SPAKE2, a PAKE
draft-irtf-cfrg-spake2-18
Internet Research Task Force W. Ladd
Internet-Draft Cloudflare
Intended status: Informational B. Kaduk, Ed.
Expires: July 21, 2021 Akamai
January 17, 2021
SPAKE2, a PAKE
draft-irtf-cfrg-spake2-18
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. This
document predated the CFRG PAKE competition and it was not selected.
This document is a product of the Crypto Forum Research Group (CFRG)
in the IRTF.
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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Internet-Drafts are draft documents valid for a maximum of six months
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This Internet-Draft will expire on July 21, 2021.
Copyright Notice
Copyright (c) 2021 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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Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 2
2. Requirements Notation . . . . . . . . . . . . . . . . . . . . 2
3. Definition of SPAKE2 . . . . . . . . . . . . . . . . . . . . 2
4. Key Schedule and Key Confirmation . . . . . . . . . . . . . . 5
5. Per-User M and N . . . . . . . . . . . . . . . . . . . . . . 6
6. Ciphersuites . . . . . . . . . . . . . . . . . . . . . . . . 6
7. Security Considerations . . . . . . . . . . . . . . . . . . . 9
8. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 9
9. Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . 9
10. References . . . . . . . . . . . . . . . . . . . . . . . . . 10
Appendix A. Algorithm used for Point Generation . . . . . . . . 12
Appendix B. Test Vectors . . . . . . . . . . . . . . . . . . . . 13
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 16
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.This document represents the consensus of the Crypto Forum
Research Group (CFRG).
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 gap 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 [SEC1] uncompressed or compressed for elliptic curve groups
or big endian integers of a fixed (per-group) length for prime field
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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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