Requirements for PAKE schemes
draft-irtf-cfrg-pake-reqs-07
Network Working Group J. Schmidt
Internet-Draft secunet Security Networks
Intended status: Informational September 5, 2016
Expires: March 9, 2017
Requirements for PAKE schemes
draft-irtf-cfrg-pake-reqs-07
Abstract
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).
Status of This Memo
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This Internet-Draft will expire on March 9, 2017.
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Table of Contents
1. Requirements notation . . . . . . . . . . . . . . . . . . . . 2
2. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 2
3. PAKE Taxonomy . . . . . . . . . . . . . . . . . . . . . . . . 3
3.1. Storage of the Password . . . . . . . . . . . . . . . . . 3
3.2. Transmission of Public Keys . . . . . . . . . . . . . . . 4
3.3. Two Party versus Multiparty . . . . . . . . . . . . . . . 4
4. Security of PAKEs . . . . . . . . . . . . . . . . . . . . . . 5
4.1. Implementation Aspects . . . . . . . . . . . . . . . . . 6
4.2. Special case: Elliptic Curves . . . . . . . . . . . . . . 6
5. Protocol Considerations and Applications . . . . . . . . . . 6
6. Privacy . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
7. Performance . . . . . . . . . . . . . . . . . . . . . . . . . 8
8. Requirements . . . . . . . . . . . . . . . . . . . . . . . . 8
9. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 9
10. Security Considerations . . . . . . . . . . . . . . . . . . . 9
11. References . . . . . . . . . . . . . . . . . . . . . . . . . 9
11.1. Normative References . . . . . . . . . . . . . . . . . . 9
11.2. Informative References . . . . . . . . . . . . . . . . . 9
Author's Address . . . . . . . . . . . . . . . . . . . . . . . . 10
1. Requirements notation
The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
"SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this
document are to be interpreted as described in [RFC2119].
2. Introduction
Passwords are the predominant method of accessing the Internet today
due, in large part, to their intuitiveness and ease of use. Since a
user needs to enter passwords repeatedly in many connections and
applications, these passwords tend to be easy to remember and be able
to be entered repeatedly with a low probability of error. They tend
to be low-grade and not-so-random secrets that are susceptible to
brute-force guessing attacks.
A Password-Authenticated Key Exchange (PAKE) attempts to address this
issue by constructing a cryptographic key exchange that does not
result in the password, or password-derived data, being transmitted
across an unsecured channel. Two parties in the exchange prove
possession of the shared password without revealing it. Such
exchanges are therefore resistant to off-line, brute-force dictionary
attacks. The idea was initially described by Bellovin and Merritt in
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[BM92] and has received considerable cryptographic attention since
then. PAKEs are especially interesting due to the fact that they can
achieve mutual authentication without requiring any Public Key
Infrastructure (PKI).
Different types of PAKE schemes are reviewed in this document. It
defines requirements for new schemes and gives additional
recommendations for designers of PAKE schemes. The specific
recommendations are discussed throughout Section 3 till Section 7.
Section 8 summarizes the requirements.
This document represents the consensus of the Crypto Forum Research
Group (CFRG).
3. PAKE Taxonomy
Broadly speaking, different PAKEs satisfy their goals in a number of
common ways. This leads to various design choices: how public keys
are transmitted (encrypted or not), whether both parties possess the
same representation of the password (balanced versus augmented) and
the number of parties (two party versus multiparty).
3.1. Storage of the Password
When both sides of a PAKE store the same representation of the
password, the PAKE is said to be "balanced". In a balanced PAKE the
password can be stored directly, in a salted state by hashing it with
a random salt, or by representing the credential as an element in a
finite field (by, for instance, multiplying a generator from a finite
field and the password represented as a number to produce a "password
element"). The benefits of such PAKEs are that they are applicable
to situations where either party can initiate the exchange or both
parties can initiate simultaneously, i.e. where they both believe
themselves to be the "initiator". This sort of PAKE can be useful
for mesh networking (see, for example, [DOT11]) or Internet-of-Things
applications.
When one side maintains a transform of the password and the other
maintains the raw password, the PAKE is said to be "augmented".
Typically, a client will maintain the raw password (or some
representation of it as in the balanced case), and a server will
maintain a transformed element generated with a one-way function.
The benefit of an augmented PAKE is that it provides some protection
for the server's password in a way that is not possible with a
balanced PAKE. In particular, an adversary that has successfully
obtained the server's PAKE credentials cannot directly use them to
impersonate the users to other servers. The adversary has to learn
the individual passwords first, e.g. by performing an (offline)
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dictionary attack. This sort of PAKE is useful for strict client-
server protocols such as the one discussed in [RFC5246].
3.2. Transmission of Public Keys
All known PAKEs use public key cryptography. A fundamental
difference in PAKEs is how the public key is communicated in the
exchange.
One class of PAKEs uses symmetric key cryptography, with a key
derived from the password, to encrypt an ephemeral public key. The
ability of the peer to demonstrate it has successfully decrypted the
public key proves knowledge of the shared password. Examples of this
exchange include the first PAKE called the Encrypted Key Exchange
(EKE) which was introduced in [BM92].
Another class of PAKEs transmits unencrypted public keys, like the
J-PAKE protocol [JPAKE]. During key agreement, ephemeral public keys
and values derived using the shared password are exchanged. In the
case that the passwords match both parties can compute a common
secret by combining password, public keys and private keys. The
SPEKE [SPEKE] scheme also exchanges public keys, namely Diffie-
Hellman values. Here, the generator for the public keys is derived
from the shared secret. Afterwards, only the public Diffie-Hellman
values are exchanged, the generator is kept secret. In both cases,
the values that are transmitted across the unsecured medium is an
element in a finite field and not a random blob.
A combination of the EKE and SPEKE is used in PACE as described in
[BFK09], which is e.g. used in international travel documents. In
this method a nonce is encrypted rather than a key. This nonce is
used to generate a common base for the key agreement. Without
knowing the password, the nonce cannot be determined and hence, the
subsequent key agreement will fail.
3.3. Two Party versus Multiparty
The majority of PAKE protocols allow two parties to agree on a shared
key based on a shared password. Nevertheless, there exist proposals
that allow key agreement for more than two parties. Those protocols
allow key establishment for a group of parties and are hence called
Group PAKEs or GPAKEs. Examples of such protocols can be found in
[ABCP06], while [ACGP11] and [HYCS15] propose a generic construction
that allows the transformation of any two-party PAKE into a GPAKE
protocol. Another possibility of defining a multi-party PAKE
protocol is to assume the existence of a trusted server with which
each party shares a password. This server enables different parties
to agree on a common secret key without the need to share a password
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among each other. Each party has only a shared secret with the
trusted server. For example, Abdalla et al. designed such a protocol
as discussed in [AFP05].
4. Security of PAKEs
PAKE schemes are modelled on the scenario of two parties, typically
Alice and Bob, who share a password (or perhaps Bob shares a function
of the password) and would like to use it to establish a secure
session key over an untrusted link. There is a powerful adversary,
typically Eve, who would like to subvert the exchange. Eve has
access to a dictionary that is likely to contain Alice and Bob's
password, and Eve is capable of enumerating through the dictionary in
a brute-force manner to try and discover Alice and Bob's password.
All PAKEs have a limitation. If Eve guesses the password, she can
subvert the exchange. It is therefore necessary to model likelihood
that Eve will guess the password to access the security of a PAKE.
If the probability of her discovering the password is a function of
interaction with the protocol participants and not a function of
computation, then the PAKE is secure. That is, if Eve is unable to
take information from a passive attack or from a single active
attack. Thus, she cannot enumerate through her dictionary without
interacting with Alice or Bob for each password guess, i.e. the only
attack left is repeated guessing. Eve learns one thing from a single
active attack: whether her single guess is correct or not.
In other words, the security of a PAKE scheme is based on the idea
that Eve, who is trying to impersonate Alice, cannot efficiently
verify a password guess without interacting with Bob (or Alice). If
she were to interact with either, she would thereby be detected.
Thus, it is to balance restricting the number of allowed
authentication attempts with the potential of a denial-of-service
vulnerability. In order to judge and compare the security of PAKE
schemes, security proofs in commonly accepted models SHOULD be used.
Each proof and model, however, is based on assumptions. Often
security proofs show that if an adversary is able to break the
scheme, the adversary is also able to solve a problem that is assumed
to be hard such as computing a discrete logarithm. By conversion,
breaking the scheme is considered to be a hard problem as well.
A PAKE scheme MUST be accompanied with a security proof with clearly
stated assumptions and models used. In particular, the proof MUST
show that the probability is negligible that an active adversary
would be able to pass authentication, learn additional information
about the password or learn anything about the established key.
Moreover, the authors MAY specify which underlying primitives are to
be used with the scheme or MAY consider specific use cases or
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assumptions like resistance to quantum computers. A clear and
comprehensive proof is the foundation for users to trust in the
security of the scheme.
4.1. Implementation Aspects
Aside from the theoretical security of a scheme, practical
implementation pitfalls have to be considered as well. If not
carefully implemented, even a scheme that is secure in a well-defined
mathematical model can leak information via side-channels. The
design of the scheme might allow or prevent easy protection against
information leakage. In a network scenario, an adversary can measure
the time the computation of an answer takes and derive information
about secret parameters of the scheme. If a device operates in a
potentially hostile environment, such as a smart card, other side-
channels like power consumption and electromagnetic emanations or
even active implementation attacks have to be taken into account as
well.
The developers of a scheme SHOULD keep the implementation aspects in
mind and show how to implement the protocol in constant time.
Furthermore, adding a discussion about how to protect implementations
of the scheme in potential hostile environments is encouraged.
4.2. Special case: Elliptic Curves
Since Elliptic Curve Cryptography (ECC) allows for a smaller key-
length compared to traditional schemes based on the discrete
logarithm problem in finite fields at similar security levels, using
ECC for PAKE schemes is also of interest. In contrast to schemes
that can use the finite field element directly, an additional
challenge has to be considered for some schemes based on ECC, namely
the mapping of a random string to an element that can be computed
with, i.e. a point on the curve. In some cases, also the opposite is
needed, i.e. the mapping of a curve point to a string that is not
distinguishable from a random one. When choosing a mapping, it is
crucial to consider the implementation aspects as well.
In the case that the PAKE scheme is intended to be used with ECC, the
authors SHOULD state whether there is a mapping function needed, and
if so, discuss its requirements. Alternatively, the authors MAY
define a mapping to be used with the scheme.
5. Protocol Considerations and Applications
In most cases, the PAKE scheme is a building block in a more complex
protocol like IPSEC or TLS. This can influence the choice of a
suitable PAKE scheme. For example, an augmented scheme can be
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beneficial for protocols that have a strict server-client
relationship. In the case that both parties can initiate a
connection of a protocol, a balanced PAKE might be more appropriate.
A special variation of the network password problem, called Password
Authenticated Key Distribution, is defined in [P1363] as password
authenticated key retrieval: "The retrieval of a key from a secure
key repository or escrow requiring authentication derived in part
from a password."
In addition to key retrieval from escrow, there is also the variant
of two parties exchanging public keys using a PAKE in lieu of
certificates. In this variant, public keys can be encrypted using a
password. Authentication key distribution can be performed because
each side knows the private key associated with its unencrypted
public key and can also decrypt the peer's public key. This
technique can be used to transform a short, one-time code into a
long-term public key.
Another possible variant of a PAKE scheme allows combining
authentication with certificates and the use of passwords. In this
variant, the private key of the certificate is used to blind the
password key agreement. For verification, the message is unblinded
with the public key. A correct key establishment therefore implies
the possession of the private key belonging to the certificate. This
method enables one-sided authentication as well as mutual
authentication when the password is used.
The authors of a PAKE scheme MAY discuss variations of their scheme
and explain application scenarios where these variations are
beneficial. In particular, techniques that allow long-term (public)
key agreement are encouraged.
6. Privacy
In order to establish a connection, each party of the PAKE protocol
needs to know the identity of its communication partner to identify
the right password for the agreement. In cases where a user wants to
establish a secure channel with a server, the user first has to let
the server know which password to use by sending some kind of
identifier to the server. If this identifier is not protected,
everyone who is able to eavesdrop on the connection can identify the
user. In order to prevent this and protect the privacy of the user,
the scheme might provide a way to protect the transmission of the
user's identity. A simple way to achieve privacy of a user that
communicates with a server is to use a public key provided by the
server to encrypt the user's identity.
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The PAKE scheme MAY discuss special ideas and solutions how to
protect the privacy of the users of the scheme.
7. Performance
The performance of a scheme can be judged along different lines
depending on the optimization goals of the target application.
Potential metrics include latency, code-size/area, power consumption,
or exchanged messages. In addition, there might be application
scenarios in which a constrained client communicates with a powerful
server. In such a case, the scheme has to require minimal efforts on
the client side. Note that for some clients the computations might
even be carried out in a hardware implementation, which require
different optimizations compared to software.
Furthermore, the design of the scheme can influence the cost of
protecting the implementation from adversaries exploiting its
physical properties (see Section 4.1).
The authors of a PAKE scheme MAY discuss their design choices and the
influence of these choices on the performance. In particular, the
optimization goals could be stated.
8. Requirements
This section formulates the requirements for PAKE schemes based on
the previous discussed properties.
R1: A PAKE scheme MUST clearly state its features regarding
balanced/augmented versions.
R2: A PAKE scheme SHOULD come with a security proof and clearly
state its assumptions and models.
R3: The authors SHOULD show how to protect their PAKE scheme
implementation in hostile environments, particularly, how to
implement their scheme in constant time to prevent timing attacks.
R4: In the case that the PAKE scheme is intended to be used with
ECC, the authors SHOULD discuss their requirements for a potential
mapping or define a mapping to be used with the scheme.
R5: The authors of a PAKE scheme MAY discuss its design choice
with regard to performance, i.e., its optimization goals.
R6: The authors of a scheme MAY discuss variations of their scheme
that allows the use in special application scenarios. In
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particular, techniques that facilitate long-term (public) key
agreement are encouraged.
R7: Authors of a scheme MAY discuss special ideas and solutions on
privacy protection of its users.
R8: The authors MUST follow the IRTF IPR policy <https://irtf.org/
ipr>.
9. IANA Considerations
This document makes no request of IANA.
10. Security Considerations
This document analyses requirements for a cryptographic scheme.
Security considerations are discussed throughout the document.
11. References
11.1. 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,
<http://www.rfc-editor.org/info/rfc2119>.
11.2. Informative References
[ABCP06] Abdalla, M., Bresson, E., Chevassut, O., and D.
Pointcheval, "Password-Based Group Key Exchange in a
Constant Number of Rounds", PKC 2006, LNCS 3958, 2006.
[ACGP11] Abdalla, M., Chevalier, C., Granboulan, L., and D.
Pointcheval, "Contributory Password-Authenticated Group
Key Exchange with Join Capability", CT-RSA 2011,
LNCS 6558, 2011.
[AFP05] Abdalla, M., Fouque, P., and D. Pointcheval, "Password-
based authenticated key exchange in the three-party
setting", PKC 2005, LNCS 3386, 2005.
[BFK09] Bender, J., Fischlin, M., and D. Kuegler, "Security
Analysis of the PACE Key-Agreement Protocol", ISC 2009,
LNCS 5735, 2009.
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[BM92] Bellovin, S. and M. Merritt, "Encrypted Key Exchange:
Password-Based Protocols Secure Against Dictionary
Attacks", Proc. of the Symposium on Security and
Privacy Oakland, 1992.
[DOT11] IEEE Computer Society, "Telecommunications and information
exchange between systems Local and metropolitan area
networks", Part 11: Wireless LAN Medium Access Control
(MAC) and Physical Layer (PHY) Specifications IEEE Std
802.11-2012, 2012.
[HYCS15] Hao, F., Yi, X., Chen, L., and S. Shahandashti, "The
Fairy-Ring Dance: Password Authenticated Key Exchange in a
Group", IoTPTS 2015, ACM , 2015.
[JPAKE] Hao, F. and P. Ryan, "Password Authenticated Key Exchange
by Juggling", SP 2008, LNCS 6615, 2008.
[P1363] IEEE Microprocessor Standards Committee, "Draft Standard
for Specifications for Password-based Public Key
Cryptographic Techniques", IEEE P1363.2, 2006.
[RFC5246] Dierks, T. and E. Rescorla, "The Transport Layer Security
(TLS) Protocol Version 1.2", RFC 5246,
DOI 10.17487/RFC5246, August 2008,
<http://www.rfc-editor.org/info/rfc5246>.
[SPEKE] Jablon, D., "Strong Password-Only Authenticated Key
Exchange", ACM Computer Communications Review October
1996, 1996.
Author's Address
Joern-Marc Schmidt
secunet Security Networks
Mergenthaler Allee 77
65760 Eschborn
Germany
Email: joern-marc.schmidt@secunet.com
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