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Versions: 00 01 draft-irtf-cfrg-spake2

Internet Draft                                                   W. Ladd
<draft-ladd-spake2-00.txt>                                     UC Berkeley
Category: Informational
Expires 9 July 2015                                       9 October 2014

                             SPAKE2, a PAKE
                       <draft-ladd-spake2-00.txt>

Status of this Memo

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Copyright Notice

   Copyright (c) 2014 IETF Trust and the persons identified as the
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Abstract

   This Internet-Draft describes SPAKE2, a secure, efficient password



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   based key exchange


















































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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




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   [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



















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