The OPAQUE Asymmetric PAKE Protocol
draft-krawczyk-cfrg-opaque-02
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| Last updated | 2019-07-06 | ||
| Replaced by | draft-irtf-cfrg-opaque, draft-irtf-cfrg-opaque | ||
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draft-krawczyk-cfrg-opaque-02
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
draft-krawczyk-cfrg-opaque-02
Abstract
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
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material or to cite them other than as "work in progress."
This Internet-Draft will expire on January 8, 2020.
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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
decryption.
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
messages.
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
[I-D.ietf-tls-esni]).
1.1. Terminology
In this document, the key words "MUST", "MUST NOT", "REQUIRED",
"SHALL", "SHALL NOT", "SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY",
and "OPTIONAL" are to be interpreted as described in BCP 14, RFC 2119
[RFC2119]
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
specification).
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).
2. DH-OPRF
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
oracle).
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
beta=alpha^k
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
therein.
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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
PwdU").
o U generates an "envelope" EnvU defined as
EnvU = AuthEnc(RwdU; PrivU, PubU, PubS)
where AuthEnc is an authenticated encryption function with the
"key committing" property and is specified 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
record.
Note (salt). We note that in OPAQUE the OPRF key acts as the secret
salt value that ensures the infeasibility of pre-computation attacks.
No extra salt value is needed.
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
alternative.
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
zeros).
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
follows:
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
application).
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
zeros.
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
[I-D.sullivan-tls-opaque].
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
certificates.
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Client Server
ClientHello
key_share
+ userid + DH-OPRF1 -------->
ServerHello
key_share
{+ DH-OPRF2 + vU + EnvU}
{+ ServerSignature}
<-------- {ServerFinished}
{+ ClientSignature}
{ClientFinished} -------->
Figure 1: Integration of OPAQUE in TLS 1.3 (no userid
confidentiality)
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
message).
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
messages.
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
ClientHello
key_share -------->
ServerHello
key_share
{Certificate}
{CertificateVerify}
<-------- {ServerFinished}
{+ userid + DH-OPRF1} -------->
{+ DH-OPRF2 + EnvU}
{+ DH-OPRF2 + vU + EnvU}
<-------- {+ ServerSignature*}
{ClientSignature}
{ClientFinished} -------->
Figure 2: Integration of OPAQUE in TLS 1.3 (with userid
confidentiality)
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
users.
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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,
<https://www.rfc-editor.org/info/rfc2119>.
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.
[Canetti01]
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.
[I-D.barnes-tls-pake]
Barnes, R. and O. Friel, "Usage of PAKE with TLS 1.3",
draft-barnes-tls-pake-04 (work in progress), July 2018.
[I-D.ietf-tls-esni]
Rescorla, E., Oku, K., Sullivan, N., and C. Wood,
"Encrypted Server Name Indication for TLS 1.3", draft-
ietf-tls-esni-03 (work in progress), March 2019.
[I-D.ietf-tls-exported-authenticator]
Sullivan, N., "Exported Authenticators in TLS", draft-
ietf-tls-exported-authenticator-09 (work in progress), May
2019.
[I-D.irtf-cfrg-argon2]
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.
[I-D.irtf-cfrg-hash-to-curve]
Scott, S., Sullivan, N., and C. Wood, "Hashing to Elliptic
Curves", draft-irtf-cfrg-hash-to-curve-03 (work in
progress), March 2019.
[I-D.irtf-cfrg-spake2]
Ladd, W. and B. Kaduk, "SPAKE2, a PAKE", draft-irtf-cfrg-
spake2-08 (work in progress), March 2019.
[I-D.sullivan-cfrg-voprf]
Davidson, A., Sullivan, N., and C. Wood, "Oblivious
Pseudorandom Functions (OPRFs) using Prime-Order Groups",
draft-sullivan-cfrg-voprf-03 (work in progress), March
2019.
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[I-D.sullivan-tls-opaque]
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,
<https://www.rfc-editor.org/info/rfc2945>.
[RFC5869] Krawczyk, H. and P. Eronen, "HMAC-based Extract-and-Expand
Key Derivation Function (HKDF)", RFC 5869,
DOI 10.17487/RFC5869, May 2010,
<https://www.rfc-editor.org/info/rfc5869>.
[RFC6628] Shin, S. and K. Kobara, "Efficient Augmented Password-Only
Authentication and Key Exchange for IKEv2", RFC 6628,
DOI 10.17487/RFC6628, June 2012,
<https://www.rfc-editor.org/info/rfc6628>.
[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,
<https://www.rfc-editor.org/info/rfc8018>.
[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,
<https://www.rfc-editor.org/info/rfc8446>.
[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",
https://signal.org/docs/specifications/
doubleratchet/#recommended-cryptographic-algorithms ,
2016.
[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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