Internet DRAFT - draft-irtf-cfrg-opaque
draft-irtf-cfrg-opaque
Network Working Group D. Bourdrez
Internet-Draft
Intended status: Informational H. Krawczyk
Expires: 14 September 2023 Algorand Foundation
K. Lewi
Novi Research
C. A. Wood
Cloudflare, Inc.
13 March 2023
The OPAQUE Asymmetric PAKE Protocol
draft-irtf-cfrg-opaque-10
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
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provisions of BCP 78 and BCP 79.
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This Internet-Draft will expire on 14 September 2023.
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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 . . . . . . . . . . . . . . . . . . . . . . 12
4.1.1. Envelope Structure . . . . . . . . . . . . . . . . . 12
4.1.2. Envelope Creation . . . . . . . . . . . . . . . . . . 13
4.1.3. Envelope Recovery . . . . . . . . . . . . . . . . . . 13
5. Offline Registration . . . . . . . . . . . . . . . . . . . . 14
5.1. Registration Messages . . . . . . . . . . . . . . . . . . 16
5.2. Registration Functions . . . . . . . . . . . . . . . . . 16
5.2.1. CreateRegistrationRequest . . . . . . . . . . . . . . 17
5.2.2. CreateRegistrationResponse . . . . . . . . . . . . . 17
5.2.3. FinalizeRegistrationRequest . . . . . . . . . . . . . 18
6. Online Authenticated Key Exchange . . . . . . . . . . . . . . 19
6.1. AKE Messages . . . . . . . . . . . . . . . . . . . . . . 22
6.2. AKE Functions . . . . . . . . . . . . . . . . . . . . . . 23
6.2.1. ClientInit . . . . . . . . . . . . . . . . . . . . . 23
6.2.2. ServerInit . . . . . . . . . . . . . . . . . . . . . 23
6.2.3. ClientFinish . . . . . . . . . . . . . . . . . . . . 24
6.2.4. ServerFinish . . . . . . . . . . . . . . . . . . . . 25
6.3. Credential Retrieval . . . . . . . . . . . . . . . . . . 26
6.3.1. Credential Retrieval Messages . . . . . . . . . . . . 26
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6.3.2. Credential Retrieval Functions . . . . . . . . . . . 27
6.4. AKE Protocol . . . . . . . . . . . . . . . . . . . . . . 30
6.4.1. Key Creation . . . . . . . . . . . . . . . . . . . . 31
6.4.2. Key Schedule Functions . . . . . . . . . . . . . . . 31
6.4.3. 3DH Client Functions . . . . . . . . . . . . . . . . 33
6.4.4. 3DH Server Functions . . . . . . . . . . . . . . . . 35
7. Configurations . . . . . . . . . . . . . . . . . . . . . . . 37
8. Application Considerations . . . . . . . . . . . . . . . . . 38
9. Implementation Considerations . . . . . . . . . . . . . . . . 39
9.1. Implementation Safeguards . . . . . . . . . . . . . . . . 39
9.2. Error Considerations . . . . . . . . . . . . . . . . . . 40
10. Security Considerations . . . . . . . . . . . . . . . . . . . 41
10.1. Notable Design Differences . . . . . . . . . . . . . . . 41
10.2. Security Analysis . . . . . . . . . . . . . . . . . . . 44
10.3. Related Protocols . . . . . . . . . . . . . . . . . . . 45
10.4. Identities . . . . . . . . . . . . . . . . . . . . . . . 45
10.5. Export Key Usage . . . . . . . . . . . . . . . . . . . . 46
10.6. Static Diffie-Hellman Oracles . . . . . . . . . . . . . 46
10.7. Input Validation . . . . . . . . . . . . . . . . . . . . 47
10.8. OPRF Key Stretching . . . . . . . . . . . . . . . . . . 47
10.9. Client Enumeration . . . . . . . . . . . . . . . . . . . 47
10.10. Protecting the Registration Masking Key . . . . . . . . 48
10.11. Password Salt and Storage Implications . . . . . . . . . 49
10.12. AKE Private Key Storage . . . . . . . . . . . . . . . . 49
11. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 49
12. References . . . . . . . . . . . . . . . . . . . . . . . . . 49
12.1. Normative References . . . . . . . . . . . . . . . . . . 50
12.2. Informative References . . . . . . . . . . . . . . . . . 50
Appendix A. Acknowledgments . . . . . . . . . . . . . . . . . . 53
Appendix B. Alternate Key Recovery Mechanisms . . . . . . . . . 53
Appendix C. Alternate AKE Instantiations . . . . . . . . . . . . 54
C.1. HMQV Instantiation Sketch . . . . . . . . . . . . . . . . 54
C.2. SIGMA-I Instantiation Sketch . . . . . . . . . . . . . . 55
Appendix D. Test Vectors . . . . . . . . . . . . . . . . . . . . 55
D.1. Real Test Vectors . . . . . . . . . . . . . . . . . . . . 56
D.1.1. OPAQUE-3DH Real Test Vector 1 . . . . . . . . . . . . 56
D.1.2. OPAQUE-3DH Real Test Vector 2 . . . . . . . . . . . . 59
D.1.3. OPAQUE-3DH Real Test Vector 3 . . . . . . . . . . . . 62
D.1.4. OPAQUE-3DH Real Test Vector 4 . . . . . . . . . . . . 64
D.2. Fake Test Vectors . . . . . . . . . . . . . . . . . . . . 67
D.2.1. OPAQUE-3DH Fake Test Vector 1 . . . . . . . . . . . . 67
D.2.2. OPAQUE-3DH Fake Test Vector 2 . . . . . . . . . . . . 68
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 70
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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, a PKI-free secure aPAKE that is
secure against pre-computation attacks. 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 [_3DH]. Other instantiations are
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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 10.9 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.
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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 such that the client
learns the PRF output and neither party learns the input of the
other. This specification depends on the prime-order OPRF
construction specified in [OPRF], draft version -20, using the OPRF
mode (0x00) from [OPRF], Section 3.1.
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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): Derive a private and public key pair
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 buf.
* 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:
* Extract(salt, ikm): Extract a pseudorandom key of fixed length Nx
bytes from input keying material ikm and an optional byte string
salt.
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* 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 collision-resistant Message
Authentication Code (MAC) with the following API and parameters:
* 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, params): Apply a key stretching function with
parameters params 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. 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" 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 this single pair of keys with multiple clients and
can opt to use multiple seeds (so long as they are kept consistent
for each client).
3.2. Offline Registration
Registration is the only stage in OPAQUE that requires a server-
authenticated and confidential channel: 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., 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:
creds parameters
| |
v v
Client Server
------------------------------------------------
registration request
------------------------->
registration response
<-------------------------
record
------------------------->
------------------------------------------------
| |
v v
export_key record
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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:
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.
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The rest of this document describes the details 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.
Future variants of OPAQUE may use different key recovery mechanisms.
See Section 4.1 for details.
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.
* 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.
These credential values are used in the CleartextCredentials
structure as follows:
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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
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 DeriveAuthKeyPair() 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;
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nonce: A unique 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 DeriveAuthKeyPair in this function can fail
with negligible probability. If this occurs, servers should re-run
the function, sampling a new envelope_nonce, to completion.
Store
Input:
- randomized_pwd, 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_pwd, server_public_key, server_identity, client_identity):
envelope_nonce = random(Nn)
masking_key = Expand(randomized_pwd, "MaskingKey", Nh)
auth_key = Expand(randomized_pwd, concat(envelope_nonce, "AuthKey"), Nh)
export_key = Expand(randomized_pwd, concat(envelope_nonce, "ExportKey"), Nh)
seed = Expand(randomized_pwd, concat(envelope_nonce, "PrivateKey"), Nseed)
(_, client_public_key) = DeriveAuthKeyPair(seed)
cleartext_creds =
CreateCleartextCredentials(server_public_key, client_public_key,
server_identity, client_identity)
auth_tag = MAC(auth_key, concat(envelope_nonce, cleartext_creds))
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_pwd, 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.
- export_key, an additional client key.
Exceptions:
- EnvelopeRecoveryError, the envelope fails to be recovered.
def Recover(randomized_pwd, server_public_key, envelope,
server_identity, client_identity):
auth_key = Expand(randomized_pwd, concat(envelope.nonce, "AuthKey"), Nh)
export_key = Expand(randomized_pwd, concat(envelope.nonce, "ExportKey"), Nh)
seed = Expand(randomized_pwd, concat(envelope.nonce, "PrivateKey"), Nseed)
(client_private_key, client_public_key) = DeriveAuthKeyPair(seed)
cleartext_creds = CreateCleartextCredentials(server_public_key,
client_public_key, server_identity, client_identity)
expected_tag = MAC(auth_key, concat(envelope.nonce, cleartext_creds))
If !ct_equal(envelope.auth_tag, expected_tag)
raise EnvelopeRecoveryError
return (client_private_key, export_key)
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_private_key: The server private key for the AKE protocol.
* server_public_key: The server public key for the AKE protocol.
* credential_identifier: A unique identifier for the client's
credential, generated by the server.
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* 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 10.9. The server_private_key may be unique
for each client.
Both client and server MUST validate the other party's public key
before use. See Section 10.7 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.
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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 to preserve
confidentiality of the envelope during login to defend 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 a 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, params)
randomized_pwd = Extract("", concat(oprf_output, stretched_oprf_output))
(envelope, client_public_key, masking_key, export_key) =
Store(randomized_pwd, 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. The output export_key MUST NOT be used in any way
before the protocol completes successfully. 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 = ClientInit(password)
ke1
------------------------->
ke2 = ServerInit(server_identity, server_private_key,
server_public_key, record,
credential_identifier, oprf_seed, ke1)
ke2
<-------------------------
(ke3,
session_key,
export_key) = ClientFinish(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.
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
internal functions used for retrieving client credentials, and
Section 6.4 discusses how these functions are used to execute the
authenticated key exchange protocol.
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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_keyshare[Npk];
} AuthRequest;
client_nonce: A fresh randomly generated nonce of length Nn.
client_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_keyshare[Npk];
uint8 server_mac[Nm];
} AuthResponse;
server_nonce: A fresh randomly generated nonce of length Nn.
server_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;
credential_response: A CredentialResponse structure.
auth_response: An AuthResponse structure.
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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. ClientInit
The ClientInit function begins the AKE protocol and produces the
client's KE1 output for the server.
ClientInit
State:
- state, a ClientState structure.
Input:
- password, an opaque byte string containing the client's password.
Output:
- ke1, a KE1 message structure.
def ClientInit(password):
request, blind = CreateCredentialRequest(password)
state.password = password
state.blind = blind
ke1 = AuthClientStart(request)
return ke1
6.2.2. ServerInit
The ServerInit function continues the AKE protocol by processing the
client's KE1 message and producing the server's KE2 output.
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ServerInit
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 ServerInit(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)
auth_response = AuthServerRespond(server_identity, server_private_key,
client_identity, record.client_public_key, ke1, credential_response)
Create KE2 ke2 with (credential_response, auth_response)
return ke2
6.2.3. ClientFinish
The ClientFinish 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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ClientFinish
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 ClientFinish(client_identity, server_identity, ke2):
(client_private_key, server_public_key, export_key) =
RecoverCredentials(state.password, state.blind, ke2.credential_response,
server_identity, client_identity)
(ke3, session_key) =
AuthClientFinalize(client_identity, client_private_key, server_identity,
server_public_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.
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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)
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.
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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.
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 a 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 a client that has yet to register).
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In the case of an existing record with the corresponding identifier
credential_identifier, the server invokes the following function to
produce a CredentialResponse:
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
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* record.envelope is set to the byte string consisting only of zeros
of length Nn + Nm
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 locate 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 client's private key for the AKE protocol.
- server_public_key, the public key of the server.
- 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, params)
randomized_pwd = Extract("", concat(oprf_output, stretched_oprf_output))
masking_key = Expand(randomized_pwd, "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, export_key) =
Recover(randomized_pwd, server_public_key, envelope,
server_identity, client_identity)
return (client_private_key, server_public_key, export_key)
6.4. AKE 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. Key Creation
We assume the following functions to exist for all candidate groups
in this setting:
* DeriveAuthKeyPair(seed): Derive a private and public
authentication key pair deterministically from the input seed.
This function is implemented as DeriveKeyPair(seed, "OPAQUE-
DeriveAuthKeyPair"), where DeriveKeyPair is as specified in
[OPRF], Section 3.2.
* GenerateAuthKeyPair(): Return a randomly generated private and
public key pair. This can be implemented by invoking
DeriveAuthKeyPair with Nseed random bytes as input.
* SerializeElement(element): A member function of the underlying
group that maps element to a unique byte array, mirrored from the
definition of the similarly-named function of the OPRF group
described in [OPRF], Section 2.1.
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 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_keyshare, the corresponding field on the AuthResponse structure.
Output:
- preamble, the protocol transcript with identities and messages.
def Preamble(client_identity, ke1, server_identity, ke2):
preamble = concat("RFCXXXX",
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_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_secret, client_keyshare) = GenerateAuthKeyPair()
Create AuthRequest auth_request with (client_nonce, client_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:
- client_identity, the optional encoded client identity, which is
set to client_public_key if not specified.
- client_private_key, the client's private key.
- server_identity, the optional encoded server identity, which is
set to server_public_key if not specified.
- server_public_key, the server's public key.
- ke2, a KE2 message structure.
Output:
- ke3, a KE3 structure.
- session_key, the shared session secret.
Exceptions:
- ServerAuthenticationError, the handshake fails.
def AuthClientFinalize(client_identity, client_private_key, server_identity,
server_public_key, ke2):
dh1 = SerializeElement(state.client_secret * ke2.auth_response.server_keyshare)
dh2 = SerializeElement(state.client_secret * server_public_key)
dh3 = SerializeElement(client_private_key * ke2.auth_response.server_keyshare)
ikm = concat(dh1, dh2, dh3)
preamble = Preamble(client_identity,
state.ke1,
server_identity,
ke2.credential_response,
ke2.auth_response.server_nonce,
ke2.auth_response.server_keyshare)
Km2, Km3, session_key = DeriveKeys(ikm, preamble)
expected_server_mac = MAC(Km2, Hash(preamble))
if !ct_equal(ke2.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:
- 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.
- client_identity, the optional encoded client identity, which is set to
client_public_key if not specified.
- client_public_key, the client's public key.
- ke1, a KE1 message structure.
Output:
- auth_response, an AuthResponse structure.
def AuthServerRespond(server_identity, server_private_key, client_identity,
client_public_key, ke1, credential_response):
server_nonce = random(Nn)
(server_private_keyshare, server_keyshare) = GenerateAuthKeyPair()
preamble = Preamble(client_identity,
ke1,
server_identity,
credential_response,
server_nonce,
server_keyshare)
dh1 = SerializeElement(server_private_keyshare * ke1.auth_request.client_keyshare)
dh2 = SerializeElement(server_private_key * ke1.auth_request.client_keyshare)
dh3 = SerializeElement(server_private_keyshare * client_public_key)
ikm = concat(dh1, dh2, dh3)
Km2, Km3, session_key = DeriveKeys(ikm, preamble)
server_mac = MAC(Km2, Hash(preamble))
expected_client_mac = MAC(Km3, Hash(concat(preamble, server_mac)))
state.expected_client_mac = MAC(Km3, Hash(concat(preamble, server_mac)))
state.session_key = session_key
Create AuthResponse auth_response with (server_nonce, server_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 has fixed parameters, chosen by the application, and
implements the interface in Section 2. Examples include Argon2id
[ARGON2], scrypt [SCRYPT], and PBKDF2 [PBKDF2] with fixed
parameter choices.
* 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(t=1, p=4, m=2^21), ristretto255
* P256-SHA256, HKDF-SHA-256, HMAC-SHA-256, SHA-256, Argon2id(t=1,
p=4, m=2^21), P-256
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.
* 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 10.9. In settings
where this attack is not a concern, servers may choose to not
support this functionality.
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, implementations can incorporate the client
identity alongside the password as input to the OPRF. This provides
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additional client-side entropy which can supplement the entropy that
should be introduced by the server during an honest execution of the
protocol. This also provides domain separation between different
clients that might otherwise share the same password.
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. Implementations and deployments of OPAQUE
SHOULD consider additional checks to mitigate this type of attack:
for instance, by ensuring that there is a server-authenticated
channel over which OPAQUE registration and login are run.
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.
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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 stores a secret
private key at the server 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.
10.1. Notable Design Differences
[[RFC EDITOR: Please delete this section before publication.]]
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. An upcoming paper 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 variant is also analyzed in the new
paper referred to in the previous item. This change improves the
assumption behind the protocol by getting rid of equivocality and
random key robustness for the encryption function. The latter
property is only required for authentication and achieved by a
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collision-resistant MAC. 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 authentication 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 10.9 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.
* Per-user OPRF keys are derived from a client identity and cross-
user PRF seed as a mitigation against client enumeration attacks.
See Section 10.9 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 independent of other
values in the protocol 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
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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 password file 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 OPRF has different PRF inputs,
the protocol is secure. The choice of such inputs is up to the
application.
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
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using HMQV is included in Appendix C.1). Since 3DH satisfies the
essential requirements for the AKE as described in [JKX18] and
[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 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. In turn,
the security of the OPRF protocol from [OPRF] is proven in the random
oracle model under the One-More Diffie-Hellman assumption [JKKX16].
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
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exhaustive dictionary attack. Another essential requirement from AKE
protocols for use in OPAQUE is to provide forward secrecy (against
active attackers).
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.
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
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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.
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 server is
expected to maintain any client-side secrets which require a password
to access, then this export key can be used to encrypt these secrets
so that they remain hidden from the server.
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
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attempts directed at individual users.
10.7. 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
is not the point at infinity. Additionally, validation MUST ensure
the Diffie-Hellman shared secret is not the point at infinity.
10.8. 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
that balance cost and complexity. Note that in OPAQUE, the key
stretching function is executed by the client, as opposed to the
server. 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.
10.9. Client Enumeration
Client enumeration refers to attacks where the attacker tries to
learn extra information about the behavior of clients that have
registered with the server. There are two types of attacks we
consider:
1) An attacker tries to learn whether a given client identity is
registered with a server, and 2) An attacker tries to learn whether a
given client identity has recently completed registration, re-
registered (e.g. after a password change), or changed its identity.
OPAQUE prevents these attacks during the authentication flow. The
first is prevented 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
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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.
Preventing the second type of attack requires the server to supply a
credential_identifier value for a given client identity, consistently
between the registration response and credential response; see
Section 5.2.2 and Section 6.3.2.2. Note that credential_identifier
can be set to client_identity for simplicity.
In the event of a server compromise that results in a re-registration
of credentials for all compromised clients, the oprf_seed value MUST
be resampled, resulting in a change in the oprf_key value for each
client. Although this change can be detected by an adversary, it is
only leaked upon password rotation after the exposure of the
credential files, and equally affects all registered clients.
Finally, applications must use the same key recovery mechanism when
using this prevention throughout their lifecycle. The envelope size
may vary between mechanisms, so a switch could then be detected.
OPAQUE does not prevent either 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.
10.10. Protecting the Registration Masking Key
The user enumeration prevention method described in this documents
uses a symmetric encryption key generated by the client on
registration that is sent to the server over an authenticated
channel, such as one provided by TLS [RFC8446]. In the event that
this channel is compromised, this encryption key could be leaked to
an attacker.
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One mitigation against this threat is to additionally encrypt the
RegistrationRecord sent from client to server at the application
layer using public key encryption, e.g., with HPKE [RFC9180].
However, the details of this mechanism are out of scope of this
document.
10.11. 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 aPAKE protocol. (OPAQUE
enables defense against such offline dictionary attacks by
distributing the server so that an offline attack is only possible if
all - or a minimal number of - servers are compromised [JKX18].)
Furthermore, if the server does not sample this OPRF key 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. Applications
should move such checks to the client. Note that limited checks at
the server are possible to implement, e.g., detecting repeated
passwords.
10.12. 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
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
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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
[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.
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[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", Euroctypt 2006 , 2006.
[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.
[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.
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[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 report,
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>.
[PAKE-Selection]
"CFRG PAKE selection process repository", n.d.,
<https://github.com/cfrg/pake-selection>.
[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>.
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[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>.
[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>.
[SPAKE2plus]
Shoup, V., "Security Analysis of SPAKE2+",
http://eprint.iacr.org/2020/313 , 2020.
[WhatsAppE2E]
"Security of End-to-End Encrypted Backups", n.d.,
<https://www.whatsapp.com/security/
WhatsApp_Security_Encrypted_Backups_Whitepaper.pdf>.
[_3DH] "Simplifying OTR deniability",
https://signal.org/blog/simplifying-otr-deniability ,
2016.
Appendix A. Acknowledgments
The OPAQUE protocol and its analysis is the joint work of the author
with Stanislaw Jarecki and Jiayu Xu. 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, Eric
Crockett, Paul Grubbs, Fredrik Kuivinen, Payman Mohassel, Jason
Resch, Greg Rubin, and Nick Sullivan.
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 of
application data encrypted under session_key (or a key derived from
it) with a quantum-safe encryption function.
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_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:
s' = (eskS + s \* skS) mod p
IKM = (epkU \* pkU^u)^s'
In both cases, u would be computed as follows:
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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.
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
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.
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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-10 of [OPRF].
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
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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
server_keyshare: c8c39f573135474c51660b02425bca633e339cec4e1acc69c94d
d48497fe4028
client_keyshare: 0c3a00c961fead8a16f818929cc976f0475e4f723519318b96f4
947a7a5f9663
server_private_keyshare: 2e842960258a95e28bcfef489cffd19d8ec99cc1375d
840f96936da7dbb0b40d
client_private_keyshare: 22c919134c9bdd9dc0c5ef3450f18b54820f43f646a9
5223bf4a85b2018c2001
blind_registration: 76cfbfe758db884bebb33582331ba9f159720ca8784a2a070
a265d9c2d6abe01
blind_login: 6ecc102d2e7a7cf49617aad7bbe188556792d4acd60a1a8a8d2b65d4
b0790308
D.1.1.3. Intermediate Values
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client_public_key: 2ec892bdbf9b3e2ea834be9eb11f5d187e64ba661ec041c0a3
b66db8b7d6cc30
auth_key: 6cd32316f18d72a9a927a83199fa030663a38ce0c11fbaef82aa9003773
0494fc555c4d49506284516edd1628c27965b7555a4ebfed2223199f6c67966dde822
randomized_pwd: aac48c25ab036e30750839d31d6e73007344cb1155289fb7d329b
eb932e9adeea73d5d5c22a0ce1952f8aba6d66007615cd1698d4ac85ef1fcf150031d
1435d9
envelope: ac13171b2f17bc2c74997f0fce1e1f35bec6b91fe2e12dbd323d23ba7a3
8dfecb9dbe7d48cf714fc3533becab6faf60b783c94d258477eb74ecc453413bf61c5
3fd58f0fb3c1175410b674c02e1b59b2d729a865b709db3dc4ee2bb45703d5a8
handshake_secret: 562564da0d4efdc73cb6efbb454388dabfa5052d4e7e83f4d02
40c5afd8352881e762755c2f1a9110e36b05fe770f0f48658489c9730dcd365e6c2d4
049c8fe3
server_mac_key: 59473632c53a647f9f4ab4d6c3b81e241dd9cb19ca05f0eabed7e
593f0407ff57e7f060621e5e48d5291be600a1959fbecbc26d4a7157bd227a993c37b
645f73
client_mac_key: f2d019bad603b45b2ac50376279a0a37d097723b5405aa4fb20a5
9f60cdbdd52ec043372cedcdbbdb634c54483e1be51a88d13a5798180acb84c10b129
7069fd
oprf_key: 5d4c6a8b7c7138182afb4345d1fae6a9f18a1744afbcc3854f8f5a2b4b4
c6d05
D.1.1.4. Output Values
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registration_request: 5059ff249eb1551b7ce4991f3336205bde44a105a032e74
7d21bf382e75f7a71
registration_response: 7408a268083e03abc7097fc05b587834539065e86fb0c7
b6342fcf5e01e5b019b2fe7af9f48cc502d016729d2fe25cdd433f2c4bc904660b2a3
82c9b79df1a78
registration_upload: 2ec892bdbf9b3e2ea834be9eb11f5d187e64ba661ec041c0
a3b66db8b7d6cc301ac5844383c7708077dea41cbefe2fa15724f449e535dd7dd562e
66f5ecfb95864eadddec9db5874959905117dad40a4524111849799281fefe3c51fa8
2785c5ac13171b2f17bc2c74997f0fce1e1f35bec6b91fe2e12dbd323d23ba7a38dfe
cb9dbe7d48cf714fc3533becab6faf60b783c94d258477eb74ecc453413bf61c53fd5
8f0fb3c1175410b674c02e1b59b2d729a865b709db3dc4ee2bb45703d5a8
KE1: c4dedb0ba6ed5d965d6f250fbe554cd45cba5dfcce3ce836e4aee778aa3cd44d
da7e07376d6d6f034cfa9bb537d11b8c6b4238c334333d1f0aebb380cae6a6cc0c3a0
0c961fead8a16f818929cc976f0475e4f723519318b96f4947a7a5f9663
KE2: 7e308140890bcde30cbcea28b01ea1ecfbd077cff62c4def8efa075aabcbb471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KE3: df9a13cd256091f90f0fcb2ef6b3411e4aebff07bb0813299c0ec7f5dedd33a7
681231a001a82f1dece1777921f42abfeee551ee34392e1c9743c5cc1dc1ef8c
export_key: 1ef15b4fa99e8a852412450ab78713aad30d21fa6966c9b8c9fb3262a
970dc62950d4dd4ed62598229b1b72794fc0335199d9f7fcc6eaedde92cc04870e63f
16
session_key: 8a0f9f4928fc0c3b5bb261c4b7b3997600405424a8128632e85a5667
b4b742484ed791933971be6d3fcf2b23c56b8e8f7e7edcae19a03b8fd87f5999fce12
9d2
D.1.2. OPAQUE-3DH Real Test Vector 2
D.1.2.1. Configuration
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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
server_keyshare: c8c39f573135474c51660b02425bca633e339cec4e1acc69c94d
d48497fe4028
client_keyshare: 0c3a00c961fead8a16f818929cc976f0475e4f723519318b96f4
947a7a5f9663
server_private_keyshare: 2e842960258a95e28bcfef489cffd19d8ec99cc1375d
840f96936da7dbb0b40d
client_private_keyshare: 22c919134c9bdd9dc0c5ef3450f18b54820f43f646a9
5223bf4a85b2018c2001
blind_registration: 76cfbfe758db884bebb33582331ba9f159720ca8784a2a070
a265d9c2d6abe01
blind_login: 6ecc102d2e7a7cf49617aad7bbe188556792d4acd60a1a8a8d2b65d4
b0790308
Bourdrez, et al. Expires 14 September 2023 [Page 60]
Internet-Draft OPAQUE March 2023
D.1.2.3. Intermediate Values
client_public_key: 2ec892bdbf9b3e2ea834be9eb11f5d187e64ba661ec041c0a3
b66db8b7d6cc30
auth_key: 6cd32316f18d72a9a927a83199fa030663a38ce0c11fbaef82aa9003773
0494fc555c4d49506284516edd1628c27965b7555a4ebfed2223199f6c67966dde822
randomized_pwd: aac48c25ab036e30750839d31d6e73007344cb1155289fb7d329b
eb932e9adeea73d5d5c22a0ce1952f8aba6d66007615cd1698d4ac85ef1fcf150031d
1435d9
envelope: ac13171b2f17bc2c74997f0fce1e1f35bec6b91fe2e12dbd323d23ba7a3
8dfec1ac902dc5589e9a5f0de56ad685ea8486210ef41449cd4d8712828913c5d2b68
0b2b3af4a26c765cff329bfb66d38ecf1d6cfa9e7a73c222c6efe0d9520f7d7c
handshake_secret: bc2abaa979af9cbb6859856b7d5d201a038fbdfa7e10f11d131
d3f8f6fc3b263bde4db6d2d9207d4648ff80415a276d5f157f9d37a3eade559db2e5f
3fa026b2
server_mac_key: 2420461c589866700b08c8818cbf390c872629a14cf32a264dad3
375f85f33188c8f04bdb71880b2d4613187a0e416808ab62b45858b88319882602371
ef5f75
client_mac_key: 156e4ab0b9f71ef994bbbb73928e6d14d7335cf9561f113d61ac6
b41fab35f9c72fe827d3c4d7dd91d8398ee619810e4f9286e6b32f329eb6b1476ce18
fa8500
oprf_key: 5d4c6a8b7c7138182afb4345d1fae6a9f18a1744afbcc3854f8f5a2b4b4
c6d05
D.1.2.4. Output Values
Bourdrez, et al. Expires 14 September 2023 [Page 61]
Internet-Draft OPAQUE March 2023
registration_request: 5059ff249eb1551b7ce4991f3336205bde44a105a032e74
7d21bf382e75f7a71
registration_response: 7408a268083e03abc7097fc05b587834539065e86fb0c7
b6342fcf5e01e5b019b2fe7af9f48cc502d016729d2fe25cdd433f2c4bc904660b2a3
82c9b79df1a78
registration_upload: 2ec892bdbf9b3e2ea834be9eb11f5d187e64ba661ec041c0
a3b66db8b7d6cc301ac5844383c7708077dea41cbefe2fa15724f449e535dd7dd562e
66f5ecfb95864eadddec9db5874959905117dad40a4524111849799281fefe3c51fa8
2785c5ac13171b2f17bc2c74997f0fce1e1f35bec6b91fe2e12dbd323d23ba7a38dfe
c1ac902dc5589e9a5f0de56ad685ea8486210ef41449cd4d8712828913c5d2b680b2b
3af4a26c765cff329bfb66d38ecf1d6cfa9e7a73c222c6efe0d9520f7d7c
KE1: c4dedb0ba6ed5d965d6f250fbe554cd45cba5dfcce3ce836e4aee778aa3cd44d
da7e07376d6d6f034cfa9bb537d11b8c6b4238c334333d1f0aebb380cae6a6cc0c3a0
0c961fead8a16f818929cc976f0475e4f723519318b96f4947a7a5f9663
KE2: 7e308140890bcde30cbcea28b01ea1ecfbd077cff62c4def8efa075aabcbb471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KE3: a86ece659d90525e2476aa1756d313b067581cb7b0643b97be6b8ab8d0f10843
57e514ecfaff9dc18f6cca37da630545f0048393f16bc175eb819653ebc45b60
export_key: 1ef15b4fa99e8a852412450ab78713aad30d21fa6966c9b8c9fb3262a
970dc62950d4dd4ed62598229b1b72794fc0335199d9f7fcc6eaedde92cc04870e63f
16
session_key: 0968e91efeb702d6aa09023a9a79803332d8bd3442a79b8ad09490b9
267161013bf475bed945238a5e976ef7d7de7ff41ae30439fe2fc39758fb3e56f2683
e60
D.1.3. OPAQUE-3DH Real Test Vector 3
D.1.3.1. Configuration
Bourdrez, et al. Expires 14 September 2023 [Page 62]
Internet-Draft OPAQUE March 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.1.3.2. 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
server_keyshare: 020e67941e94deba835214421d2d8c90de9b0f7f925d11e2032c
e19b1832ae8e0f
client_keyshare: 03493f36ca12467d1f5eaaabea67ca31377c4869c1e9a62346b6
f01a991624b95d
server_private_keyshare: 9addab838c920fa7044f3a46b91ecaea24b0e7203992
8ee7d4c37a5b9bc17349
client_private_keyshare: 89d5a7e18567f255748a86beac13913df755a5adf776
d69e143147b545d22134
blind_registration: 411bf1a62d119afe30df682b91a0a33d777972d4f2daa4b34
ca527d597078153
blind_login: c497fddf6056d241e6cf9fb7ac37c384f49b357a221eb0a802c989b9
942256c1
D.1.3.3. Intermediate Values
Bourdrez, et al. Expires 14 September 2023 [Page 63]
Internet-Draft OPAQUE March 2023
client_public_key: 02dc91b178ba2c4bbf9b9403fca25457b906a7f507e59b6e70
3031e09114ba2be0
auth_key: 5bd4be1602516092dc5078f8d699f5721dc1720a49fb80d8e5c16377abd
0987b
randomized_pwd: 06be0a1a51d56557a3adad57ba29c5510565dcd8b5078fa319151
b9382258fb0
envelope: a921f2a014513bd8a90e477a629794e89fec12d12206dde662ebdcf6567
0e51fe155412cb432898eda63529c3b2633521f770cccbd25d7548a4e20665a45e65a
handshake_secret: c59197dd9269abfdb3037ea1c203a97627e2c0aa142000d1c3f
06a2c8713077d
server_mac_key: a431a5c1d3cb5772cbc66af0c2851e23dd9ad153a0c8b99081c7d
0d543173fde
client_mac_key: 7329ffd54df21db5532fce8794fca78b505fef9397aad28a424f6
ea3f97c51ca
oprf_key: 2dfb5cb9aa1476093be74ca0d43e5b02862a05f5d6972614d7433acdc66
f7f31
D.1.3.4. Output Values
registration_request: 029e949a29cfa0bf7c1287333d2fb3dc586c41aa652f507
0d26a5315a1b50229f8
registration_response: 0350d3694c00978f00a5ce7cd08a00547e4ab5fb5fc2b2
f6717cdaa6c89136efef035f40ff9cf88aa1f5cd4fe5fd3da9ea65a4923a5594f84fd
9f2092d6067784874
registration_upload: 02dc91b178ba2c4bbf9b9403fca25457b906a7f507e59b6e
703031e09114ba2be07f0ed53532d3ae8e505ecc70d42d2b814b6b0e48156def71ea0
29148b2803aafa921f2a014513bd8a90e477a629794e89fec12d12206dde662ebdcf6
5670e51fe155412cb432898eda63529c3b2633521f770cccbd25d7548a4e20665a45e
65a
KE1: 037342f0bcb3ecea754c1e67576c86aa90c1de3875f390ad599a26686cdfee6e
07ab3d33bde0e93eda72392346a7a73051110674bbf6b1b7ffab8be4f91fdaeeb1034
93f36ca12467d1f5eaaabea67ca31377c4869c1e9a62346b6f01a991624b95d
KE2: 0246da9fe4d41d5ba69faa6c509a1d5bafd49a48615a47a8dd4b0823cc147648
1138fe59af0df2c79f57b8780278f5ae47355fe1f817119041951c80f612fdfc6d2f0
c547f70deaeca54d878c14c1aa5e1ab405dec833777132eea905c2fbb12504a67dcbe
0e66740c76b62c13b04a38a77926e19072953319ec65e41f9bfd2ae2687bd3348bfe3
3cb0bb9864fdb3b307f7dd68a17f3f150074a0bfc830ab889717d71cd9960ecef2fe0
d0f7494986fa3d8b2bb01963537e60efb13981e138e3d4a1020e67941e94deba83521
4421d2d8c90de9b0f7f925d11e2032ce19b1832ae8e0fb5166145361a2c344d9737dd
5c826fede3bbfafa418ad379ce4fa65fbb15db6e
KE3: 272d04758b2b436bf0239ba7b9bd0a1686a9b6542ceaaf08732054beda956498
export_key: c3c9a1b0e33ac84dd83d0b7e8af6794e17e7a3caadff289fbd9dc769a
853c64b
session_key: a224790a010afc0a3f37e23c1b7a5cb7f9e73e3d9a924116510d97d8
0e2a1e0c
D.1.4. OPAQUE-3DH Real Test Vector 4
Bourdrez, et al. Expires 14 September 2023 [Page 64]
Internet-Draft OPAQUE March 2023
D.1.4.1. 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.1.4.2. 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
server_keyshare: 020e67941e94deba835214421d2d8c90de9b0f7f925d11e2032c
e19b1832ae8e0f
client_keyshare: 03493f36ca12467d1f5eaaabea67ca31377c4869c1e9a62346b6
f01a991624b95d
server_private_keyshare: 9addab838c920fa7044f3a46b91ecaea24b0e7203992
8ee7d4c37a5b9bc17349
client_private_keyshare: 89d5a7e18567f255748a86beac13913df755a5adf776
d69e143147b545d22134
blind_registration: 411bf1a62d119afe30df682b91a0a33d777972d4f2daa4b34
ca527d597078153
blind_login: c497fddf6056d241e6cf9fb7ac37c384f49b357a221eb0a802c989b9
942256c1
Bourdrez, et al. Expires 14 September 2023 [Page 65]
Internet-Draft OPAQUE March 2023
D.1.4.3. Intermediate Values
client_public_key: 02dc91b178ba2c4bbf9b9403fca25457b906a7f507e59b6e70
3031e09114ba2be0
auth_key: 5bd4be1602516092dc5078f8d699f5721dc1720a49fb80d8e5c16377abd
0987b
randomized_pwd: 06be0a1a51d56557a3adad57ba29c5510565dcd8b5078fa319151
b9382258fb0
envelope: a921f2a014513bd8a90e477a629794e89fec12d12206dde662ebdcf6567
0e51f4d7773a36a208a866301dbb2858e40dc5638017527cf91aef32d3848eebe0971
handshake_secret: 0ee4a82c4a34992f72bfbcb5d2ce64044477dfe200b9d8c92bf
1759b219b3485
server_mac_key: 77ebd7511216a51e9c2f3368ce6c1e40513f24b6f42085ef18e7f
737b427aab5
client_mac_key: e48e2064cf570dbd18eb42550d4459c58ac4ae4e28881d1aefbab
d668f7f1df9
oprf_key: 2dfb5cb9aa1476093be74ca0d43e5b02862a05f5d6972614d7433acdc66
f7f31
D.1.4.4. Output Values
registration_request: 029e949a29cfa0bf7c1287333d2fb3dc586c41aa652f507
0d26a5315a1b50229f8
registration_response: 0350d3694c00978f00a5ce7cd08a00547e4ab5fb5fc2b2
f6717cdaa6c89136efef035f40ff9cf88aa1f5cd4fe5fd3da9ea65a4923a5594f84fd
9f2092d6067784874
registration_upload: 02dc91b178ba2c4bbf9b9403fca25457b906a7f507e59b6e
703031e09114ba2be07f0ed53532d3ae8e505ecc70d42d2b814b6b0e48156def71ea0
29148b2803aafa921f2a014513bd8a90e477a629794e89fec12d12206dde662ebdcf6
5670e51f4d7773a36a208a866301dbb2858e40dc5638017527cf91aef32d3848eebe0
971
KE1: 037342f0bcb3ecea754c1e67576c86aa90c1de3875f390ad599a26686cdfee6e
07ab3d33bde0e93eda72392346a7a73051110674bbf6b1b7ffab8be4f91fdaeeb1034
93f36ca12467d1f5eaaabea67ca31377c4869c1e9a62346b6f01a991624b95d
KE2: 0246da9fe4d41d5ba69faa6c509a1d5bafd49a48615a47a8dd4b0823cc147648
1138fe59af0df2c79f57b8780278f5ae47355fe1f817119041951c80f612fdfc6d2f0
c547f70deaeca54d878c14c1aa5e1ab405dec833777132eea905c2fbb12504a67dcbe
0e66740c76b62c13b04a38a77926e19072953319ec65e41f9bfd2ae268d7f10604202
1c80300e4c6f585980cf39fc51a4a6bba41b0729f9b240c729e5671cd9960ecef2fe0
d0f7494986fa3d8b2bb01963537e60efb13981e138e3d4a1020e67941e94deba83521
4421d2d8c90de9b0f7f925d11e2032ce19b1832ae8e0fdca637d2a5390f4c809a67b4
6977c536fe9f643f703178a17a413d14e4bb523c
KE3: 298cd0077d018f122bc95d706e5fef06537814c567f08d5e40b0c0ae918f9287
export_key: c3c9a1b0e33ac84dd83d0b7e8af6794e17e7a3caadff289fbd9dc769a
853c64b
session_key: 0c59872e9bcdde274f4f52f6ba0fd1acca211d6eb7db98677b457a73
9ef1f0d8
Bourdrez, et al. Expires 14 September 2023 [Page 66]
Internet-Draft OPAQUE March 2023
D.2. Fake Test Vectors
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
Bourdrez, et al. Expires 14 September 2023 [Page 67]
Internet-Draft OPAQUE March 2023
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
server_keyshare: 5236e2e06d49f0b496db2a786f6ee1016f15b4fd6c0dbd95d6b1
17055d914157
server_private_keyshare: 6d8fba9741a357584770f85294430bce2252fe212a8a
372152a73c7ffe414503
masking_key: 39ebd51f0e39a07a1c2d2431995b0399bca9996c5d10014d6ebab445
3dc10ce5cef38ed3df6e56bfff40c2d8dd4671c2b4cf63c3d54860f31fe40220d690b
b71
KE1: b0a26dcaca2230b8f5e4b1bcab9c84b586140221bb8b2848486874b0be448905
42d4e61ed3f8d64cdd3b9d153343eca15b9b0d5e388232793c6376bd2d9cfd0a0e4ed
8bcc15f3dd01a30365c97c0c0de0a3dd3fbf5d3cbec55fb6ac1d3bf740f
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
Bourdrez, et al. Expires 14 September 2023 [Page 68]
Internet-Draft OPAQUE March 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.2.2.2. 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
server_keyshare: 03f42965d5bcba2a590a49eb2418061effe40b5c29a34b8e5163
e0ef32044b2e4c
server_private_keyshare: 1a2a0ff27f3ca75221378a2a21fe5222ce0b439452f8
70475857a34197ba8f6d
masking_key: caecc6ccb4cae27cb54d8f3a1af1bac52a3d53107ce08497cdd362b1
992e4e5e
KE1: 0396875da2b4f7749bba411513aea02dc514a48d169d8a9531bd61d3af3fa9ba
ae42d4e61ed3f8d64cdd3b9d153343eca15b9b0d5e388232793c6376bd2d9cfd0a039
94d4f1221bfd205063469e92ea4d492f7cc76a327223633ab74590c30cf7285
D.2.2.3. Output Values
Bourdrez, et al. Expires 14 September 2023 [Page 69]
Internet-Draft OPAQUE March 2023
KE2: 0201198dcd13f9792eb75dcfa815f61b049abfe2e3e9456d4bbbceec5f442efd
049c035896a043e70f897d87180c543e7a063b83c1bb728fbd189c619e27b6e5a6fac
da65ce0a97b9085e7af07f61fd3fdd046d257cbf2183ce8766090b8041a8bf28d79dd
4c9031ddc75bb6ddb4c291e639937840e3d39fc0d5a3d6e7723c09f7945df485bcf9a
efe3fe82d149e84049e259bb5b33d6a2ff3b25e4bfb7eff0962821e10f6eeab2a7a42
0bf09da9b27a4639645622c46358de9cf7ae813055ae2d1203f42965d5bcba2a590a4
9eb2418061effe40b5c29a34b8e5163e0ef32044b2e4c196137813ed8ec48627f0b0d
90d9427f4ec137f8360769df167c25836eae5d91
Authors' Addresses
Daniel Bourdrez
Email: d@bytema.re
Hugo Krawczyk
Algorand Foundation
Email: hugokraw@gmail.com
Kevin Lewi
Novi Research
Email: lewi.kevin.k@gmail.com
Christopher A. Wood
Cloudflare, Inc.
Email: caw@heapingbits.net
Bourdrez, et al. Expires 14 September 2023 [Page 70]
