]>

d@bytema.re

Algorand Foundation

hugokraw@gmail.com

Novi Research

lewi.kevin.k@gmail.com

Cloudflare, Inc.

caw@heapingbits.net

Internet-Draft 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 Source for this draft and an issue tracker can be found at .

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 for requirements of the OPRF and AKE protocols.) This document specifies one OPAQUE instantiation based on . Other instantiations are possible, as discussed in , 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 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 .

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 when, and only when, they appear in all capitals, as shown here.

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 . 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.
• 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 , 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 .

Cryptographic Dependencies OPAQUE depends on the following cryptographic protocols and primitives:

• Oblivious Pseudorandom Function (OPRF);
• Key Derivation Function (KDF);
• Message Authentication Code (MAC);
• Cryptographic Hash Function;
• Key Stretching Function (KSF);
• Key Recovery Mechanism;
• Authenticated Key Exchange (AKE) protocol;

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.

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 , draft version -09, using the OPRF mode (0x00) from . 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 this 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:

• Evaluate(k, blinded_element): Evaluate blinded input element blinded_element using input key k, yielding output element evaluated_element. This is equivalent to the Evaluate function described in , where k is the private key parameter.
• DeriveKeyPair(seed, info): Derive a private and public key pair deterministically from a seed, as described in . In this specification, the info parameter to DeriveKeyPair is set to "OPAQUE-DeriveKeyPair".

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 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.

This specification uses the OPRF mode (0x00) from .

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.
• Expand(prk, info, L): Expand a pseudorandom key prk using 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.

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.

A Key Stretching Function (KSF) 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.

Key Recovery Method OPAQUE relies on a key recovery mechanism for storing authentication material on the server and recovering it on the client. This material is encapsulated in an envelope, whose structure, encoding, and size must be specified by the key recovery mechanism. The size of the envelope is denoted Ne and may vary between mechanisms. The key recovery storage mechanism takes as input a private seed and outputs an envelope. The retrieval process takes as input a private seed and envelope and outputs authentication material. The signatures for these functionalities are as follows:

• Store(private_seed): build and return an Envelope structure and the client's public key.
• Recover(private_seed, envelope): recover and return the authentication material for the AKE from the Envelope. This function raises an error if the private seed cannot be used for recovering authentication material from the input envelope.

The key recovery mechanism MUST return an error when trying to recover authentication material from an envelope with a private seed that was not used in producing the envelope. Moreover, it MUST be compatible with the chosen AKE. For example, the key recovery mechanism specified in directly recovers a private key from a seed, and the cryptographic primitive in the AKE must therefore support such a possibility. If applications implement , they MUST use the same mechanism throughout their lifecycle in order to avoid activity leaks due to switching.

Authenticated Key Exchange (AKE) Protocol OPAQUE additionally depends on a three-message Authenticated Key Exchange (AKE) protocol which satisfies the forward secrecy and KCI properties discussed in . The AKE must define three messages AuthInit, AuthResponse and AuthFinish and provide the following functions for the client:

• Start(): Initiate the AKE by producing message AuthInit.
• ClientFinish(client_identity, client_private_key, server_identity, server_public_key, AuthInit): upon receipt of the server's response AuthResponse, complete the protocol for the client, produce AuthFinish.

The AKE protocol must provide the following functions for the server:

• Response(server_identity, server_private_key, client_identity, client_public_key, AuthInit): upon receipt of a client's request AuthInit, engage in the AKE.
• ServerFinish(AuthFinish): upon receipt of a client's final AKE message AuthFinish, complete the protocol for the server.

Both ClientFinish and ServerFinish return an error if authentication failed. In this case, clients and servers MUST NOT use any outputs from the protocol, such as session_key or export_key (defined below). Prior to the execution of these functions, both the client and the server MUST agree on a configuration; see for details. This specification defines one particular AKE based on 3DH; see . 3DH assumes a prime-order group as described in .

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 the client recovers its authentication material and uses it to perform a mutually authenticated key exchange.

Setup Previously to both stages, the client and server agree on a configuration, which fully specifies the cryptographic algorithm dependencies necessary to run the protocol; see for details. The client chooses its password, and the server chooses its own 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 the same pair of keys with multiple clients and can opt to use multiple seeds (so long as they are kept consistent for each client).

Offline Registration Registration is the only part in OPAQUE that requires a server-authenticated and confidential channel, either physical, out-of-band, PKI-based, etc. The client inputs its credentials, which includes its password and user identifier, and the server inputs its parameters, which includes 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 client registrations as needed. The registration flow is shown below: registration response <------------------------- record -------------------------> ------------------------------------------------ | | v v export_key record ]]> These messages are named RegistrationRequest, RegistrationResponse, and Record, respectively. Their contents and wire format are defined in .

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: 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):

• KE1 is composed of the CredentialRequest and AuthInit messages
• KE2 is composed of the CredentialResponse and AuthResponse messages
• KE3 represents the AuthFinish message

The CredentialRequest and CredentialResponse message contents and wire format are specified in , and those of AuthInit, AuthResponse and AuthFinish are specified in . The rest of this document describes the details of these stages in detail. describes how client credential information is generated, encoded, stored on the server on registration, and recovered on login. describes the first registration stage of the protocol, and describes the second authentication stage of the protocol. describes how to instantiate OPAQUE using different cryptographic dependencies and parameters.

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 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 for information about this identity.

These credential values are used in the CleartextCredentials structure as follows: ; uint8 client_identity<1..2^16-1>; } CleartextCredentials; ]]> The function CreateCleartextCredentials constructs a CleartextCredentials structure given application credential information.

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 key using the DeriveAuthKeyPair() function defined in .

Envelope Structure The key recovery mechanism defines its Envelope as follows: nonce: A unique nonce of length Nn used to protect this Envelope. auth_tag: Authentication tag protecting the contents of the envelope, covering the envelope nonce, and CleartextCredentials.

Envelope Creation Clients create an Envelope at registration with the function Store defined below.

Envelope Recovery Clients recover their Envelope during login with the Recover function defined below.

Offline Registration The registration process proceeds as follows. The client inputs the following values:

• password: client password.
• creds: client credentials, as described in .

The server inputs the following values:

• server_private_key: server private key for the AKE protocol.
• server_public_key: server public key for the AKE protocol.
• credential_identifier: unique identifier for the client's credential, generated by the server.
• oprf_seed: seed used to derive per-client OPRF keys.

The registration protocol then runs as shown below: response = CreateRegistrationResponse(request, server_public_key, credential_identifier, oprf_seed) response <------------------------- (record, export_key) = FinalizeRequest(response, server_identity, client_identity) record -------------------------> ]]> describes details of the functions and the corresponding parameters referenced above. Both client and server MUST validate the other party's public key before use. See 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 .

Registration Messages

data

A serialized OPRF group element.

data

A serialized OPRF group element.

server_public_key

The server's encoded public key that will be used for the online authenticated key exchange stage.

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.

Registration Functions

CreateRegistrationRequest

CreateRegistrationResponse

FinalizeRequest To create the user record used for further authentication, the client executes the following function. See for details about the output export_key usage. Upon completion of this function, the client MUST send record to the server.

Finalize Registration 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 . The server_private_key may be unique for each client.

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). 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 . 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: client password.
• client_identity: client identity, as described in .

The server inputs the following values:

• server_private_key: server private for the AKE protocol.
• server_public_key: server public for the AKE protocol.
• server_identity: server identity, as described in .
• record: RegistrationUpload corresponding to the client's registration.
• credential_identifier: an identifier that uniquely represents the credential.
• oprf_seed: 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 . The output export_key MUST NOT be used in any way before the protocol completes successfully. See 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: 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, password, 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 may have the following named fields:

• password, the input password; and
• blind, the random blinding inverter returned by Blind(); and
• client_ake_state, the client's AKE state if necessary.

The server state may have the following fields:

• server_ake_state, the server's AKE state if necessary.

The rest of this section describes these authenticated key exchange messages and their parameters in more detail. discusses internal functions used for retrieving client credentials, and discusses how these functions are used to execute the authenticated key exchange protocol.

Client Authentication Functions

Server Authentication Functions Since the OPRF is a two-message protocol, KE3 has no element of the OPRF. We can therefore call the AKE's ServerFinish() directly. The ServerFinish() function MUST take KE3 as input and MUST verify the client authentication material it contains before the session_key value can be used. This verification is paramount in order to ensure forward secrecy against active attackers. This function MUST NOT return the session_key value if the client authentication material is invalid, and may instead return an appropriate error message.

Credential Retrieval

Credential Retrieval Messages

data

A serialized OPRF group element.

data

A serialized OPRF group element.

masking_nonce

A nonce used for the confidentiality of the masked_response field.

masked_response

An encrypted form of the server's public key and the client's Envelope structure.

Credential Retrieval Functions

CreateCredentialRequest

CreateCredentialResponse 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). In the case of an existing record with the corresponding identifier credential_identifier, the server invokes the following function to produce a CredentialResponse: In the case of a record that does not exist and if client enumeration prevention is desired, the server MUST respond to the credential request to fake the existence of the record. The server SHOULD invoke the CreateCredentialResponse function with a fake client record argument that is configured so that:

• record.client_public_key is set to a randomly generated public key of length Npk
• record.masking_key is set to a random byte string of length Nh
• record.envelope is set to the byte string consisting only of zeros of length Ne

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 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.

RecoverCredentials

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 . The AKE client state client_ake_state mentioned in has the following named fields:

• client_secret, an opaque byte string of length Nsk; and
• ke1, a value of type KE1.

The server state server_ake_state mentioned in has the following fields:

• expected_client_mac, an opaque byte string of length Nm; and
• session_key, an opaque byte string of length Nx.

and specify the inner workings of client and server functions, respectively.

AKE Messages client_nonce : A fresh randomly generated nonce of length Nn. client_keyshare : Client ephemeral key share of fixed size Npk. server_nonce : A fresh randomly generated nonce of length Nn. server_keyshare : Server ephemeral key share 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. client_mac : An authentication tag computed over the handshake transcript computed using Km2, defined below.

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 .
• 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 .

Key Schedule Functions

Transcript Functions The OPAQUE-3DH key derivation procedures make use of the functions below, re-purposed from TLS 1.3 . Where CustomLabel is specified as: = "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.

Shared Secret Derivation The OPAQUE-3DH shared secret derived during the key exchange protocol is computed using the following helper function.

3DH Client Functions

3DH Server Functions

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 and implements the interface in . Examples include OPRF(ristretto255, SHA-512) and OPRF(P-256, SHA-256).
• The KDF, MAC, and Hash functions implement the interfaces in . Examples include HKDF for the KDF, HMAC for the MAC, and SHA-256 and SHA-512 for the Hash functions. If an extensible output function such as SHAKE128 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 . Examples include Argon2 , scrypt , and 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 OPRF(ristretto255, SHA-512), then Group SHOULD be ristretto255.

Context is the shared parameter used to construct the preamble in . 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:

• OPRF(ristretto255, SHA-512), HKDF-SHA-512, HMAC-SHA-512, SHA-512, Scrypt(32768,8,1), internal, ristretto255
• OPRF(P-256, SHA-256), HKDF-SHA-256, HMAC-SHA-256, SHA-256, Scrypt(32768,8,1), internal, 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 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.

Application Considerations Beyond choosing an appropriate configuration, there are several parameters which applications can use to control OPAQUE:

• Credential identifier: As described in , 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.
• Context information: As described in , 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 , 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 an identity, applications SHOULD set these identities to nil and rely solely on public key information.
• Enumeration prevention: As described in , if servers receive a credential request for a non-existent client, they SHOULD respond with a "fake" response in order 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 . In settings where this attack is not a concern, servers may choose to not support this functionality.

Implementation Considerations This section documents considerations for OPAQUE implementations. This includes implementation safeguards and error handling considerations.

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 against client enumeration attacks. As specified in and , 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 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 in order 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 is run.

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 specifiation, along with conditions that lead to each error, are as follows:

• EnvelopeRecoveryError: The envelope Recover function failed to produce any authentication key material; .
• ServerAuthenticationError: The client failed to complete the authenticated key exchange protocol with the server; .
• ClientAuthenticationError: The server failed to complete the authenticated key exchange protocol with the client; .

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 implementaton 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.

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.

Notable Design Differences [[RFC EDITOR: Please delete this section before publication.]] The specification as written here differs from the original cryptographic design in and the corresponding CFRG document , 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 . 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 , whereas the servers construct envelopes in . This change adds to the security of the protocol. 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 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 equivocability and random key robustness for the encryption function. The latter property is only required for authentication and achieved by a collision-resistant MAC. This change was made for two reasons. First, it reduces the number of bytes stored in envelopes, which is an 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 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 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 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 in 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 use of OPAQUE for end-to-end encrypted backups; see .
• The protocol admits optional application-layer client and server identities. In the absence of these identities, client and server are authenticated against their public keys. Binding authentication to identities is part of the AKE part of OPAQUE. The type of identities and their semantics are application dependent and independent of the protocol analysis. This change was made to simplify client and server interfaces to the protocol by removing the need to specify additional identities alongside their corresponding public authentication keys when not needed.
• The protocol admits application-specific context information configured out-of-band in the AKE transcript. This allows domain separation between different application uses of OPAQUE. This is a mechanism for the AKE component and is best practice as for domain separation between different applications of the protocol. This change was made to allow different applications to use OPAQUE without 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 have 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 and the corresponding CFRG document that were made to make this specification suitable for interoperable implementations.

• 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 using for 3DH using prime-order groups based on elliptic curves, as described in . This specification also delegates OPRF group choice and operations to . As such, the prime-order group as used in the OPRF and 3DH as specified in this document both adhere to the requirements as .
• 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 , which is identical to the DH-OPRF functionality in and, concretely, uses the hash-to-curve functions in . All hash-to-curve methods in are compliant with the requirement in , namely, that the output be a member of the prime-order group.
• and both used HMQV as the AKE for the protocol. However, this document fully specifies 3DH instead of HMQV (though a sketch for how to instantiate OPAQUE using HMQV is included in ). Since 3DH satisfies the essential requirements for the AKE as described in and , as recalled in , 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 , Figure 12 uses a different transcript than that which is described in this specification. In particular, the key exchange transcript specified in is a superset of the transcript as defined in . This was done to align with best practices, such as is done for key exchange protocols like TLS 1.3 .
• Neither nor 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 .

Security Analysis Jarecki et al. 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 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 is proven in the random oracle model under the One-More Diffie-Hellman assumption . OPAQUE's design builds on a line of work initiated in the seminal paper of Ford and Kaliski and is based on the HPAKE protocol of Xavier Boyen and the (1,1)-PPSS protocol from Jarecki et al. . None of these papers considered security against pre-computation attacks or presented a proof of aPAKE security (not even in a weak model). The KCI property required from AKE protocols for use with OPAQUE states that knowledge of a party's private key does not allow an attacker to impersonate others to that party. This is an important security property achieved by most public-key based AKE protocols, including protocols that use signatures or public key encryption for authentication. It is also a property of many implicitly authenticated protocols, e.g., HMQV, but not all of them. We also note that key exchange protocols based on shared keys do not satisfy the KCI requirement, hence they are not considered in the OPAQUE setting. We note that KCI is needed to ensure a crucial property of OPAQUE: even upon compromise of the server, the attacker cannot impersonate the client to the server without first running an exhaustive dictionary attack. Another essential requirement from AKE protocols for use in OPAQUE is to provide forward secrecy (against active attackers).

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 and SPAKE2+ . 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 , these protocols, and any aPAKE in the model from , 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 , 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.

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 envelope (hence determined during password registration) and to tie server_identity to the server identity used by the client to initiate an offline password registration or online authenticated key exchange session. server_identity and client_identity can also be part of the envelope or be tied to the parties' public keys. In principle, identities may change across different sessions as long as there is a policy that can establish if the identity is acceptable or not to the peer. However, we note that the public keys of both the server and the client must always be those defined at the time of password registration. The client identity (client_identity) and server identity (server_identity) are optional parameters that are left to the application to designate as aliases for the client and server. If the application layer does not supply values for these parameters, then they will be omitted from the creation of the envelope during the registration stage. Furthermore, they will be substituted with client_identity = client_public_key and server_identity = server_public_key during the authenticated key exchange stage. The advantage to 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.

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.

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 and Cheon 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 for more information. For OPAQUE, these attacks are particularly impractical as they translate into an infeasible number of failed authentication attempts directed at individual users.

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 . 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.

OPRF Key Stretching Applying a key streching 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.

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 its behavior with existing registered clients. Servers do this by simulating a fake CredentialResponse as specified in for unregistered users, and also encrypting both CredentialResponse using a masking key. In this way, real and fake CredentialResponse messages are indistinguishable from one another. Implementations must also take care to avoid side-channel leakage (e.g., timing attacks) from helping differentiate these operations from a regular server response. Note that this may introduce possible abuse vectors since the server's cost of generating a CredentialResponse is less than that of the client's cost of generating a CredentialRequest. Server implementations may choose to forego the construction of a simulated credential response message for an unregistered client if these client enumeration attacks can be mitigated through other application-specific means or are otherwise not applicable for their threat model. 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 and . 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.

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 .) 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.

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 . 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.

IANA Considerations This document makes no IANA requests.

References Normative References In many standards track documents several words are used to signify the requirements in the specification. These words are often capitalized. This document defines these words as they should be interpreted in IETF documents. This document specifies an Internet Best Current Practices for the Internet Community, and requests discussion and suggestions for improvements. RFC 2119 specifies common key words that may be used in protocol specifications. This document aims to reduce the ambiguity by clarifying that only UPPERCASE usage of the key words have the defined special meanings. Security systems are built on strong cryptographic algorithms that foil pattern analysis attempts. However, the security of these systems is dependent on generating secret quantities for passwords, cryptographic keys, and similar quantities. The use of pseudo-random processes to generate secret quantities can result in pseudo-security. A sophisticated attacker may find it easier to reproduce the environment that produced the secret quantities and to search the resulting small set of possibilities than to locate the quantities in the whole of the potential number space. Choosing random quantities to foil a resourceful and motivated adversary is surprisingly difficult. This document points out many pitfalls in using poor entropy sources or traditional pseudo-random number generation techniques for generating such quantities. It recommends the use of truly random hardware techniques and shows that the existing hardware on many systems can be used for this purpose. It provides suggestions to ameliorate the problem when a hardware solution is not available, and it gives examples of how large such quantities need to be for some applications. This document specifies an Internet Best Current Practices for the Internet Community, and requests discussion and suggestions for improvements. Brave Software Cloudflare, Inc. Cloudflare, Inc. Cloudflare, Inc. An Oblivious Pseudorandom Function (OPRF) is a two-party protocol between client and server for computing the output of a Pseudorandom Function (PRF). The server provides the PRF secret key, and the client provides the PRF input. At the end of the protocol, the client learns the PRF output without learning anything about the PRF secret key, and the server learns neither the PRF input nor output. An OPRF can also satisfy a notion of 'verifiability', called a VOPRF. A VOPRF ensures clients can verify that the server used a specific private key during the execution of the protocol. A VOPRF can also be partially-oblivious, called a POPRF. A POPRF allows clients and servers to provide public input to the PRF computation. This document specifies an OPRF, VOPRF, and POPRF instantiated within standard prime-order groups, including elliptic curves. This document describes HMAC, a mechanism for message authentication using cryptographic hash functions. HMAC can be used with any iterative cryptographic hash function, e.g., MD5, SHA-1, in combination with a secret shared key. The cryptographic strength of HMAC depends on the properties of the underlying hash function. This memo provides information for the Internet community. This memo does not specify an Internet standard of any kind Brave Software Cloudflare, Inc. Cloudflare, Inc. Cloudflare, Inc. An Oblivious Pseudorandom Function (OPRF) is a two-party protocol between client and server for computing the output of a Pseudorandom Function (PRF). The server provides the PRF secret key, and the client provides the PRF input. At the end of the protocol, the client learns the PRF output without learning anything about the PRF secret key, and the server learns neither the PRF input nor output. An OPRF can also satisfy a notion of 'verifiability', called a VOPRF. A VOPRF ensures clients can verify that the server used a specific private key during the execution of the protocol. A VOPRF can also be partially-oblivious, called a POPRF. A POPRF allows clients and servers to provide public input to the PRF computation. This document specifies an OPRF, VOPRF, and POPRF instantiated within standard prime-order groups, including elliptic curves. Informative References n.d. n.d. National Institute of Standards and Technology (NIST) n.d. n.d. This document describes a cryptographically strong network authentication mechanism known as the Secure Remote Password (SRP) protocol. [STANDARDS-TRACK] This document specifies a simple Hashed Message Authentication Code (HMAC)-based key derivation function (HKDF), which can be used as a building block in various protocols and applications. The key derivation function (KDF) is intended to support a wide range of applications and requirements, and is conservative in its use of cryptographic hash functions. This document is not an Internet Standards Track specification; it is published for informational purposes. Password-Authenticated Key Agreement (PAKE) schemes are interactive protocols that allow the participants to authenticate each other and derive shared cryptographic keys using a (weaker) shared password. This document reviews different types of PAKE schemes. Furthermore, it presents requirements and gives recommendations to designers of new schemes. It is a product of the Crypto Forum Research Group (CFRG). This document specifies version 1.3 of the Transport Layer Security (TLS) protocol. TLS allows client/server applications to communicate over the Internet in a way that is designed to prevent eavesdropping, tampering, and message forgery. This document updates RFCs 5705 and 6066, and obsoletes RFCs 5077, 5246, and 6961. This document also specifies new requirements for TLS 1.2 implementations. This document provides recommendations for the implementation of public-key cryptography based on the RSA algorithm, covering cryptographic primitives, encryption schemes, signature schemes with appendix, and ASN.1 syntax for representing keys and for identifying the schemes. This document represents a republication of PKCS #1 v2.2 from RSA Laboratories' Public-Key Cryptography Standards (PKCS) series. By publishing this RFC, change control is transferred to the IETF. This document also obsoletes RFC 3447. This document describes the Argon2 memory-hard function for password hashing and proof-of-work applications. We provide an implementer-oriented description with test vectors. The purpose is to simplify adoption of Argon2 for Internet protocols. This document is a product of the Crypto Forum Research Group (CFRG) in the IRTF. This document specifies the password-based key derivation function scrypt. The function derives one or more secret keys from a secret string. It is based on memory-hard functions, which offer added protection against attacks using custom hardware. The document also provides an ASN.1 schema. This document provides recommendations for the implementation of password-based cryptography, covering key derivation functions, encryption schemes, message-authentication schemes, and ASN.1 syntax identifying the techniques. This memo provides information for the Internet community. Cloudflare, Inc. Cornell Tech Cloudflare, Inc. Stanford University Cloudflare, Inc. This document specifies a number of algorithms for encoding or hashing an arbitrary string to a point on an elliptic curve. This document is a product of the Crypto Forum Research Group (CFRG) in the IRTF.

Acknowledgments The OPAQUE protocol and its analysis is 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.

Alternate Key Recovery Mechanisms Client authentication material can be stored and retrieved using different key recovery mechanisms, provided these mechanisms adhere to the requirements specified in . 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., . 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.

Alternate AKE Instantiations It is possible to instantiate OPAQUE with other AKEs, such as 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 . 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.

HMQV Instantiation Sketch An HMQV instantiation would work similar to OPAQUE-3DH, differing primarily in the key schedule . First, the key schedule preamble value would use a different constant prefix -- "HMQV" instead of "3DH" -- as shown below. 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: Likewise, servers would compute IKM as follows: In both cases, u would be computed as follows: Likewise, s would be computed as follows: 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.

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 key shares exchanged between client and server.

Test Vectors This section contains real and fake test vectors for the OPAQUE-3DH specification. Each real test vector in specifies the configuration information, protocol inputs, intermediate values computed during registration and authentication, and protocol outputs. Similarly, each fake test vector in specifies the configuration information, protocol inputs, and protocol outputs computed during 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 . client_public_key is used as the fake record's public key, and masking_key for the fake record's masking key parameter. All values are encoded in hexadecimal strings. The configuration information includes the (OPRF, Hash, KSF, KDF, MAC, Group, Context) tuple, where the Group matches that which is used in the OPRF. These test vectors were generated using draft-09 of .

Real Test Vectors

OPAQUE-3DH Real Test Vector 1

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OPAQUE-3DH Real Test Vector 2

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OPAQUE-3DH Real Test Vector 3

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OPAQUE-3DH Real Test Vector 4

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Fake Test Vectors

OPAQUE-3DH Fake Test Vector 1

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OPAQUE-3DH Fake Test Vector 2

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