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Crypto Forum Research Group                                  H. Krawczyk
Internet-Draft                                       Algorand Foundation
Intended status: Informational                             July 07, 2019
Expires: January 8, 2020

                  The OPAQUE Asymmetric PAKE Protocol


   This draft 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.
   Prior aPAKE protocols did not use salt and if they did, the salt was
   transmitted in the clear from server to user allowing for the
   building of targeted pre-computed dictionaries.  OPAQUE security has
   been proven by Jarecki et al.  (Eurocrypt 2018) in a strong and
   universally composable formal model of aPAKE security.  In addition,
   the protocol provides forward secrecy and the ability to hide the
   password from the server even during password registration.

   Strong security, versatility through modularity, good performance,
   and an array of additional features make OPAQUE a natural candidate
   for practical use and for adoption as a standard.  To this end, this
   draft presents several optimized instantiations of OPAQUE and ways of
   integrating OPAQUE with TLS.

Status of This Memo

   This Internet-Draft is submitted in full conformance with the
   provisions of BCP 78 and BCP 79.

   Internet-Drafts are working documents of the Internet Engineering
   Task Force (IETF).  Note that other groups may also distribute
   working documents as Internet-Drafts.  The list of current Internet-
   Drafts is at https://datatracker.ietf.org/drafts/current/.

   Internet-Drafts are draft documents valid for a maximum of six months
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   time.  It is inappropriate to use Internet-Drafts as reference
   material or to cite them other than as "work in progress."

   This Internet-Draft will expire on January 8, 2020.

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Copyright Notice

   Copyright (c) 2019 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
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   include Simplified BSD License text as described in Section 4.e of
   the Trust Legal Provisions and are provided without warranty as
   described in the Simplified BSD License.

1.  Introduction

   Password authentication is the prevalent form of authentication in
   the web and in most other applications.  In the most common
   implementation, a user authenticates to a server by entering its user
   id and password where both values are transmitted to the server under
   the protection of TLS.  This makes the password vulnerable to TLS
   failures, including many forms of PKI attacks, certificate
   mishandling, termination outside the security perimeter, visibility
   to middle boxes, and more.  Moreover, even under normal operation,
   passwords are always visible in plaintext form at the server upon TLS

   Asymmetric (or augmented) Password Authenticated Key Exchange (aPAKE)
   protocols are designed to provide password authentication and
   mutually authenticated key exchange without relying on PKI (except
   during user/password 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, namely, it should only be open to inevitable attacks:
   online impersonation attempts with guessed user passwords and offline
   dictionary attacks upon the compromise of a server and leakage of its
   password file.  In the latter case, the attacker learns a mapping of
   a user'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 or
   otherwise the attacker can pre-compute a deterministic list of mapped
   passwords leading to almost instantaneous leakage of passwords upon
   server compromise.

   Quite surprisingly, in spite of the existence of multiple designs for
   (PKI-free) aPAKE protocols, none of these protocols is secure against
   pre-computation attacks.  In particular, none of these protocols can

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   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 salt at all or, if they do, they
   transmit the salt from server to user in the clear, hence losing the
   secrecy of the salt and its defense against pre-computation.
   Furthermore, the transmission of salt may incur additional protocol

   This draft describes OPAQUE, a PKI-free secure aPAKE that is secure
   against pre-computation attacks and capable of using secret salt.
   OPAQUE has been recently defined and studied by Jarecki et al.
   [OPAQUE] who prove the security of the protocol in a strong aPAKE
   model that ensures security against pre-computation attacks and is
   formulated in the Universal Composability framework [Canetti01] under
   the random oracle model.  In contrast, very few aPAKE protocols have
   been proven formally and those proven were analyzed in a weak
   security model that allows for pre-computation attacks (e.g.,
   [GMR06]).  This is not just a formal issue: these protocols are
   actually vulnerable to such attacks!  Furthermore, as far as we know,
   protocols discussed recently as candidates for standardization (e.g.,
   SPAKE2+ [I-D.irtf-cfrg-spake2] and AugPAKE [RFC6628]) do not enjoy a
   proof of security, not even in a weak model.  The same holds for the
   SRP protocol [RFC2945].  VTBPEKE is analyzed in [VTBPEKE] in a weak
   model that allows for pre-computation attacks and, as in all the
   above cases (except OPAQUE), does not accommodate secret salt.

   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).

   In addition to its proven resistance to pre-computation attacks,
   OPAQUE's security features include forward secrecy (essential for
   protecting past communications in case of password leakage) and the
   ability to hide the password from the server - even during password
   registration.  Moreover, good performance and an array of additional
   features make OPAQUE a natural candidate for practical use and for
   adoption as a standard.  Such features include the ability to
   increase the difficulty of offline dictionary attacks via iterated
   hashing (or other hardening schemes) and offloading these operations
   to the client; extensibility of the protocol to support storage and
   retrieval of user's secrets solely based on a password; and being
   amenable to a multi-server distributed implementation where offline
   dictionary attacks are not possible without breaking into a threshold
   of servers (such distributed solution requires no change or awareness
   on the client side relative to a single-server implementation).

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   OPAQUE is defined and proven as the composition of two
   functionalities: An Oblivious PRF (OPRF) and a key-exchange protocol.
   It can be seen as a "compiler" for transforming any key-exchange
   protocol (with KCI security - see below) into a secure aPAKE
   protocol.  In OPAQUE, the user 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 TLS.  The latter aspect is of prime
   importance as the use of OPAQUE with TLS constitutes a major security
   improvement relative to the standard password-over-TLS practice.  At
   the same time, the combination with TLS builds OPAQUE as a fully
   functional secure communications protocol and can help provide
   privacy to account information sent by the user to the server prior
   to authentication.

   The KCI property required from KE 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 KE 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 user to the server without first running an
   exhaustive dictionary attack.

   This draft defines OPAQUE with a specific, efficient instantiation
   over elliptic curves of the OPRF component and with a few KE schemes,
   including the HMQV [HMQV] and SIGMA [SIGMA] protocols, as well as
   several suggestions for integrating OPAQUE with TLS 1.3 [RFC8446]
   offering different tradeoffs between simplicity, performance and user
   privacy.  See also the companion draft [I-D.sullivan-tls-opaque].  In
   general, the modularity of OPAQUE's design makes it easy to integrate
   with additional key-exchange protocols, e.g., IKE.

   The computational cost of OPAQUE is determined by the cost of the
   OPRF, the cost of a regular Diffie-Hellman exchange, and the cost of
   authenticating such exchange.  In our elliptic-curve implementation
   of the OPRF, the cost for the client is two exponentiations (one or
   two of which can be fixed base) and one hashing-into-curve operation
   [I-D.irtf-cfrg-hash-to-curve]; for the server, it is just one

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   exponentiation.  The cost of a Diffie-Hellman exchange is as usual
   two exponentiations per party (one of which is fixed-base).  Finally,
   the cost of authentication per party depends on the specific KE
   protocol: it is just 1/6 of an exponentiation with HMQV and it is one
   signature in the case of SIGMA and TLS 1.3.  These instantiations
   preserve the number of messages (two or three) in the underlying KE
   protocol except in one of the TLS instantiations where user privacy
   requires an additional round trip (this can be saved if using a
   mechanism similar to the proposed ESNI extension

1.1.  Terminology

   In this document, the key words "MUST", "MUST NOT", "REQUIRED",
   and "OPTIONAL" are to be interpreted as described in BCP 14, RFC 2119

1.2.  Notation

   Throughout this document the first argument to a keyed function
   represents the key; separated by a semicolon are the function inputs
   typically implemented as an unambiguous concatenation of strings
   (details of encodings are left for a future, more detailed

   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").

   The name OPAQUE: A homonym of O-PAKE where O is for Oblivious (the
   name OPAKE was taken).


   A fundamental piece in the definition of OPAQUE is an Oblivious
   Pseudo Random Function (OPRF).

   An Oblivious PRF (OPRF) is an interactive protocol between a server S
   and a user U defined by a special pseudorandom function (PRF),
   denoted F.  The server's input to the protocol is a key k for PRF F
   and the user's input is a value x in the domain of F.  At the end of
   the protocol, U learns F(k;x) and nothing else while S learns nothing
   from the protocol execution (in particular nothing about x or the
   value F(k;x)).

   OPAQUE uses a specific OPRF instantiation, called DH-OPRF, where the
   PRF, denoted F, is defined as follows.

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   [To do: Align this OPRF specification with [I-D.sullivan-cfrg-voprf]
   and its defined instantiation suites.]

   Parameters: Hash function H (e.g., a SHA2 or SHA3 function), a cyclic
   group G of prime order q, a generator g of G, and hash function H'
   mapping arbitrary strings into G (where H' is modeled as a random

   o  DH-OPRF domain: Any string

   o  DH-OPRF range: The range of the hash function H

   o  DH-OPRF key: A random element k in [0..q-1]; denote v=g^k

   o  DH-OPRF Operation: F(k; x) = H(x, v, H'(x)^k)

   Protocol for computing DH-OPRF, U with input x and S with input k:

   o  U: choose random r in [0..q-1], send alpha=H'(x)*g^r to S

   o  S: upon receiving a value alpha, respond with v=g^k and

   o  U: upon receiving values beta and v, set the PRF output to
      H(x, v, beta*v^{-r})

   All received values (alpha, beta, v) are checked to be elements in G
   other than the identity.  A party aborts if the check fails.  In the
   case of Elliptic Curves this test is typically inexpensive - see
   [I-D.irtf-cfrg-spake2] for ways to deal with this check (including
   co-factor exponentiation) that apply to DH-OPRF as well.

   Note (exponential blinding): An alternative way of computing DH-OPRF
   is for U to send alpha=(H'(x))^r in the first message and set the
   function output to H(x,v,beta^{1/r}) upon receiving S's response.
   However, note that the multiplicative blinding above allows for a
   more efficient implementation as the g^r exponentiation uses a fixed
   base.  Moreover, in cases where the user caches v (e.g., for sites it
   visits often) then one can also use a fixed-base optimized
   computation of the exponentiation v^{-r}.  In any case, it is up to
   the user to decide on what form of blinding it uses; the server's
   response is the same in both cases.

   Note: For elliptic curve implementations of DH-OPRF, the hashing into
   the curve operation has been studied extensively with known efficient
   implementations, see [I-D.irtf-cfrg-hash-to-curve] and references

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2.1.  Hardening OPRF via user iterations

   Protocol OPAQUE can be further strengthened against offline
   dictionary attacks by applying to the output of DH-OPRF an iterated
   hash for some number n of iterations.  This increases the cost of an
   offline attack upon the compromise of the server as the attacker will
   need to perform n iterations for each guess of PwdU it tries to
   validate.  For this purpose we would re-define DH-OPRF as
   F(k;x) = I^n( H(x, v, H'(x)^k) ) where I is an appropriately chosen
   function and the symbol I^n denotes n iterations of function I.  More
   generally, any form of hardened password-based key derivation can be
   used, e.g., PBKDF2 [RFC8018], Argon 2 [I-D.irtf-cfrg-argon2], scrypt
   [RFC7914].  As we will see, in OPAQUE it is the user who runs this
   key derivation.  The iteration value n or any other parameter
   required by these functions can be set as public constants or can be
   set at time of password registration and later communicated by the
   server as part of its OPAQUE message.  (Note; these hardened KDFs
   often require a salt value as input; for OPAQUE this value can be be
   set to a constant, e.g., all zeros.)

3.  OPAQUE Specification

   OPAQUE consists of the concurrent run of an OPRF protocol and a key-
   exchange protocol KE (one that provides mutual authentication based
   on public keys and satisfies the KCI requirement).  We first define
   OPAQUE in a generic way based on any OPRF and any PK-based KE, and
   later show specific instantiation using DH-OPRF (defined in
   Section 2) and several KE protocols.  The user takes the role of
   initiator in these protocols and the server the responder's.  The
   private-public keys for the user are denoted PrivU and PubU, and for
   the server PrivS and PubS.  In Section 3.4 we augment the protocol
   with user-side hardening to increase resistance to offline attacks in
   case of server compromise.

3.1.  Password registration

   Password registration is run between a user U and a server S.  It is
   assumed that the user can authenticate the server during this
   registration phase (this is the only part in OPAQUE that requires
   some form of authenticated channel, either physical, out-of-band,
   PKI-based, etc.)

   o  U chooses password PwdU and a pair of private-public keys PrivU
      and PubU for the given protocol KE.

   o  S chooses OPRF key kU (random and independent for each user U) and
      sets vU = g^kU; it also chooses its own pair of private-public

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      keys PrivS and PubS for use with protocol KE (the server can use
      the same pair of keys with multiple users), and sends PubS to U.

   o  U and S run OPRF(kU;PwdU) as defined in Section 2 with only U
      learning the result, denoted RwdU (mnemonics for "Randomized

   o  U generates an "envelope" EnvU defined as

      EnvU = AuthEnc(RwdU; PrivU, PubU, PubS)

      where AuthEnc is an authenticated encryption function with the
      "key committing" property and is specified in Section 3.1.1 below.
      In EnvU, all values require authentication and PrivU also requires
      encryption.  However, for simplicity and to hide the EnvU
      contents, we specify that all values are encrypted (not just
      authenticated).  PubU can be omitted from EnvU if it is not needed
      for running the key-exchange protocol by the client or if it can
      be reconstructed from PrivU.

   o  U sends EnvU and PubU to S and erases PwdU, RwdU and all keys.
      S stores (EnvU, PubS, PrivS, PubU, kU, vU) in a user-specific
      record.  If PrivS and PubS are used for multiple users, S can
      store these values separately and omit them from the user's

   Note (salt).  We note that in OPAQUE the OPRF key acts as the secret
   salt value that ensures the infeasibility of pre-computation attacks.
   No extra salt value is needed.

   Note (password rules).  The above procedure has the significant
   advantage that the user's password is not disclosed to the server
   even during registration.  Some sites require learning the user's
   password for enforcing password rules.  Doing so voids this important
   security property of OPAQUE and is not recommended.  Moving the
   password check procedure to the client side is a more secure

3.1.1.  Implementing the EnvU envelop

   The function AuthEnc used to compute EnvU needs to satisfy a property
   called "key committing" (a.k.a. robust encryption).  That is, given a
   pair of random AuthEnc keys, it should be infeasible to create an
   authenticated ciphertext that successfully decrypts under the two
   keys.  Not all AuthEnc schemes enjoy this property, and this includes
   the standard GCM mode.  To address this issue we slightly modify GCM
   to achieve robustness.

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   To the plaintext specified by the definition of EnvU, concatenate a
   string of all zeros so that the last full block of the resultant
   plaintext is an all-zero block (of the length of the underlying block
   cipher, i.e., 128 for AES).  Use regular GCM on this augmented
   plaintext with a nonce value of zero.

   [Author note: A random nonce can be used if one assumes that the
   following problem is infeasible: Given two random keys for the block
   cipher, find an input of a block length that encrypts to the same
   ciphertext under both keys.  Is AES secure in this sense?]

   Following are two alternative methods to achieve encryption
   robustness (presented here for completeness in case any of these are
   preferred to the above method):

   (1) Encrypt-then-HMAC: Implement the AuthEnc scheme using any
   encryption function in encrypt-then-MAC mode where the MAC is
   implemented with HMAC with a tag size of at least 256 bits (HMAC
   ensures a collision-resistant property needed to ensure robustness).
   This requires two separate keys, one for encryption and one for HMAC,
   which can be derived from RwdU using, for example, the HKDF-Expand
   function from [RFC5869].

   [Author note: Is there a standardized definition of Encrypt-then-HMAC
   that one can refer?  Here is a description from signal [SIGNAL].]

   (2) Fixed-string MAC: Any AuthEnc method is key committing if one
   concatenates to the AuthEnc output a MAC computed on a fixed string.
   Specifically, one derives two keys from RwdU: one is a key to the
   AuthEnc function and the other is a key to a MAC (any secure MAC
   function works).  EnvU is then defined as before except that to the
   output of AuthEnc one concatenates the output of the MAC function
   computed with the second derived key on a fixed string (e.g., all

3.2.  Online OPAQUE protocol

   After registration, the user and server can run the OPAQUE protocol
   as a password-authenticated key exchange.  The protocol proceeds as

   o  User transmits user/account information to the server so that the
      server can retrieve the user's record.

   o  Server sends EnvU and vU to user.

   o  Server and User execute the OPRF protocol as defined in Section 2;
      User sets RwdU to the result of this computation.

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   o  User decrypts EnvU using RwdU to obtain PrivU, PubU, PubS.

   o  User and server run the specified KE protocol using their
      respective public and private keys.

   Note that the steps preceding the run of KE can be arranged in just
   two messages (one from the user and a response from the server).
   Furthermore, OPAQUE is optimized by running the OPRF and KE
   concurrently with interleaved and combined messages (while preserving
   the internal ordering of messages in each protocol).  In all cases,
   the user needs to obtain EnvU, vU and RwdU (i.e., complete the OPRF
   protocol) before it can use its own private key PrivU and the
   server's public key PubS in the run of KE.

3.3.  OPAQUE Instantiations

   We present several instantiations of OPAQUE using DH-OPRF as the OPRF
   and different KE protocols.  For the sake of concreteness and
   performance we focus on KE protocols consisting of two or three
   messages, denoted K1, K2, K3 (in 2-message protocols K3 is omitted)
   and such that K1 and K2 include DH values sent by user and server,
   respectively.  These DH values will ensure forward secrecy.

   Generic OPAQUE with 3-message KE:

   o  C to S: Uid, alpha=H'(PwdU)*g^r, KE1

   o  S to C: beta=alpha^kU, vU, EnvU, KE2

   o  C to S: KE3

   Key derivation and other details of the protocol are fully specified
   by the KE scheme.

   We provide two instantiations of OPAQUE (with HMQV and SIGMA-I) next
   and discuss integration with TLS in [RFC8446].

3.3.1.  Instantiation with HMQV

   The integration of OPAQUE with HMQV [HMQV] leads to the most
   efficient instantiation of OPAQUE.  It results in a full aAPKE
   protocol with implicit authentication in just two messages (this
   includes the DH-OPRF messages) and with explicit mutual
   authentication in three.  Performance is close to optimal due to the
   negligible cost of authentication in HMQV: Just 1/6 of an
   exponentiation for each party over the cost of a regular DH exchange.
   The private and public keys of the parties are Diffie-Hellman keys,

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   namely, PubU=g^PrivU and PubS=g^PrivS.  The HMQV exchange can be
   represented schematically as follows:

   o  KE1 = g^x

   o  KE2 = g^y, Mac(Km1; g^x, g^y)

   o  KE3 = Mac(Km2; g^y, g^x)

   The third message can be removed (as well as the server's Mac) if one
   is to provide implicit authentication only (e.g., if explicit
   authentication is achieved by the subsequent protocol or

   Keys in HMQV, namely, MAC keys Km1, Km2 and session/traffic keys are
   derived from a common key K computed as follows:

   C computes K = H((g^y * PubS^e)^{x + d*PrivU))

   S computes K = H((g^x * PubU^d)^{y + e*PrivS))

   where d = H(g^x, IdS) and e = H(g^y, IdU), and IdU, IdS represent the
   identities of user and server (typically, a user id and domain name,
   respectively, and can include the party's public key value).  The
   function H can be the same as used for the DH-OPRF computation.
   Using multi-exponentiation optimization, the computation of K
   involves a single multi-exponentiation whose cost is only 17% more
   than a regular exponentiation.

   This is a minimal skeleton.  A fully-specified protocol will include
   additional details and a careful key derivation scheme.  In
   particular, the Mac computation will cover the whole preceding
   transcript.  In addition, the parties will check group membership for
   g^x, g^y or use co-factor computation, e.g., as in
   [I-D.irtf-cfrg-spake2]; in any case the value is rejected if it
   equals the identity.  The check for PubU and PubS can be done only
   once at user registration.

   Note (IP disclosure): IBM has a patent that covers HMQV.  If there is
   interest in standardizing this mode one can check if a free license
   of the HMQV patent could be provided for such use.

3.3.2.  Instantiation with SIGMA-I

   We show how OPAQUE can be built around the 3-message SIGMA-I protocol
   [SIGMA].  This example is significant as it shows integration with a
   signature-based KE protocol and because TLS 1.3 follows the design of

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   SIGMA-I hence the example helps understanding the proposed
   integration of OPAQUE with TLS in [RFC8446].

   SIGMA-I can be represented schematically as follows:

   o  KE1 = g^x

   o  KE2 = g^y, Sig(PrivS; g^x, g^y), Mac(Km1; IdS)

   o  KE3 = Sig(PrivU; g^y, g^x), Mac(Km2; IdU)

   In this case, the private keys of both users and servers are
   signature keys.  Key derivation is based on the DH value g^xy.
   K3 cannot be omitted.

   As before, this is only a skeleton to illustrate the protocol.
   Full details need to be filled in for a self-contained specification.

3.4.  Hardening OPAQUE via hardened key derivation

   As noted in Section 2.1 one can increase the resistance of OPAQUE to
   offline attacks in case of server compromise by applying a password-
   hardening key derivation function (KDF) on top of the regular DH-OPRF
   when computing RwdU.  Specifically, the user computes the OPRF in
   interaction with the server and inputs its result into the KDF in
   lieu of the password on which this function acts.  The output of this
   computation is set as the value RwdU.  Parameters to the KDF function
   can be set to public values or set at the time of password
   registration and stored at the server.  In this case, the server
   communicates these parameters to the user during OPAQUE executions
   together with the second OPRF message.  We note that the salt value
   typically input into the KDF can be set to a constant, e.g., all

4.  Integrating OPAQUE with TLS 1.3

   Note: This section is intended as a basis for discussion on ways to
   integrate OPAQUE with TLS (particularly TLS 1.3).  Precise protocol
   details are left for a future specification.  A preliminary draft is

   As stated in the introduction, the standard password-over-TLS
   mechanism for password authentication suffers from significant
   weaknesses due to the essential reliance of the protocol on PKI and
   the exposure of passwords to the server (and other observers) upon
   TLS decryption.  Here we propose integrating OPAQUE with TLS in order
   to remove these vulnerabilities while at the same time armoring TLS
   itself against PKI failures.  Such integration also benefits OPAQUE

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   by leveraging the standardized negotiation and record-layer security
   of TLS.  Furthermore, TLS can offer an initial PKI-authenticated
   channel to protect the privacy of account information such as user
   name transmitted between client and server.

   If one is willing to forgo protection of user account information
   transmitted between user and server, integrating OPAQUE with TLS 1.3
   is relatively straightforward and follows essentially the same
   approach as with SIGMA-I in Section 3.3.2.  Specifically, one reuses
   the Diffie-Hellman exchange from TLS and uses the user's private key
   PrivU retrieved from the server as a signature key for TLS client
   authentication.  The integrated protocol will have as its first
   message the TLS's Client Hello augmented with user account
   information and with the DH-OPRF first message (the value alpha).
   The server's response includes the regular TLS 1.3 second flight
   augmented with the second OPRF message which includes the values
   beta, vU and EnvU.  For its TLS signature, the server uses the
   private key PrivS whose corresponding public key PubS is
   authenticated as part of the user envelope EnvU (there is no need to
   send a regular TLS certificate in this case).  Finally, the third
   flight consists of the standard client Finish message with client
   authentication where the client's signature is produced with the
   user's private key PrivU retrieved from EnvU and verified by the
   server using public key PubU.

   The above scheme is depicted in Figure 1 where the sign + indicates
   fields added by OPAQUE, and DH-OPRF1, DH-OPRF2 denote the two DH-OPRF
   messages.  Other messages in the figure are the same as in TLS 1.3.
   Notation {...} indicates encryption under handshake keys.  Note that
   ServerSignature and ClientSignature are performed with the private
   keys defined by OPAQUE and they replace signatures by traditional TLS

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           Client                                               Server

           + userid + DH-OPRF1     -------->
                                              {+ DH-OPRF2 + vU + EnvU}
                                                   {+ ServerSignature}
                                   <--------          {ServerFinished}

           {+ ClientSignature}
           {ClientFinished}        -------->

           Figure 1: Integration of OPAQUE in TLS 1.3 (no userid

   Note that in order to send DH-OPRF1 in the first message, the client
   needs to know the DH group the server uses for OPRF, or it needs to
   "guess" it.  This issue already appears in TLS 1.3 where the client
   needs to guess the key_share group and it should be handled similarly
   in OPAQUE (e.g., the client may try one or more groups in its first

   Protection of user's account information can be added through TLS 1.3
   pre-shared/resumption mechanisms where the account information
   appended to the ClientHello message would be encrypted under the pre-
   shared key.

   When a resumable session or pre-shared key between the client and the
   server do not exist, user account protection requires a server
   certificate.  One option that does not add round trips is to use a
   mechanism similar to the proposed ESNI extension [I-D.ietf-tls-esni].
   Without such extension, one would run a TLS 1.3 handshake augmented
   with the two OPAQUE messages interleaved between the second and third
   flight of the regular TLS handshake.  That is, the protocol consists
   of five flights as follows: (i) A regular 2-flight 1-RTT handshake to
   produce handshake traffic keys authenticated by the server's TLS
   certificate; (ii) two messages that include user identification
   information, the DH-OPRF messages exchanged between client and
   server, and the retrieved vU and EnvU, all encrypted under the
   handshake traffic keys (thus providing privacy to user account
   information); (iii) the TLS 1.3 client authentication flight where
   client authentication uses the user's private signature key PrivU
   retrieved from the server in step (ii).

   Note that server authentication in (i) uses TLS certificates hence
   user account privacy (but not user authentication) is dependent on

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   PKI.  In cases where PKI authentication for the server is deemed
   acceptable then there is no need for further server authentication.
   However, if one wants to enforce server authentication without
   reliance on PKI, then the server needs to authenticate using the
   private key PrivS whose corresponding public key PubS is sent to the
   user as part of EnvU.  There are two options: If PubS is the same as
   the public key the server used in the 1-RTT authentication (step (i))
   then there is no need for further authentication.  In this case, U
   gets assurance from the authenticated EnvU, not (only) from the PKI
   certificates.  Otherwise, the server needs to send a signature under
   PrivS that is piggybacked to the second OPAQUE message in (ii).  In
   this case the signature would cover the running transcript hash as is
   standard in TLS 1.3.  The client signature in the last message also
   covers the transcript hash including the regular handshake and OPAQUE

   The above scheme is depicted in Figure 2.  Please refer to the text
   before Figure 1 describing notation.  Note the asterisk in the
   ServerSignature message.  This indicates that this message is
   optional as it is used only if the server's key PubS in OPAQUE is
   different than the one in the server's certificate (transmitted in
   the second protocol flight).

           Client                                               Server

           key_share               -------->
                                   <--------           {ServerFinished}

           {+ userid + DH-OPRF1}   -------->

                                                    {+ DH-OPRF2 + EnvU}
                                               {+ DH-OPRF2 + vU + EnvU}
                                   <--------       {+ ServerSignature*}

           {ClientFinished}        -------->

          Figure 2: Integration of OPAQUE in TLS 1.3 (with userid

   We note that the above approaches for integration of OPAQUE with TLS
   may benefit from the post-handshake client authentication mechanism
   of TLS 1.3 and the exported authenticators from

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   [I-D.ietf-tls-exported-authenticator].  Also, formatting of messages
   and negotiation information suggested in [I-D.barnes-tls-pake] can be
   used in the OPAQUE setting.

5.  User enumeration

   User enumeration refers to attacks where the attacker tries to learn
   whether a given user identity is registered with a server.
   Preventing such attack requires the server to act with unknown user
   identities in a way that is indistinguishable from its behavior with
   existing users.  Here we suggest a way to implement such defense,
   namely, a way for simulating the values beta, vU and EnvU for non-
   existing users.  Note that if the same pair of user identity UId and
   value alpha is received twice by the server, the response needs to be
   the same in both cases (since this would be the case for real users).
   For this, the server S will have two keys MK, MK' for a PRF f (this
   refers to a regular PRF such as HMAC or CMAC).  Upon receiving a pair
   of user identity UId and value alpha for a non-existing user UId, S
   computes kU=f(MK; UId) and kU'=f(MK'; UId) and responds with three
   values beta=alpha^kU, vU=g^kU and EnvU where the latter is computed
   as the AuthEnc function with key kU' applied to the all-zero string
   (of the length of a regular EnvU plaintext).  Care needs to be taken
   to avoid side channel leakage (e.g., timing) from helping
   differentiate these operations from a regular server response.  The
   above requires changes to the server-side implementation but not to
   the protocol itself or the client side.

   There is one form of leakage that the above allows and whose
   prevention would require a change in OPAQUE.  Note that an attacker
   that tests a UId (and same alpha) twice and receives different
   responses can conclude that either the user registered with the
   service between these two activations or that the user was registered
   before but changed its password in between the activations (assuming
   the server changes kU at the time of a password change).  In any
   case, this indicates that UId is a registered user at the time of the
   second activation.  To conceal this information, S can implement the
   derivation of kU as kU=f(MK; UId) also for registered users.  Hiding
   changes in EnvU, however, requires a change in the protocol.  Instead
   of sending EnvU as is, S would send an encryption of EnvU under a key
   that the user derives from the OPRF result (similarly to RwdU) and
   that S stores during password registration.  During login, the user
   will derive this key from the OPRF result, use it to decrypt EnvU,
   and continue with the regular protocol.  If S uses a randomized
   encryption, the encrypted EnvU will look each time as a fresh random
   string, hence S can simulate the encrypted EnvU also for non-existing

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   [Author note: How significant is the user enumeration issue?  The
   first case above does not change the protocol so its implementation
   is a server's decision.  The second case, however, requires a change
   in OPAQUE so it would be important to have feedback on whether this
   second order attack justifies such change.]

6.  Security considerations

   This is an early draft presenting the OPAQUE concept and its
   potential instantiations.  More precise details and security
   considerations will be provided in future drafts.  We note that the
   security of OPAQUE is formally proved in [OPAQUE] under a strong
   model of aPAKE security assuming the security of the OPRF function
   and of the underlying key-exchange protocol.  In turn, the security
   of DH-OPRF is proven in the random oracle model under the One-More
   Diffie-Hellman assumption [JKKX16].

   Best practices regarding implementation of cryptographic schemes
   apply to OPAQUE.  Particular care needs to be given to the
   implementation of the OPRF regarding testing group membership and
   avoiding timing and other side channel leakage in the hash-to-curve
   mapping.  Drafts [I-D.irtf-cfrg-hash-to-curve] and
   [I-D.sullivan-cfrg-voprf] have detailed instantiation and
   implementation guidance.

   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 the case that
   q-1 or q+1, where q is the order of the group G, has a t-bit divisor,
   they show an attack that calls the OPRF on 2^t chosen inputs and
   reduces security by t/2 bits, i.e., it can find the OPRF key in time
   2^{q/2-t/2} and 2^{q/2-t/2} memory.  For typical curves, the attack
   requires an infeasible number of calls and/or results in
   insignificant security loss [*].  Moreover, in the OPAQUE
   application, these attacks are completely impractical as the number
   of calls to the function translates to an equal number of failed
   authentication attempts by a _single_ user.  For example, one would
   need a billion impersonation attempts to reduce security by 15 bits
   and a trillion to reduce it by 20 bits - and most curves will not
   even allow for such attacks in the first place (note that this
   theoretical loss of security is with respect to computing discrete
   logarithms, not in reducing the password strength).

   [*] Some examples (courtesy of Dan Brown): For P-384, 2^90 calls
   reduce security from 192 to 147 bits; for NIST P-256 the options are
   6-bit reduction with 2153 OPRF calls, about 14 bit reduction with 187

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   million calls and 20 bits with a trillion calls.  For Curve25519,
   attacks are completely infeasible (require over 2^100 calls) but its
   twist form allows an attack with 25759 calls that reduces security by
   7 bits and one with 117223 calls that reduces security by 8.4 bits.

   Note on user authentication vs. authenticated key exchange.  OPAQUE
   provides PAKE (password-based authenticated key exchange)
   functionality in the client-server setting.  While in the case of
   user identification, focus is often on the authentication part, we
   stress that the key exchange element is not less crucial.  Indeed, in
   most cases user authentication is performed to enforce some policy,
   and the key exchange part is essential for binding this enforcement
   to the authentication step.  Skipping the key exchange part is
   analogous to carefully checking visitor credentials at the door and
   then leaving the door open after a first visitor is allowed to enter.

   This draft complies with the requirements for PAKE protocols set
   forth in [RFC8125].

7.  Acknowledgments

   The OPAQUE protocol and its analysis is joint work of the author with
   Stas Jarecki and Jiayu Xu.  This draft has benefited from comments by
   multiple people.  Special thanks to Dan Brown, Eric Crockett, Fredrik
   Kuivinen, Jason Resch, Nick Sullivan.

8.  References

8.1.  Normative References

   [RFC2119]  Bradner, S., "Key words for use in RFCs to Indicate
              Requirement Levels", BCP 14, RFC 2119,
              DOI 10.17487/RFC2119, March 1997,

8.2.  Informative References

   [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.

              Canetti, R., "Universally composable security: A new
              paradigm for cryptographic protocols", IEEE Symposium on
              Foundations of Computer Science (FOCS) , 2001.

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   [Cheon06]  Cheon, J., "Security analysis of the strong Diffie-Hellman
              problem", Euroctypt 2006 , 2006.

   [FK00]     Ford, W. and B. 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.

              Barnes, R. and O. Friel, "Usage of PAKE with TLS 1.3",
              draft-barnes-tls-pake-04 (work in progress), July 2018.

              Rescorla, E., Oku, K., Sullivan, N., and C. Wood,
              "Encrypted Server Name Indication for TLS 1.3", draft-
              ietf-tls-esni-03 (work in progress), March 2019.

              Sullivan, N., "Exported Authenticators in TLS", draft-
              ietf-tls-exported-authenticator-09 (work in progress), May

              Biryukov, A., Dinu, D., Khovratovich, D., and S.
              Josefsson, "The memory-hard Argon2 password hash and
              proof-of-work function", draft-irtf-cfrg-argon2-06 (work
              in progress), June 2019.

              Scott, S., Sullivan, N., and C. Wood, "Hashing to Elliptic
              Curves", draft-irtf-cfrg-hash-to-curve-03 (work in
              progress), March 2019.

              Ladd, W. and B. Kaduk, "SPAKE2, a PAKE", draft-irtf-cfrg-
              spake2-08 (work in progress), March 2019.

              Davidson, A., Sullivan, N., and C. Wood, "Oblivious
              Pseudorandom Functions (OPRFs) using Prime-Order Groups",
              draft-sullivan-cfrg-voprf-03 (work in progress), March

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              Sullivan, N., Krawczyk, H., Friel, O., and R. Barnes,
              "Usage of OPAQUE with TLS 1.3", draft-sullivan-tls-
              opaque-00 (work in progress), March 2019.

   [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.

   [OPAQUE]   Jarecki, S., Krawczyk, H., and J. Xu, "OPAQUE: An
              Asymmetric PAKE Protocol Secure Against Pre-Computation
              Attacks", Eurocrypt , 2018.

   [RFC2945]  Wu, T., "The SRP Authentication and Key Exchange System",
              RFC 2945, DOI 10.17487/RFC2945, September 2000,

   [RFC5869]  Krawczyk, H. and P. Eronen, "HMAC-based Extract-and-Expand
              Key Derivation Function (HKDF)", RFC 5869,
              DOI 10.17487/RFC5869, May 2010,

   [RFC6628]  Shin, S. and K. Kobara, "Efficient Augmented Password-Only
              Authentication and Key Exchange for IKEv2", RFC 6628,
              DOI 10.17487/RFC6628, June 2012,

   [RFC7914]  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/info/rfc7914>.

   [RFC8018]  Moriarty, K., Ed., Kaliski, B., and A. Rusch, "PKCS #5:
              Password-Based Cryptography Specification Version 2.1",
              RFC 8018, DOI 10.17487/RFC8018, January 2017,

   [RFC8125]  Schmidt, J., "Requirements for Password-Authenticated Key
              Agreement (PAKE) Schemes", RFC 8125, DOI 10.17487/RFC8125,
              April 2017, <https://www.rfc-editor.org/info/rfc8125>.

   [RFC8446]  Rescorla, E., "The Transport Layer Security (TLS) Protocol
              Version 1.3", RFC 8446, DOI 10.17487/RFC8446, August 2018,

   [SIGMA]    Krawczyk, H., "SIGMA: The SIGn-and-MAc approach to
              authenticated Diffie-Hellman and its use in the IKE
              protocols", CRYPTO , 2003.

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   [SIGNAL]   "Signal recommended cryptographic algorithms",
              doubleratchet/#recommended-cryptographic-algorithms ,

   [VTBPEKE]  Pointcheval, D. and G. Wang, "Verifier-based Two-Basis
              Password Exponential Key Exchange", AsiaCCS , 2017.

Author's Address

   Hugo Krawczyk
   Algorand Foundation

   Email: hugokraw@gmail.com

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