Password-Authenticated Key (PAK) Diffie-Hellman Exchange
RFC 5683

Document Type RFC - Informational (February 2010; No errata)
Last updated 2015-10-14
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Independent Submission                                    A. Brusilovsky
Request for Comments: 5683                                   I. Faynberg
Category: Informational                                       Z. Zeltsan
ISSN: 2070-1721                                           Alcatel-Lucent
                                                                S. Patel
                                                            Google, Inc.
                                                           February 2010

        Password-Authenticated Key (PAK) Diffie-Hellman Exchange

Abstract

   This document proposes to add mutual authentication, based on a
   human-memorizable password, to the basic, unauthenticated Diffie-
   Hellman key exchange.  The proposed algorithm is called the Password-
   Authenticated Key (PAK) exchange.  PAK allows two parties to
   authenticate themselves while performing the Diffie-Hellman exchange.

   The protocol is secure against all passive and active attacks.  In
   particular, it does not allow either type of attacker to obtain any
   information that would enable an offline dictionary attack on the
   password.  PAK provides Forward Secrecy.

Status of This Memo

   This document is not an Internet Standards Track specification; it is
   published for informational purposes.

   This is a contribution to the RFC Series, independently of any other
   RFC stream.  The RFC Editor has chosen to publish this document at
   its discretion and makes no statement about its value for
   implementation or deployment.  Documents approved for publication by
   the RFC Editor are not a candidate for any level of Internet
   Standard; see Section 2 of RFC 5741.

   Information about the current status of this document, any errata,
   and how to provide feedback on it may be obtained at
   http://www.rfc-editor.org/info/rfc5683.

Brusilovsky, et al.           Informational                     [Page 1]
RFC 5683               PAK Diffie-Hellman Exchange         February 2010

Copyright Notice

   Copyright (c) 2010 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
   (http:trustee.ietf.org/license-info) in effect on the date of
   publication of this document.  Please review these documents
   carefully, as they describe your rights and restrictions with respect
   to this document.

Table of Contents

   1. Introduction ....................................................3
   2. Conventions .....................................................3
   3. Password-Authenticated Key Exchange .............................4
   4. Selection of Parameters .........................................5
      4.1. General Considerations .....................................5
      4.2. Over-the-Air Service Provisioning (OTASP) and Wireless
           Local Area Network (WLAN) Diffie-Hellman Parameters and
           Key Expansion Functions ....................................5
   5. Security Considerations .........................................7
   6. Acknowledgments .................................................8
   7. References ......................................................8
      7.1. Normative References .......................................8
      7.2. Informative References .....................................8

Brusilovsky, et al.           Informational                     [Page 2]
RFC 5683               PAK Diffie-Hellman Exchange         February 2010

1.  Introduction

   PAK has the following advantages:

   -  It provides a secure, authenticated key-exchange protocol.
   -  It is secure against offline dictionary attacks when passwords are
      used.
   -  It ensures Forward Secrecy.
   -  It has been proven to be as secure as the Diffie-Hellman solution.

   The PAK protocol ([BMP00], [MP05], [X.1035]) has been proven to be as
   secure as the Diffie-Hellman ([RFC2631], [DH76]) in the random oracle
   model [BR93].  That is, PAK retains its security when used with low-
   entropy passwords.  Therefore, it can be seamlessly integrated into
   existing applications, requiring secure authentication based on such
   low-entropy shared secrets.

2.  Conventions

   -  A is an identity of Alice.

   -  B is an identity of Bob.

   -  Ra is a secret random exponent selected by A.

   -  Rb is a secret random exponent selected by B.

   -  Xab denotes a value (X presumably computed by A) as derived by B.

   -  Yba denotes a value (Y presumably computed by B) as derived by A.

   -  A mod b denotes the least non-negative remainder when a is divided
      by b.

   -  Hi(u) denotes an agreed-on function (e.g., based on SHA-1,
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