Network Working Group J. Schmidt
Internet-Draft secunet Security Networks
Intended status: Standards Track May 3, 2016
Expires: November 4, 2016

Requirements for PAKE schemes


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 and discusses their requirements.

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Table of Contents

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 largely to their intuitiveness and ease of use. Since a user needs to enter her password repeatedly over the course of many connections to the Internet, these passwords tend to be easy to remember and 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. In other words, they are horrible credentials to use for authentication.

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 to the exchange prove possession of the shared password without revealing it. Such exchanges are therefore resistant to an off-line, brute-force dictionary attack. PAKEs are especially interesting due to the fact that they can achieve mutual authentication without requiring any Public Key Infrastructure (PKI).

The problem was initially described by Bellovin and Merritt in [BM92] and has received considerable cryptographic attention since then.

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 it is applicable to situations where either party can initiate the exchange or both parties can initiate simultaneously (where they both believe themselves to be the "initiator"). This sort of PAKE can be useful for mesh networking (e.g. [DOT11]) or Internet-of-Things applications.

When one side maintains are uninvertable 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 and a server will maintain a transformed element generated with a one-way function. The benefit of an augmented PAKE is that the server's password database is protected in a way that is not possible with a balanced PAKE. Augmented PAKEs are resistant to Key Compromise Impersonation (KCI) where an adversary who has successfully attacked Bob can impersonate Bob to everyone, but it is not possible to impersonate everyone back to Bob. An adversary that has successfully obtained the server's PAKE credentials is still required to perform a dictionary attack in order to learn an individual password. This sort of PAKE is useful for strict client-server protocols, such as [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 presented by [BM92], the Encrypted Key Exchange (EKE). A variant of this method, as it is e.g. used in international travel documents by PACE [BFK09], is to encrypt a nonce instead of a key, which is later used for the derivation of the shared key.

The other class of PAKEs transmits unencrypted public keys. These public keys may be blinded by some function of the shared password, but the public key that is transmitted across the unsecured medium is an element in a finite field, not a random blob. The ability of the peer to successfully use that public key (for example, possibly unblinding it) proves knowledge of the shared password. Examples of this exchange include [SPEKE].

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, hence are called Group PAKEs or GPAKEs. Examples of such protocols include [ABCP06], while [ACGP11] and [HYCS15] propose a generic construction that allows transferring any two-party PAKE into a GPAKE protocol. Another possibility to define a multi-party PAKE protocol is to assume the existence of a trusted server each party shares a password with. This server enables different parties to agree on a common secret key without the need to share a password among each other. Each party has only a shared secret with the trusted server. For example Abdalla et al. designed such a protocol [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 flaw: if Eve guesses the password she can subvert the exchange. Therefore to consider security of a PAKE it is necessary to model the difficulty of that happening. If the probability of 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 a single active attack and enumerate through her dictionary then the only attack left is repeated guessing attacks. 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) and hence is detected. Thus, it is essential to keep a balance of allowed tries to reduce the probability of Eve to succeed on the one hand and to limit the risk of a denial of service vulnerability on the other hand. In order to judge and compare the security of PAKE schemes, security proofs in commonly accepted models should be used. However, each proof and model is based on assumptions: Often, a security proof shows that in case an adversary is able to break the scheme, she is also able to solve a problem that is assumed to be hard, like computing a discrete logarithm. By conversion, breaking the scheme is considered as a hard problem, too. In addition, proofs sometimes rely on idealized versions of hash functions and/or block ciphers, called random oracles and ideal ciphers.

A PAKE scheme should come with a security proof and also clearly state its assumptions and used models. In particular, the proof must show that the probability of an active adversary to pass authentication, to learn anything about the password or to learn anything about the established key equals, up to a negligible term, the chance of randomly guessing the password, while each guess requires an interaction with a legitimate party. Moreover, the authors may specify which underlying primitives to be used with their scheme.

4.1. Implementation Aspects

Besides the theoretical security of a scheme, pitfalls when implementing it in practice have to be considered as well. Even a scheme that is secure in a well-defined mathematical model can leak information via side-channels, if it is not carefully implemented. The design of the scheme may allow or prevent an easy protection against information leakage. In a network scenario, an adversary may measure the time the computation of an answer takes and derive information about secret parameters of the scheme. If a device operates in a potential hostile environment, e.g. in case it is implemented on 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 how to protect implementations of their 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: 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 required, 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 case the PAKE scheme is intended to be used with ECC, the authors should state whether there is a mapping function required and if so, discuss its requirements. Alternatively, the authors may define a mapping to be used with their 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 suited PAKE scheme. For example, an augmented scheme can be beneficial for protocols that have a strict server-client relationship. In case both parties may initiate a connection of a protocol, a balanced PAKE may 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 retrieval of a key from escrow, there is the variant of two parties exchanging public keys using a PAKE in lieu of certificates-- public keys can be encrypted using a password and the ability of each side to both know the private key associated with its unencrypted public key and also decrypt the peer's public key performs authenticated key distribution. This technique can be used to parlay a short one-time code, into a long-lived 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 authentication of one side as well as mutual authentication in addition to the authentication using the password.

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 agreeing on a long-term (public) key 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 use 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, i.e. send 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, i.e. to protect the privacy of the user, the scheme might come with 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.

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 what is the scarcest resource in the application field. 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, i.e., a scheme that requires minimal efforts on client side is most suited. Note that for some clients the computations might even be carried out in a hardware implementation, asking for different optimizations compared to software.

Furthermore, the design of the scheme may also influence the cost of protecting its 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.

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.

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.
[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.
[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.
[SPEKE] Jablon, D., "Strong Password-Only Authenticated Key Exchange", ACM Computer Communications Review October 1996, 1996.

Author's Address

Jörn-Marc Schmidt secunet Security Networks Mergenthaler Allee 77 65760 Eschborn, Germany EMail: