SPAKE2, a PAKE
draft-irtf-cfrg-spake2-07

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Last updated 2018-11-04
Replaces draft-ladd-spake2
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Network Working Group                                            W. Ladd
Internet-Draft                                               UC Berkeley
Intended status: Informational                             B. Kaduk, Ed.
Expires: May 8, 2019                                              Akamai
                                                        November 4, 2018

                             SPAKE2, a PAKE
                       draft-irtf-cfrg-spake2-07

Abstract

   This document describes SPAKE2, a means for two parties that share a
   password to derive a strong shared key with no risk of disclosing the
   password.  This method is compatible with any group, is
   computationally efficient, and has a security proof.

Status of This Memo

   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
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   This Internet-Draft will expire on May 8, 2019.

Copyright Notice

   Copyright (c) 2018 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
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   described in the Simplified BSD License.

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Table of Contents

   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   2
   2.  Requirements Notation . . . . . . . . . . . . . . . . . . . .   2
   3.  Definition of SPAKE2  . . . . . . . . . . . . . . . . . . . .   2
   4.  Table of points for common groups . . . . . . . . . . . . . .   4
   5.  Security Considerations . . . . . . . . . . . . . . . . . . .   7
   6.  IANA Considerations . . . . . . . . . . . . . . . . . . . . .   7
   7.  Acknowledgments . . . . . . . . . . . . . . . . . . . . . . .   8
   8.  References  . . . . . . . . . . . . . . . . . . . . . . . . .   8
   Authors' Addresses  . . . . . . . . . . . . . . . . . . . . . . .   9

1.  Introduction

   This document describes SPAKE2, a means for two parties that share a
   password to derive a strong shared key with no risk of disclosing the
   password.  This password-based key exchange protocol is compatible
   with any group (requiring only a scheme to map a random input of
   fixed length per group to a random group element), is computationally
   efficient, and has a security proof.  Predetermined parameters for a
   selection of commonly used groups are also provided for use by other
   protocols.

2.  Requirements Notation

   The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
   "SHOULD", "SHOULD NOT", "RECOMMENDED", "NOT RECOMMENDED", "MAY", and
   "OPTIONAL" in this document are to be interpreted as described in BCP
   14 [RFC2119] [RFC8174] when, and only when, they appear in all
   capitals, as shown here.

3.  Definition of SPAKE2

3.1.  Setup

   Let G be a group in which the Diffie-Hellman (DH) problem is hard of
   order p*h, with p a big prime and h a cofactor.  We denote the
   operations in the group 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 [RFC6234].  We assume there is a
   representation of elements of G as byte strings: common choices would
   be SEC1 compressed [SEC1] for elliptic curve groups or big endian
   integers of a fixed (per-group) length for prime field DH.

   || denotes concatenation of strings.  We also let len(S) denote the
   length of a string in bytes, represented as an eight-byte little-
   endian number.

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   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.  G is
   specified in the document defining the group, and so we do not repeat
   it here.

   Let A and B be two parties.  We will assume that A and B also have
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