Internet Draft W. Ladd UC Berkeley Category: Informational Expires 9 July 2015 9 October 2014 SPAKE2, a PAKE Status of this Memo Distribution of this memo is unlimited. 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), its areas, and its working groups. Note that other groups may also distribute working documents as Internet- Drafts. Internet-Drafts are draft documents valid for a maximum of six months and may be updated, replaced, or obsoleted by other documents at any time. It is inappropriate to use Internet-Drafts as reference material or to cite them other than as "work in progress." The list of current Internet-Drafts can be accessed at http://www.ietf.org/ietf/1id-abstracts.txt. The list of Internet-Draft Shadow Directories can be accessed at http://www.ietf.org/shadow.html. This Internet-Draft will expire on date. Copyright Notice Copyright (c) 2014 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. Abstract This Internet-Draft describes SPAKE2, a secure, efficient password Ladd, Watson Expires 9 July 2014 [Page 1] Internet Draft ladd-spake2 5 January 2014 based key exchange Ladd, Watson Expires 9 July 2014 [Page 2] Internet Draft ladd-spake2 5 January 2014 Table of Contents 1. Introduction ....................................................3 2. Defintion of SPAKE2..............................................3 3. Table of points .................................................3 4. Security considerations .........................................4 5. IANA actions ....................................................4 6. References.......................................................4 1. Introduction This document describes a means for two parties that share a password to derive a shared key. 2. Definition of SPAKE2 Let G be a group in which the Diffie-Hellman problem is hard of prime order p, written additively. Let H be a hash function from arbitrary strings to bit strings of a fixed length. Common choices for H are SHA256 or SHA512. We assume there is a representation of elements of G as byte strings. || denotes concatenation of strings. We also let len(S) denote the length of a string in bytes, rrepresented as an eight-byte big-endian number. We fix two elements M and N as defined in the table in this document for common groups, as well as a generator g of the group. Let A and B be two parties. We will assume that A and B are also representations of the parties such as MAC addresses or other names (hostnames, usernames, etc). We assume they share an element of Zp w. Typically w will be the hash of a user-supplied password, truncated and taken mod p. Protocols using this protocol must define w. A picks x randomly and uniformly from the integers in [0,p), and calculates X=xg and T=wM+X, then transmits T to B. B selects y randomly and uniformly from the integers in [0,p), and calculates Y=yg, S=wN+Y, then transmits S to A. Both A and B calculate a group element K. A calculates it as x(S-wN), while B calculates it as y(T-wM). Both A and B can now calculate a shared key as H(len(A)||len(B)||len(S)||len(T)||A||B||S||T||K). 3. Table of points Ladd, Watson Expires 9 July 2014 [Page 3] Internet Draft ladd-spake2 5 January 2014 [TODO] 4. Security Considerations A security proof is found in [REF]. Note that the choice of M and N is critical: anyone who is aware of an x such that xN=M, or xg=N or M can break the scheme above. The points in the table of points were picked in standard ways to eliminate this risk. There is no key-confirmation as this is a one round protocol. It is expected that a protocol using this key exchange mechanism provides key confirmation separately if desired. Elements should be checked for group membership: failure to properly validate group elements can lead to attacks. 5. IANA Considerations No IANA action is required. 6. References [REF] Abdalla, M. and Pointcheval, D. Simple Password-Based Encrypted Key Exchange Protocols. Appears in A. Menezes, editor. Topics in Cryptography-CT-RSA 2005, Volume 3376 of Lecture Notes in Computer Science, pages 191-208, San Francisco, CA, US Feb. 14-18, 2005. Springer-Verlag, Berlin, Germany. Author Addresses Watson Ladd watsonbladd@gmail.com Berkeley, CA Ladd, Watson Expires 9 July 2014 [Page 4]