End-to-End Encrypted Backups",
n.d., <https://www.whatsapp.com/security/
WhatsApp_Security_Encrypted_Backups_Whitepaper.pdf>.
Appendix A. Acknowledgments
We are indebted to the OPAQUE reviewers during CFRG's aPAKE selection
process, particularly Julia Hesse and Bjorn Tackmann. This draft has
benefited from comments by multiple people. Special thanks to
Richard Barnes, Dan Brown, Matt Campagna, Eric Crockett, Paul Grubbs,
Fredrik Kuivinen, Payman Mohassel, Jason Resch, Greg Rubin, and Nick
Sullivan. Hugo Krawczyk wishes to thank his OPAQUE co-authors Stas
Jarecki and Jiayu Xu without whom this work would have not been
possible.
Appendix B. Alternate Key Recovery Mechanisms
Client authentication material can be stored and retrieved using
different key recovery mechanisms. Any key recovery mechanism that
encrypts data in the envelope MUST use an authenticated encryption
scheme with random key-robustness (or key-committing). Deviating
from the key-robustness requirement may open the protocol to attacks,
e.g., [LGR20]. This specification enforces this property by using a
MAC over the envelope contents.
We remark that export_key for authentication or encryption requires
no special properties from the authentication or encryption schemes
as long as export_key is used only after authentication material is
successfully recovered, i.e., after the MAC in RecoverCredentials
passes verification.
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Appendix C. Alternate AKE Instantiations
It is possible to instantiate OPAQUE with other AKEs, such as HMQV
[HMQV] and [SIGMA-I]. HMQV is similar to 3DH but varies in its key
schedule. SIGMA-I uses digital signatures rather than static DH keys
for authentication. Specification of these instantiations is left to
future documents. A sketch of how these instantiations might change
is included in the next subsection for posterity.
OPAQUE may also be instantiated with any post-quantum (PQ) AKE
protocol that has the message flow above and security properties (KCI
resistance and forward secrecy) outlined in Section 10. Note that
such an instantiation is not quantum-safe unless the OPRF is quantum-
safe. However, an OPAQUE instantiation where the AKE is quantum-
safe, but the OPRF is not, would still ensure the confidentiality and
integrity of application data encrypted under session_key (or a key
derived from it) with a quantum-safe encryption function. However,
the only effect of a break of the OPRF by a future quantum attacker
would be the ability of this attacker to run at that time an
exhaustive dictionary attack against the old user's password and only
for users whose envelopes were harvested while in use (in the case of
OPAQUE run over a TLS channel with the server, harvesting such
envelopes requires targeted active attacks).
C.1. HMQV Instantiation Sketch
An HMQV instantiation would work similar to OPAQUE-3DH, differing
primarily in the key schedule [HMQV]. First, the key schedule
preamble value would use a different constant prefix -- "HMQV"
instead of "3DH" -- as shown below.
preamble = concat("HMQV",
I2OSP(len(client_identity), 2), client_identity,
KE1,
I2OSP(len(server_identity), 2), server_identity,
KE2.credential_response,
KE2.auth_response.server_nonce,
KE2.auth_response.server_public_keyshare)
Second, the IKM derivation would change. Assuming HMQV is
instantiated with a cyclic group of prime order p with bit length L,
clients would compute IKM as follows:
u' = (eskU + u \* skU) mod p
IKM = (epkS \* pkS^s)^u'
Likewise, servers would compute IKM as follows:
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s' = (eskS + s \* skS) mod p
IKM = (epkU \* pkU^u)^s'
In both cases, u would be computed as follows:
hashInput = concat(I2OSP(len(epkU), 2), epkU,
I2OSP(len(info), 2), info,
I2OSP(len("client"), 2), "client")
u = Hash(hashInput) mod L
Likewise, s would be computed as follows:
hashInput = concat(I2OSP(len(epkS), 2), epkS,
I2OSP(len(info), 2), info,
I2OSP(len("server"), 2), "server")
s = Hash(hashInput) mod L
Hash is the same hash function used in the main OPAQUE protocol for
key derivation. Its output length (in bits) must be at least L.
Both parties should perform validation (as in Section 10.8) on each
other's public keys before computing the above parameters.
C.2. SIGMA-I Instantiation Sketch
A [SIGMA-I] instantiation differs more drastically from OPAQUE-3DH
since authentication uses digital signatures instead of Diffie-
Hellman. In particular, both KE2 and KE3 would carry a digital
signature, computed using the server and client private keys
established during registration, respectively, as well as a MAC,
where the MAC is computed as in OPAQUE-3DH.
The key schedule would also change. Specifically, the key schedule
preamble value would use a different constant prefix -- "SIGMA-I"
instead of "3DH" -- and the IKM computation would use only the
ephemeral public keys exchanged between client and server.
Appendix D. Test Vectors
This section contains real and fake test vectors for the OPAQUE-3DH
specification. Each real test vector in Appendix D.1 specifies the
configuration information, protocol inputs, intermediate values
computed during registration and authentication, and protocol
outputs.
Similarly, each fake test vector in Appendix D.2 specifies the
configuration information, protocol inputs, and protocol outputs
computed during the authentication of an unknown or unregistered
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user. Note that masking_key, client_private_key, and
client_public_key are used as additional inputs as described in
Section 6.3.2.2. client_public_key is used as the fake record's
public key, and masking_key for the fake record's masking key
parameter.
All values are encoded in hexadecimal strings. The configuration
information includes the (OPRF, Hash, KSF, KDF, MAC, Group, Context)
tuple, where the Group matches that which is used in the OPRF. These
test vectors were generated using draft-21 of [OPRF]. The KSF used
for each test vector is the identity function (denoted Identity),
which returns as output the input message supplied to the function
without any modification, i.e., msg = Stretch(msg).
D.1. Real Test Vectors
D.1.1. OPAQUE-3DH Real Test Vector 1
D.1.1.1. Configuration
OPRF: ristretto255-SHA512
Hash: SHA512
KSF: Identity
KDF: HKDF-SHA512
MAC: HMAC-SHA512
Group: ristretto255
Context: 4f50415155452d504f43
Nh: 64
Npk: 32
Nsk: 32
Nm: 64
Nx: 64
Nok: 32
D.1.1.2. Input Values
Bourdrez, et al. Expires 20 June 2024 [Page 60]
Internet-Draft OPAQUE December 2023
oprf_seed: f433d0227b0b9dd54f7c4422b600e764e47fb503f1f9a0f0a47c6606b0
54a7fdc65347f1a08f277e22358bbabe26f823fca82c7848e9a75661f4ec5d5c1989e
f
credential_identifier: 31323334
password: 436f7272656374486f72736542617474657279537461706c65
envelope_nonce: ac13171b2f17bc2c74997f0fce1e1f35bec6b91fe2e12dbd323d2
3ba7a38dfec
masking_nonce: 38fe59af0df2c79f57b8780278f5ae47355fe1f817119041951c80
f612fdfc6d
server_private_key: 47451a85372f8b3537e249d7b54188091fb18edde78094b43
e2ba42b5eb89f0d
server_public_key: b2fe7af9f48cc502d016729d2fe25cdd433f2c4bc904660b2a
382c9b79df1a78
server_nonce: 71cd9960ecef2fe0d0f7494986fa3d8b2bb01963537e60efb13981e
138e3d4a1
client_nonce: da7e07376d6d6f034cfa9bb537d11b8c6b4238c334333d1f0aebb38
0cae6a6cc
client_keyshare_seed: 82850a697b42a505f5b68fcdafce8c31f0af2b581f063cf
1091933541936304b
server_keyshare_seed: 05a4f54206eef1ba2f615bc0aa285cb22f26d1153b5b40a
1e85ff80da12f982f
blind_registration: 76cfbfe758db884bebb33582331ba9f159720ca8784a2a070
a265d9c2d6abe01
blind_login: 6ecc102d2e7a7cf49617aad7bbe188556792d4acd60a1a8a8d2b65d4
b0790308
D.1.1.3. Intermediate Values
Bourdrez, et al. Expires 20 June 2024 [Page 61]
Internet-Draft OPAQUE December 2023
client_public_key: 76a845464c68a5d2f7e442436bb1424953b17d3e2e289ccbac
cafb57ac5c3675
auth_key: 6cd32316f18d72a9a927a83199fa030663a38ce0c11fbaef82aa9003773
0494fc555c4d49506284516edd1628c27965b7555a4ebfed2223199f6c67966dde822
randomized_password: aac48c25ab036e30750839d31d6e73007344cb1155289fb7
d329beb932e9adeea73d5d5c22a0ce1952f8aba6d66007615cd1698d4ac85ef1fcf15
0031d1435d9
envelope: ac13171b2f17bc2c74997f0fce1e1f35bec6b91fe2e12dbd323d23ba7a3
8dfec634b0f5b96109c198a8027da51854c35bee90d1e1c781806d07d49b76de6a28b
8d9e9b6c93b9f8b64d16dddd9c5bfb5fea48ee8fd2f75012a8b308605cdd8ba5
handshake_secret: 81263cb85a0cfa12450f0f388de4e92291ec4c7c7a0878b6245
50ff528726332f1298fc6cc822a432c89504347c7a2ccd70316ae3da6a15e0399e6db
3f7c1b12
server_mac_key: 0d36b26cfe38f51f804f0a9361818f32ee1ce2a4e5578653b5271
84af058d3b2d8075c296fd84d24677913d1baa109290cd81a13ed383f9091a3804e65
298dfc
client_mac_key: 91750adbac54a5e8e53b4c233cc8d369fe83b0de1b6a3cd85575e
eb0bb01a6a90a086a2cf5fe75fff2a9379c30ba9049510a33b5b0b1444a88800fc3ee
e2260d
oprf_key: 5d4c6a8b7c7138182afb4345d1fae6a9f18a1744afbcc3854f8f5a2b4b4
c6d05
D.1.1.4. Output Values
Bourdrez, et al. Expires 20 June 2024 [Page 62]
Internet-Draft OPAQUE December 2023
registration_request: 5059ff249eb1551b7ce4991f3336205bde44a105a032e74
7d21bf382e75f7a71
registration_response: 7408a268083e03abc7097fc05b587834539065e86fb0c7
b6342fcf5e01e5b019b2fe7af9f48cc502d016729d2fe25cdd433f2c4bc904660b2a3
82c9b79df1a78
registration_upload: 76a845464c68a5d2f7e442436bb1424953b17d3e2e289ccb
accafb57ac5c36751ac5844383c7708077dea41cbefe2fa15724f449e535dd7dd562e
66f5ecfb95864eadddec9db5874959905117dad40a4524111849799281fefe3c51fa8
2785c5ac13171b2f17bc2c74997f0fce1e1f35bec6b91fe2e12dbd323d23ba7a38dfe
c634b0f5b96109c198a8027da51854c35bee90d1e1c781806d07d49b76de6a28b8d9e
9b6c93b9f8b64d16dddd9c5bfb5fea48ee8fd2f75012a8b308605cdd8ba5
KE1: c4dedb0ba6ed5d965d6f250fbe554cd45cba5dfcce3ce836e4aee778aa3cd44d
da7e07376d6d6f034cfa9bb537d11b8c6b4238c334333d1f0aebb380cae6a6cc6e29b
ee50701498605b2c085d7b241ca15ba5c32027dd21ba420b94ce60da326
KE2: 7e308140890bcde30cbcea28b01ea1ecfbd077cff62c4def8efa075aabcbb471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KE3: 4455df4f810ac31a6748835888564b536e6da5d9944dfea9e34defb9575fe5e2
661ef61d2ae3929bcf57e53d464113d364365eb7d1a57b629707ca48da18e442
export_key: 1ef15b4fa99e8a852412450ab78713aad30d21fa6966c9b8c9fb3262a
970dc62950d4dd4ed62598229b1b72794fc0335199d9f7fcc6eaedde92cc04870e63f
16
session_key: 42afde6f5aca0cfa5c163763fbad55e73a41db6b41bc87b8e7b62214
a8eedc6731fa3cb857d657ab9b3764b89a84e91ebcb4785166fbb02cedfcbdfda215b
96f
D.1.2. OPAQUE-3DH Real Test Vector 2
D.1.2.1. Configuration
Bourdrez, et al. Expires 20 June 2024 [Page 63]
Internet-Draft OPAQUE December 2023
OPRF: ristretto255-SHA512
Hash: SHA512
KSF: Identity
KDF: HKDF-SHA512
MAC: HMAC-SHA512
Group: ristretto255
Context: 4f50415155452d504f43
Nh: 64
Npk: 32
Nsk: 32
Nm: 64
Nx: 64
Nok: 32
D.1.2.2. Input Values
client_identity: 616c696365
server_identity: 626f62
oprf_seed: f433d0227b0b9dd54f7c4422b600e764e47fb503f1f9a0f0a47c6606b0
54a7fdc65347f1a08f277e22358bbabe26f823fca82c7848e9a75661f4ec5d5c1989e
f
credential_identifier: 31323334
password: 436f7272656374486f72736542617474657279537461706c65
envelope_nonce: ac13171b2f17bc2c74997f0fce1e1f35bec6b91fe2e12dbd323d2
3ba7a38dfec
masking_nonce: 38fe59af0df2c79f57b8780278f5ae47355fe1f817119041951c80
f612fdfc6d
server_private_key: 47451a85372f8b3537e249d7b54188091fb18edde78094b43
e2ba42b5eb89f0d
server_public_key: b2fe7af9f48cc502d016729d2fe25cdd433f2c4bc904660b2a
382c9b79df1a78
server_nonce: 71cd9960ecef2fe0d0f7494986fa3d8b2bb01963537e60efb13981e
138e3d4a1
client_nonce: da7e07376d6d6f034cfa9bb537d11b8c6b4238c334333d1f0aebb38
0cae6a6cc
client_keyshare_seed: 82850a697b42a505f5b68fcdafce8c31f0af2b581f063cf
1091933541936304b
server_keyshare_seed: 05a4f54206eef1ba2f615bc0aa285cb22f26d1153b5b40a
1e85ff80da12f982f
blind_registration: 76cfbfe758db884bebb33582331ba9f159720ca8784a2a070
a265d9c2d6abe01
blind_login: 6ecc102d2e7a7cf49617aad7bbe188556792d4acd60a1a8a8d2b65d4
b0790308
D.1.2.3. Intermediate Values
Bourdrez, et al. Expires 20 June 2024 [Page 64]
Internet-Draft OPAQUE December 2023
client_public_key: 76a845464c68a5d2f7e442436bb1424953b17d3e2e289ccbac
cafb57ac5c3675
auth_key: 6cd32316f18d72a9a927a83199fa030663a38ce0c11fbaef82aa9003773
0494fc555c4d49506284516edd1628c27965b7555a4ebfed2223199f6c67966dde822
randomized_password: aac48c25ab036e30750839d31d6e73007344cb1155289fb7
d329beb932e9adeea73d5d5c22a0ce1952f8aba6d66007615cd1698d4ac85ef1fcf15
0031d1435d9
envelope: ac13171b2f17bc2c74997f0fce1e1f35bec6b91fe2e12dbd323d23ba7a3
8dfec1ac902dc5589e9a5f0de56ad685ea8486210ef41449cd4d8712828913c5d2b68
0b2b3af4a26c765cff329bfb66d38ecf1d6cfa9e7a73c222c6efe0d9520f7d7c
handshake_secret: 5e723bed1e5276de2503419eba9da61ead573109c4012268323
98c7e08155b885bfe7bc93451f9d887a0c1d0c19233e40a8e47b347a9ac3907f94032
a4cff64f
server_mac_key: dad66bb9251073d17a13f8e5500f36e5998e3cde520ca0738e708
5af62fd97812eb79a745c94d0bf8a6ac17f980cf435504cf64041eeb6bb237796d2c7
f81e9a
client_mac_key: f816fe2914f7c5b29852385615d7c7f31ac122adf202d7ccd4976
06d7aabd48930323d1d02b1cc9ecd456c4de6f46c7950becb18bffd921dd5876381b5
486ffe
oprf_key: 5d4c6a8b7c7138182afb4345d1fae6a9f18a1744afbcc3854f8f5a2b4b4
c6d05
D.1.2.4. Output Values
Bourdrez, et al. Expires 20 June 2024 [Page 65]
Internet-Draft OPAQUE December 2023
registration_request: 5059ff249eb1551b7ce4991f3336205bde44a105a032e74
7d21bf382e75f7a71
registration_response: 7408a268083e03abc7097fc05b587834539065e86fb0c7
b6342fcf5e01e5b019b2fe7af9f48cc502d016729d2fe25cdd433f2c4bc904660b2a3
82c9b79df1a78
registration_upload: 76a845464c68a5d2f7e442436bb1424953b17d3e2e289ccb
accafb57ac5c36751ac5844383c7708077dea41cbefe2fa15724f449e535dd7dd562e
66f5ecfb95864eadddec9db5874959905117dad40a4524111849799281fefe3c51fa8
2785c5ac13171b2f17bc2c74997f0fce1e1f35bec6b91fe2e12dbd323d23ba7a38dfe
c1ac902dc5589e9a5f0de56ad685ea8486210ef41449cd4d8712828913c5d2b680b2b
3af4a26c765cff329bfb66d38ecf1d6cfa9e7a73c222c6efe0d9520f7d7c
KE1: c4dedb0ba6ed5d965d6f250fbe554cd45cba5dfcce3ce836e4aee778aa3cd44d
da7e07376d6d6f034cfa9bb537d11b8c6b4238c334333d1f0aebb380cae6a6cc6e29b
ee50701498605b2c085d7b241ca15ba5c32027dd21ba420b94ce60da326
KE2: 7e308140890bcde30cbcea28b01ea1ecfbd077cff62c4def8efa075aabcbb471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KE3: 7a026de1d6126905736c3f6d92463a08d209833eb793e46d0f7f15b3e0f62c76
43763c02bbc6b8d3d15b63250cae98171e9260f1ffa789750f534ac11a0176d5
export_key: 1ef15b4fa99e8a852412450ab78713aad30d21fa6966c9b8c9fb3262a
970dc62950d4dd4ed62598229b1b72794fc0335199d9f7fcc6eaedde92cc04870e63f
16
session_key: ae7951123ab5befc27e62e63f52cf472d6236cb386c968cc47b7e34f
866aa4bc7638356a73cfce92becf39d6a7d32a1861f12130e824241fe6cab34fbd471
a57
D.1.3. OPAQUE-3DH Real Test Vector 3
D.1.3.1. Configuration
Bourdrez, et al. Expires 20 June 2024 [Page 66]
Internet-Draft OPAQUE December 2023
OPRF: ristretto255-SHA512
Hash: SHA512
KSF: Identity
KDF: HKDF-SHA512
MAC: HMAC-SHA512
Group: curve25519
Context: 4f50415155452d504f43
Nh: 64
Npk: 32
Nsk: 32
Nm: 64
Nx: 64
Nok: 32
D.1.3.2. Input Values
oprf_seed: a78342ab84d3d30f08d5a9630c79bf311c31ed7f85d9d4959bf492ec67
a0eec8a67dfbf4497248eebd49e878aab173e5e4ff76354288fdd53e949a5f7c9f7f1
b
credential_identifier: 31323334
password: 436f7272656374486f72736542617474657279537461706c65
envelope_nonce: 40d6b67fdd7da7c49894750754514dbd2070a407166bd2a5237cc
a9bf44d6e0b
masking_nonce: 38fe59af0df2c79f57b8780278f5ae47355fe1f817119041951c80
f612fdfc6d
server_private_key: c06139381df63bfc91c850db0b9cfbec7a62e86d80040a41a
a7725bf0e79d564
server_public_key: a41e28269b4e97a66468cc00c5a57753e192e1527669897706
88aa90486ef031
server_nonce: 71cd9960ecef2fe0d0f7494986fa3d8b2bb01963537e60efb13981e
138e3d4a1
client_nonce: da7e07376d6d6f034cfa9bb537d11b8c6b4238c334333d1f0aebb38
0cae6a6cc
client_keyshare_seed: 82850a697b42a505f5b68fcdafce8c31f0af2b581f063cf
1091933541936304b
server_keyshare_seed: 05a4f54206eef1ba2f615bc0aa285cb22f26d1153b5b40a
1e85ff80da12f982f
blind_registration: c575731ffe1cb0ca5ba63b42c4699767b8b9ab78ba39316ee
04baddb2034a70a
blind_login: 6ecc102d2e7a7cf49617aad7bbe188556792d4acd60a1a8a8d2b65d4
b0790308
D.1.3.3. Intermediate Values
Bourdrez, et al. Expires 20 June 2024 [Page 67]
Internet-Draft OPAQUE December 2023
client_public_key: 0936ea94ab030ec332e29050d266c520e916731a052d05ced7
e0cfe751142b48
auth_key: 7e880ab484f750e80e6f839d975aff476070ce65066d85ea62523d1d576
4739d91307fac47186a4ab935e6a5c7f70cb47faa9473311947502c022cc67ae9440c
randomized_password: 3a602c295a9c323d9362fe286f104567ed6862b25dbe30fa
da844f19e41cf40047424b7118e15dc2c1a815a70fea5c8de6c30aa61440cd4b4b5e8
f3963fbb2e1
envelope: 40d6b67fdd7da7c49894750754514dbd2070a407166bd2a5237cca9bf44
d6e0b20c1e81fef28e92e897ca8287d49a55075b47c3988ff0fff367d79a3e350ccac
150b4a3ff48b4770c8e84e437b3d4e68d2b95833f7788f7eb93fa6a8afb85ecb
handshake_secret: 178c8c15e025252380c3edb1c6ad8ac52573b38d536099e2f86
5786f5e31c642608550c0c6f281c37ce259667dd72768af31630e0eb36f1096a2e642
1c2aa163
server_mac_key: f3c6a8e069c54bb0d8905139f723c9e22f5c662dc08848243a665
4c8223800019b9823523d84da2ef67ca1c14277630aace464c113be8a0a658c39e181
a8bb71
client_mac_key: b1ee7ce52dbd0ab72872924ff11596cb196bbabfc319e74aca78a
de54a0f74dd15dcf5621f6d2e79161b0c9b701381d494836dedbb86e584a65b34267a
370e01
oprf_key: 62ef7f7d9506a14600c34f642aaf6ef8019cc82a6755db4fded5248ea14
6030a
D.1.3.4. Output Values
Bourdrez, et al. Expires 20 June 2024 [Page 68]
Internet-Draft OPAQUE December 2023
registration_request: 26f3dbfd76b8e5f85b4da604f42889a7d4b1bc919f65538
1a67de02c59fd5436
registration_response: 506e8f1b89c098fb89b5b6210a05f7898cafdaea221761
e8d5272fc39e0f9f08a41e28269b4e97a66468cc00c5a57753e192e15276698977068
8aa90486ef031
registration_upload: 0936ea94ab030ec332e29050d266c520e916731a052d05ce
d7e0cfe751142b486d23c6ed818882f9bdfdcf91389fcbc0b7a3faf92bd0bd6be4a1e
7730277b694fc7c6ba327fbe786af18487688e0f7c148bbd54dc2fc80c28e7a976d9e
f53c3540d6b67fdd7da7c49894750754514dbd2070a407166bd2a5237cca9bf44d6e0
b20c1e81fef28e92e897ca8287d49a55075b47c3988ff0fff367d79a3e350ccac150b
4a3ff48b4770c8e84e437b3d4e68d2b95833f7788f7eb93fa6a8afb85ecb
KE1: c4dedb0ba6ed5d965d6f250fbe554cd45cba5dfcce3ce836e4aee778aa3cd44d
da7e07376d6d6f034cfa9bb537d11b8c6b4238c334333d1f0aebb380cae6a6cc10a83
b9117d3798cb2957fbdb0268a0d63dbf9d66bde5c00c78affd80026c911
KE2: 9a0e5a1514f62e005ea098b0d8cf6750e358c4389e6add1c52aed9500fa19d00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KE3: 550e923829a544496d8316c490da2b979b78c730dd75be3a17f237a26432c19f
bba54b6a0467b1c22ecbd6794bc5fa5b04215ba1ef974c6b090baa42c5bb984f
export_key: 9dec51d6d0f6ce7e4345f10961053713b07310cc2e45872f57bbd2fe5
070fdf0fb5b77c7ddaa2f3dc5c35132df7417ad7fefe0f690ad266e5a54a21d045c9c
38
session_key: fd2fdd07c1bcc88e81c1b1d1de5ad62dfdef1c0b8209ff9d671e1fac
55ce9c34d381c1fb2703ff53a797f77daccbe33047ccc167b8105171e10ec962eea20
3aa
D.1.4. OPAQUE-3DH Real Test Vector 4
D.1.4.1. Configuration
Bourdrez, et al. Expires 20 June 2024 [Page 69]
Internet-Draft OPAQUE December 2023
OPRF: ristretto255-SHA512
Hash: SHA512
KSF: Identity
KDF: HKDF-SHA512
MAC: HMAC-SHA512
Group: curve25519
Context: 4f50415155452d504f43
Nh: 64
Npk: 32
Nsk: 32
Nm: 64
Nx: 64
Nok: 32
D.1.4.2. Input Values
client_identity: 616c696365
server_identity: 626f62
oprf_seed: a78342ab84d3d30f08d5a9630c79bf311c31ed7f85d9d4959bf492ec67
a0eec8a67dfbf4497248eebd49e878aab173e5e4ff76354288fdd53e949a5f7c9f7f1
b
credential_identifier: 31323334
password: 436f7272656374486f72736542617474657279537461706c65
envelope_nonce: 40d6b67fdd7da7c49894750754514dbd2070a407166bd2a5237cc
a9bf44d6e0b
masking_nonce: 38fe59af0df2c79f57b8780278f5ae47355fe1f817119041951c80
f612fdfc6d
server_private_key: c06139381df63bfc91c850db0b9cfbec7a62e86d80040a41a
a7725bf0e79d564
server_public_key: a41e28269b4e97a66468cc00c5a57753e192e1527669897706
88aa90486ef031
server_nonce: 71cd9960ecef2fe0d0f7494986fa3d8b2bb01963537e60efb13981e
138e3d4a1
client_nonce: da7e07376d6d6f034cfa9bb537d11b8c6b4238c334333d1f0aebb38
0cae6a6cc
client_keyshare_seed: 82850a697b42a505f5b68fcdafce8c31f0af2b581f063cf
1091933541936304b
server_keyshare_seed: 05a4f54206eef1ba2f615bc0aa285cb22f26d1153b5b40a
1e85ff80da12f982f
blind_registration: c575731ffe1cb0ca5ba63b42c4699767b8b9ab78ba39316ee
04baddb2034a70a
blind_login: 6ecc102d2e7a7cf49617aad7bbe188556792d4acd60a1a8a8d2b65d4
b0790308
D.1.4.3. Intermediate Values
Bourdrez, et al. Expires 20 June 2024 [Page 70]
Internet-Draft OPAQUE December 2023
client_public_key: 0936ea94ab030ec332e29050d266c520e916731a052d05ced7
e0cfe751142b48
auth_key: 7e880ab484f750e80e6f839d975aff476070ce65066d85ea62523d1d576
4739d91307fac47186a4ab935e6a5c7f70cb47faa9473311947502c022cc67ae9440c
randomized_password: 3a602c295a9c323d9362fe286f104567ed6862b25dbe30fa
da844f19e41cf40047424b7118e15dc2c1a815a70fea5c8de6c30aa61440cd4b4b5e8
f3963fbb2e1
envelope: 40d6b67fdd7da7c49894750754514dbd2070a407166bd2a5237cca9bf44
d6e0bb4c0eab6143959a650c5f6b32acf162b1fbe95bb36c5c4f99df53865c4d3537d
69061d80522d772cd0efdbe91f817f6bf7259a56e20b4eb9cbe9443702f4b759
handshake_secret: 13e7dc6afa5334b9dfffe26bee3caf744ef4add176caee464cd
eb3d37303b90de35a8bf095df84471ac77d705f12fe232f1571de1d6a001d3e808998
73a142dc
server_mac_key: a58135acfb2bde92d506cf59119729a6404ad94eba294e4b52a63
baf58cfe03f21bcf735222c7f2c27a60bd958be7f6aed50dc03a78f64e7ae4ac1ff07
1b95aa
client_mac_key: 1e1a8ba156aadc4a302f707d2193c9dab477b355f430d450dd407
ce40dc75613f76ec33dec494f8a6bfdcf951eb060dac33e6572c693954fe92e33730c
9ab0a2
oprf_key: 62ef7f7d9506a14600c34f642aaf6ef8019cc82a6755db4fded5248ea14
6030a
D.1.4.4. Output Values
Bourdrez, et al. Expires 20 June 2024 [Page 71]
Internet-Draft OPAQUE December 2023
registration_request: 26f3dbfd76b8e5f85b4da604f42889a7d4b1bc919f65538
1a67de02c59fd5436
registration_response: 506e8f1b89c098fb89b5b6210a05f7898cafdaea221761
e8d5272fc39e0f9f08a41e28269b4e97a66468cc00c5a57753e192e15276698977068
8aa90486ef031
registration_upload: 0936ea94ab030ec332e29050d266c520e916731a052d05ce
d7e0cfe751142b486d23c6ed818882f9bdfdcf91389fcbc0b7a3faf92bd0bd6be4a1e
7730277b694fc7c6ba327fbe786af18487688e0f7c148bbd54dc2fc80c28e7a976d9e
f53c3540d6b67fdd7da7c49894750754514dbd2070a407166bd2a5237cca9bf44d6e0
bb4c0eab6143959a650c5f6b32acf162b1fbe95bb36c5c4f99df53865c4d3537d6906
1d80522d772cd0efdbe91f817f6bf7259a56e20b4eb9cbe9443702f4b759
KE1: c4dedb0ba6ed5d965d6f250fbe554cd45cba5dfcce3ce836e4aee778aa3cd44d
da7e07376d6d6f034cfa9bb537d11b8c6b4238c334333d1f0aebb380cae6a6cc10a83
b9117d3798cb2957fbdb0268a0d63dbf9d66bde5c00c78affd80026c911
KE2: 9a0e5a1514f62e005ea098b0d8cf6750e358c4389e6add1c52aed9500fa19d00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KE3: d16344e791c3f18594d22ba068984fa18ec1e9bead662b75f66826ffd627932f
cd1ec40cd01dcf5f63f4055ebe45c7717a57a833aad360256cf1e1c20c0eae1c
export_key: 9dec51d6d0f6ce7e4345f10961053713b07310cc2e45872f57bbd2fe5
070fdf0fb5b77c7ddaa2f3dc5c35132df7417ad7fefe0f690ad266e5a54a21d045c9c
38
session_key: f6116d3aa0e4089a179713bad4d98ed5cb57e5443cae8d36ef78996f
a60f3dc6e9fcdd63c001596b06dbc1285d80211035cc0e485506b3f7a650cbf78c5bf
fc9
D.1.5. OPAQUE-3DH Real Test Vector 5
D.1.5.1. Configuration
Bourdrez, et al. Expires 20 June 2024 [Page 72]
Internet-Draft OPAQUE December 2023
OPRF: P256-SHA256
Hash: SHA256
KSF: Identity
KDF: HKDF-SHA256
MAC: HMAC-SHA256
Group: P256_XMD:SHA-256_SSWU_RO_
Context: 4f50415155452d504f43
Nh: 32
Npk: 33
Nsk: 32
Nm: 32
Nx: 32
Nok: 32
D.1.5.2. Input Values
oprf_seed: 62f60b286d20ce4fd1d64809b0021dad6ed5d52a2c8cf27ae6582543a0
a8dce2
credential_identifier: 31323334
password: 436f7272656374486f72736542617474657279537461706c65
envelope_nonce: a921f2a014513bd8a90e477a629794e89fec12d12206dde662ebd
cf65670e51f
masking_nonce: 38fe59af0df2c79f57b8780278f5ae47355fe1f817119041951c80
f612fdfc6d
server_private_key: c36139381df63bfc91c850db0b9cfbec7a62e86d80040a41a
a7725bf0e79d5e5
server_public_key: 035f40ff9cf88aa1f5cd4fe5fd3da9ea65a4923a5594f84fd9
f2092d6067784874
server_nonce: 71cd9960ecef2fe0d0f7494986fa3d8b2bb01963537e60efb13981e
138e3d4a1
client_nonce: ab3d33bde0e93eda72392346a7a73051110674bbf6b1b7ffab8be4f
91fdaeeb1
client_keyshare_seed: 633b875d74d1556d2a2789309972b06db21dfcc4f5ad51d
7e74d783b7cfab8dc
server_keyshare_seed: 05a4f54206eef1ba2f615bc0aa285cb22f26d1153b5b40a
1e85ff80da12f982f
blind_registration: 411bf1a62d119afe30df682b91a0a33d777972d4f2daa4b34
ca527d597078153
blind_login: c497fddf6056d241e6cf9fb7ac37c384f49b357a221eb0a802c989b9
942256c1
D.1.5.3. Intermediate Values
Bourdrez, et al. Expires 20 June 2024 [Page 73]
Internet-Draft OPAQUE December 2023
client_public_key: 03b218507d978c3db570ca994aaf36695a731ddb2db272c817
f79746fc37ae5214
auth_key: 5bd4be1602516092dc5078f8d699f5721dc1720a49fb80d8e5c16377abd
0987b
randomized_password: 06be0a1a51d56557a3adad57ba29c5510565dcd8b5078fa3
19151b9382258fb0
envelope: a921f2a014513bd8a90e477a629794e89fec12d12206dde662ebdcf6567
0e51fad30bbcfc1f8eda0211553ab9aaf26345ad59a128e80188f035fe4924fad67b8
handshake_secret: 83a932431a8f25bad042f008efa2b07c6cd0faa8285f335b636
3546a9f9b235f
server_mac_key: 13e928581febfad28855e3e7f03306d61bd69489686f621535d44
a1365b73b0d
client_mac_key: afdc53910c25183b08b930e6953c35b3466276736d9de2e9c5efa
f150f4082c5
oprf_key: 2dfb5cb9aa1476093be74ca0d43e5b02862a05f5d6972614d7433acdc66
f7f31
D.1.5.4. Output Values
registration_request: 029e949a29cfa0bf7c1287333d2fb3dc586c41aa652f507
0d26a5315a1b50229f8
registration_response: 0350d3694c00978f00a5ce7cd08a00547e4ab5fb5fc2b2
f6717cdaa6c89136efef035f40ff9cf88aa1f5cd4fe5fd3da9ea65a4923a5594f84fd
9f2092d6067784874
registration_upload: 03b218507d978c3db570ca994aaf36695a731ddb2db272c8
17f79746fc37ae52147f0ed53532d3ae8e505ecc70d42d2b814b6b0e48156def71ea0
29148b2803aafa921f2a014513bd8a90e477a629794e89fec12d12206dde662ebdcf6
5670e51fad30bbcfc1f8eda0211553ab9aaf26345ad59a128e80188f035fe4924fad6
7b8
KE1: 037342f0bcb3ecea754c1e67576c86aa90c1de3875f390ad599a26686cdfee6e
07ab3d33bde0e93eda72392346a7a73051110674bbf6b1b7ffab8be4f91fdaeeb1022
ed3f32f318f81bab80da321fecab3cd9b6eea11a95666dfa6beeaab321280b6
KE2: 0246da9fe4d41d5ba69faa6c509a1d5bafd49a48615a47a8dd4b0823cc147648
1138fe59af0df2c79f57b8780278f5ae47355fe1f817119041951c80f612fdfc6d2f0
c547f70deaeca54d878c14c1aa5e1ab405dec833777132eea905c2fbb12504a67dcbe
0e66740c76b62c13b04a38a77926e19072953319ec65e41f9bfd2ae26837b6ce688bf
9af2542f04eec9ab96a1b9328812dc2f5c89182ed47fead61f09f71cd9960ecef2fe0
d0f7494986fa3d8b2bb01963537e60efb13981e138e3d4a103c1701353219b53acf33
7bf6456a83cefed8f563f1040b65afbf3b65d3bc9a19b50a73b145bc87a157e8c58c0
342e2047ee22ae37b63db17e0a82a30fcc4ecf7b
KE3: e97cab4433aa39d598e76f13e768bba61c682947bdcf9936035e8a3a3ebfb66e
export_key: c3c9a1b0e33ac84dd83d0b7e8af6794e17e7a3caadff289fbd9dc769a
853c64b
session_key: 484ad345715ccce138ca49e4ea362c6183f0949aaaa1125dc3bc3f80
876e7cd1
D.1.6. OPAQUE-3DH Real Test Vector 6
Bourdrez, et al. Expires 20 June 2024 [Page 74]
Internet-Draft OPAQUE December 2023
D.1.6.1. Configuration
OPRF: P256-SHA256
Hash: SHA256
KSF: Identity
KDF: HKDF-SHA256
MAC: HMAC-SHA256
Group: P256_XMD:SHA-256_SSWU_RO_
Context: 4f50415155452d504f43
Nh: 32
Npk: 33
Nsk: 32
Nm: 32
Nx: 32
Nok: 32
D.1.6.2. Input Values
client_identity: 616c696365
server_identity: 626f62
oprf_seed: 62f60b286d20ce4fd1d64809b0021dad6ed5d52a2c8cf27ae6582543a0
a8dce2
credential_identifier: 31323334
password: 436f7272656374486f72736542617474657279537461706c65
envelope_nonce: a921f2a014513bd8a90e477a629794e89fec12d12206dde662ebd
cf65670e51f
masking_nonce: 38fe59af0df2c79f57b8780278f5ae47355fe1f817119041951c80
f612fdfc6d
server_private_key: c36139381df63bfc91c850db0b9cfbec7a62e86d80040a41a
a7725bf0e79d5e5
server_public_key: 035f40ff9cf88aa1f5cd4fe5fd3da9ea65a4923a5594f84fd9
f2092d6067784874
server_nonce: 71cd9960ecef2fe0d0f7494986fa3d8b2bb01963537e60efb13981e
138e3d4a1
client_nonce: ab3d33bde0e93eda72392346a7a73051110674bbf6b1b7ffab8be4f
91fdaeeb1
client_keyshare_seed: 633b875d74d1556d2a2789309972b06db21dfcc4f5ad51d
7e74d783b7cfab8dc
server_keyshare_seed: 05a4f54206eef1ba2f615bc0aa285cb22f26d1153b5b40a
1e85ff80da12f982f
blind_registration: 411bf1a62d119afe30df682b91a0a33d777972d4f2daa4b34
ca527d597078153
blind_login: c497fddf6056d241e6cf9fb7ac37c384f49b357a221eb0a802c989b9
942256c1
D.1.6.3. Intermediate Values
Bourdrez, et al. Expires 20 June 2024 [Page 75]
Internet-Draft OPAQUE December 2023
client_public_key: 03b218507d978c3db570ca994aaf36695a731ddb2db272c817
f79746fc37ae5214
auth_key: 5bd4be1602516092dc5078f8d699f5721dc1720a49fb80d8e5c16377abd
0987b
randomized_password: 06be0a1a51d56557a3adad57ba29c5510565dcd8b5078fa3
19151b9382258fb0
envelope: a921f2a014513bd8a90e477a629794e89fec12d12206dde662ebdcf6567
0e51f4d7773a36a208a866301dbb2858e40dc5638017527cf91aef32d3848eebe0971
handshake_secret: 80bdcc498f22de492e90ee8101fcc7c101e158dd49c77f7c283
816ae329ed62f
server_mac_key: 0f82432fbdb5b90daf27a91a3acc42299a9590dba1b77932c2207
b4cb3d4a157
client_mac_key: 7f629eb0b1b69979b07ca1f564b3e92ed22f07569fd1d11725d93
e46731fbe71
oprf_key: 2dfb5cb9aa1476093be74ca0d43e5b02862a05f5d6972614d7433acdc66
f7f31
D.1.6.4. Output Values
registration_request: 029e949a29cfa0bf7c1287333d2fb3dc586c41aa652f507
0d26a5315a1b50229f8
registration_response: 0350d3694c00978f00a5ce7cd08a00547e4ab5fb5fc2b2
f6717cdaa6c89136efef035f40ff9cf88aa1f5cd4fe5fd3da9ea65a4923a5594f84fd
9f2092d6067784874
registration_upload: 03b218507d978c3db570ca994aaf36695a731ddb2db272c8
17f79746fc37ae52147f0ed53532d3ae8e505ecc70d42d2b814b6b0e48156def71ea0
29148b2803aafa921f2a014513bd8a90e477a629794e89fec12d12206dde662ebdcf6
5670e51f4d7773a36a208a866301dbb2858e40dc5638017527cf91aef32d3848eebe0
971
KE1: 037342f0bcb3ecea754c1e67576c86aa90c1de3875f390ad599a26686cdfee6e
07ab3d33bde0e93eda72392346a7a73051110674bbf6b1b7ffab8be4f91fdaeeb1022
ed3f32f318f81bab80da321fecab3cd9b6eea11a95666dfa6beeaab321280b6
KE2: 0246da9fe4d41d5ba69faa6c509a1d5bafd49a48615a47a8dd4b0823cc147648
1138fe59af0df2c79f57b8780278f5ae47355fe1f817119041951c80f612fdfc6d2f0
c547f70deaeca54d878c14c1aa5e1ab405dec833777132eea905c2fbb12504a67dcbe
0e66740c76b62c13b04a38a77926e19072953319ec65e41f9bfd2ae268d7f10604202
1c80300e4c6f585980cf39fc51a4a6bba41b0729f9b240c729e5671cd9960ecef2fe0
d0f7494986fa3d8b2bb01963537e60efb13981e138e3d4a103c1701353219b53acf33
7bf6456a83cefed8f563f1040b65afbf3b65d3bc9a19b84922c7e5d074838a8f27859
2c53f61fb59f031e85ad480c0c71086b871e1b24
KE3: 46833578cee137775f6be3f01b80748daac5a694101ad0e9e7025480552da56a
export_key: c3c9a1b0e33ac84dd83d0b7e8af6794e17e7a3caadff289fbd9dc769a
853c64b
session_key: 27766fabd8dd88ff37fbd0ef1a491e601d10d9f016c2b28c4bd1b0fb
7511a3c3
D.2. Fake Test Vectors
Bourdrez, et al. Expires 20 June 2024 [Page 76]
Internet-Draft OPAQUE December 2023
D.2.1. OPAQUE-3DH Fake Test Vector 1
D.2.1.1. Configuration
OPRF: ristretto255-SHA512
Hash: SHA512
KSF: Identity
KDF: HKDF-SHA512
MAC: HMAC-SHA512
Group: ristretto255
Context: 4f50415155452d504f43
Nh: 64
Npk: 32
Nsk: 32
Nm: 64
Nx: 64
Nok: 32
D.2.1.2. Input Values
client_identity: 616c696365
server_identity: 626f62
oprf_seed: 743fc168d1f826ad43738933e5adb23da6fb95f95a1b069f0daa0522d0
a78b617f701fc6aa46d3e7981e70de7765dfcd6b1e13e3369a582eb8dc456b10aa53b
0
credential_identifier: 31323334
masking_nonce: 9c035896a043e70f897d87180c543e7a063b83c1bb728fbd189c61
9e27b6e5a6
client_private_key: 2b98980aa95ab53a0f39f0291903d2fdf04b00c167f081416
9922df873002409
client_public_key: 84f43f9492e19c22d8bdaa4447cc3d4db1cdb5427a9f852c47
07921212c36251
server_private_key: c788585ae8b5ba2942b693b849be0c0426384e41977c18d2e
81fbe30fd7c9f06
server_public_key: 825f832667480f08b0c9069da5083ac4d0e9ee31b49c4e0310
031fea04d52966
server_nonce: 1e10f6eeab2a7a420bf09da9b27a4639645622c46358de9cf7ae813
055ae2d12
client_keyshare_seed: a270dc715dc2b4612bc7864312a05c3e9788ee1bad1f276
d1e15bdeb4c355e94
server_keyshare_seed: 360b0937f47d45f6123a4d8f0d0c0814b6120d840ebb8bc
5b4f6b62df07f78c2
masking_key: 39ebd51f0e39a07a1c2d2431995b0399bca9996c5d10014d6ebab445
3dc10ce5cef38ed3df6e56bfff40c2d8dd4671c2b4cf63c3d54860f31fe40220d690b
b71
KE1: b0a26dcaca2230b8f5e4b1bcab9c84b586140221bb8b2848486874b0be448905
42d4e61ed3f8d64cdd3b9d153343eca15b9b0d5e388232793c6376bd2d9cfd0ab641d
7f20a245a09f1d4dbb6e301661af7f352beb0791d055e48d3645232f77f
Bourdrez, et al. Expires 20 June 2024 [Page 77]
Internet-Draft OPAQUE December 2023
D.2.1.3. Output Values
KE2: 928f79ad8df21963e91411b9f55165ba833dea918f441db967cdc09521d22925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D.2.2. OPAQUE-3DH Fake Test Vector 2
D.2.2.1. Configuration
OPRF: ristretto255-SHA512
Hash: SHA512
KSF: Identity
KDF: HKDF-SHA512
MAC: HMAC-SHA512
Group: curve25519
Context: 4f50415155452d504f43
Nh: 64
Npk: 32
Nsk: 32
Nm: 64
Nx: 64
Nok: 32
D.2.2.2. Input Values
Bourdrez, et al. Expires 20 June 2024 [Page 78]
Internet-Draft OPAQUE December 2023
client_identity: 616c696365
server_identity: 626f62
oprf_seed: 66e650652a8266b2205f31fdd68adeb739a05b5e650b19e7edc75e734a
1296d6088188ca46c31ae8ccbd42a52ed338c06e53645387a7efbc94b6a0449526155
e
credential_identifier: 31323334
masking_nonce: 9c035896a043e70f897d87180c543e7a063b83c1bb728fbd189c61
9e27b6e5a6
client_private_key: 288bf63470199221847bb035d99f96531adf8badd14cb1571
b48f7a506649660
client_public_key: 3c64a3153854cc9f0c23aab3c1a19106ec8bab4730736d1d00
3880a1d5a59005
server_private_key: 30fbe7e830be1fe8d2187c97414e3826040cbe49b893b6422
9bab5e85a588846
server_public_key: 78b3040047ff26572a7619617601a61b9c81899bee92f00cfc
aa5eed96863555
server_nonce: 1e10f6eeab2a7a420bf09da9b27a4639645622c46358de9cf7ae813
055ae2d12
client_keyshare_seed: a270dc715dc2b4612bc7864312a05c3e9788ee1bad1f276
d1e15bdeb4c355e94
server_keyshare_seed: 360b0937f47d45f6123a4d8f0d0c0814b6120d840ebb8bc
5b4f6b62df07f78c2
masking_key: 79ad2621b0757a447dff7108a8ae20a068ce67872095620f415ea611
c9dcc04972fa359538cd2fd6528775ca775487b2b56db642049b8a90526b975a38484
c6a
KE1: b0a26dcaca2230b8f5e4b1bcab9c84b586140221bb8b2848486874b0be448905
42d4e61ed3f8d64cdd3b9d153343eca15b9b0d5e388232793c6376bd2d9cfd0ac059b
7ba2aec863933ae48816360c7a9022e83d822704f3b0b86c0502a66e574
D.2.2.3. Output Values
KE2: 6606b6fedbb33f19a81a1feb5149c600fe77252f58acd3080d7504d3dad4922f
9c035896a043e70f897d87180c543e7a063b83c1bb728fbd189c619e27b6e5a67db39
8c0f65d8c298eac430abdae4c80e82b552fb940c00f0cbcea853c0f96c1c15099f3d4
b0e83ecc249613116d605b8d77bb68bdf76994c2bc507e2dcae4176f00afed68ad25c
f3040a0e991acece31ca532117f5c12816997372ff031ad04ebcdce06c501da24e7b4
db95343456e2ed260895ec362694230a1fa20e24a9c71e10f6eeab2a7a420bf09da9b
27a4639645622c46358de9cf7ae813055ae2d122d9055eb8f83e1b497370adad5cc2a
417bf9be436a792def0c7b7ccb92b9e275d7c663104ea4655bd70570d975c05351655
d55fbfb392286edb55600a23b55ce18f8c60e0d1960c960412dd08eabc81ba7ca8ae2
b04aad65462321f51c298010
D.2.3. OPAQUE-3DH Fake Test Vector 3
D.2.3.1. Configuration
Bourdrez, et al. Expires 20 June 2024 [Page 79]
Internet-Draft OPAQUE December 2023
OPRF: P256-SHA256
Hash: SHA256
KSF: Identity
KDF: HKDF-SHA256
MAC: HMAC-SHA256
Group: P256_XMD:SHA-256_SSWU_RO_
Context: 4f50415155452d504f43
Nh: 32
Npk: 33
Nsk: 32
Nm: 32
Nx: 32
Nok: 32
D.2.3.2. Input Values
client_identity: 616c696365
server_identity: 626f62
oprf_seed: bb1cd59e16ac09bc0cb6d528541695d7eba2239b1613a3db3ade77b362
80f725
credential_identifier: 31323334
masking_nonce: 9c035896a043e70f897d87180c543e7a063b83c1bb728fbd189c61
9e27b6e5a6
client_private_key: d423b87899fc61d014fc8330a4e26190fcfa470a3afe59243
24294af7dbbc1dd
client_public_key: 03b81708eae026a9370616c22e1e8542fe9dbebd36ce8a2661
b708e9628f4a57fc
server_private_key: 34fbe7e830be1fe8d2187c97414e3826040cbe49b893b6422
9bab5e85a5888c7
server_public_key: 0221e034c0e202fe883dcfc96802a7624166fed4cfcab4ae30
cf5f3290d01c88bf
server_nonce: 1e10f6eeab2a7a420bf09da9b27a4639645622c46358de9cf7ae813
055ae2d12
client_keyshare_seed: a270dc715dc2b4612bc7864312a05c3e9788ee1bad1f276
d1e15bdeb4c355e94
server_keyshare_seed: 360b0937f47d45f6123a4d8f0d0c0814b6120d840ebb8bc
5b4f6b62df07f78c2
masking_key: caecc6ccb4cae27cb54d8f3a1af1bac52a3d53107ce08497cdd362b1
992e4e5e
KE1: 0396875da2b4f7749bba411513aea02dc514a48d169d8a9531bd61d3af3fa9ba
ae42d4e61ed3f8d64cdd3b9d153343eca15b9b0d5e388232793c6376bd2d9cfd0a021
47a6583983cc9973b5082db5f5070890cb373d70f7ac1b41ed2305361009784
D.2.3.3. Output Values
Bourdrez, et al. Expires 20 June 2024 [Page 80]
Internet-Draft OPAQUE December 2023
KE2: 0201198dcd13f9792eb75dcfa815f61b049abfe2e3e9456d4bbbceec5f442efd
049c035896a043e70f897d87180c543e7a063b83c1bb728fbd189c619e27b6e5a6fac
da65ce0a97b9085e7af07f61fd3fdd046d257cbf2183ce8766090b8041a8bf28d79dd
4c9031ddc75bb6ddb4c291e639937840e3d39fc0d5a3d6e7723c09f7945df485bcf9a
efe3fe82d149e84049e259bb5b33d6a2ff3b25e4bfb7eff0962821e10f6eeab2a7a42
0bf09da9b27a4639645622c46358de9cf7ae813055ae2d12023f82bbb24e75b8683fd
13b843cd566efae996cd0016cffdcc24ee2bc937d026f80144878749a69565b433c10
40aff67e94f79345de888a877422b9bbe21ec329
Authors' Addresses
Daniel Bourdrez
Email: d@bytema.re
Hugo Krawczyk
AWS
Email: hugokraw@gmail.com
Kevin Lewi
Meta
Email: lewi.kevin.k@gmail.com
Christopher A. Wood
Cloudflare, Inc.
Email: caw@heapingbits.net
Bourdrez, et al. Expires 20 June 2024 [Page 81]
