SPAKE2, a PAKE
draft-irtf-cfrg-spake2-09

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Network Working Group                                            W. Ladd
Internet-Draft                                                Cloudflare
Intended status: Informational                             B. Kaduk, Ed.
Expires: April 5, 2020                                            Akamai
                                                         October 3, 2019

                             SPAKE2, a PAKE
                       draft-irtf-cfrg-spake2-09

Abstract

   This document describes SPAKE2 which is a protocol 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 SPAKE2 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 April 5, 2020.

Copyright Notice

   Copyright (c) 2019 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
   (https://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
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   include Simplified BSD License text as described in Section 4.e of
   the Trust Legal Provisions and are provided without warranty as
   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.  Key Schedule and Key Confirmation . . . . . . . . . . . . . .   5
   5.  Ciphersuites  . . . . . . . . . . . . . . . . . . . . . . . .   6
   6.  Security Considerations . . . . . . . . . . . . . . . . . . .   8
   7.  IANA Considerations . . . . . . . . . . . . . . . . . . . . .   8
   8.  Acknowledgments . . . . . . . . . . . . . . . . . . . . . . .   8
   9.  References  . . . . . . . . . . . . . . . . . . . . . . . . .   8
   Appendix A.  Algorithm used for Point Generation  . . . . . . . .  10
   Appendix B.  Test Vectors . . . . . . . . . . . . . . . . . . . .  12
   Authors' Addresses  . . . . . . . . . . . . . . . . . . . . . . .  18

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 computational Diffie-Hellman (CDH)
   problem is hard.  Suppose G has order p*h where p is a large prime; h
   will be called the cofactor.  Let I be the unit element in G, e.g.,
   the point at infinity if G is an elliptic curve group.  We denote the
   operations in the group additively.  We assume there is a
   representation of elements of G as byte strings: common choices would
   be SEC1 uncompressed or compressed [SEC1] for elliptic curve groups
   or big endian integers of a fixed (per-group) length for prime field
   DH.  We fix two elements M and N in the prime-order subgroup of G as
   defined in the table in this document for common groups, as well as a

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   generator P of the (large) prime-order subgroup of G.  In the case of