Alternative Elliptic Curve Representations
draft-ietf-lwig-curve-representations-08

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lwig                                                           R. Struik
Internet-Draft                               Struik Security Consultancy
Intended status: Informational                             July 24, 2019
Expires: January 25, 2020

               Alternative Elliptic Curve Representations
                draft-ietf-lwig-curve-representations-08

Abstract

   This document specifies how to represent Montgomery curves and
   (twisted) Edwards curves as curves in short-Weierstrass form and
   illustrates how this can be used to carry out elliptic curve
   computations using existing implementations of, e.g., ECDSA and ECDH
   using NIST prime curves.

Requirements Language

   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 RFC
   2119 [RFC2119].

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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   material or to cite them other than as "work in progress."

   This Internet-Draft will expire on January 25, 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

Struik                  Expires January 25, 2020                [Page 1]
Internet-Draft         lwig-curve-representations              July 2019

   (https://trustee.ietf.org/license-info) in effect on the date of
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   described in the Simplified BSD License.

Table of Contents

   1.  Fostering Code Reuse with New Elliptic Curves . . . . . . . .   4
   2.  Specification of Wei25519 . . . . . . . . . . . . . . . . . .   4
   3.  Use of Representation Switches  . . . . . . . . . . . . . . .   5
   4.  Examples  . . . . . . . . . . . . . . . . . . . . . . . . . .   6
     4.1.  Implementation of X25519  . . . . . . . . . . . . . . . .   6
     4.2.  Implementation of Ed25519 . . . . . . . . . . . . . . . .   6
     4.3.  Specification of ECDSA25519 . . . . . . . . . . . . . . .   7
     4.4.  Other Uses  . . . . . . . . . . . . . . . . . . . . . . .   7
   5.  Caveats . . . . . . . . . . . . . . . . . . . . . . . . . . .   7
   6.  Implementation Considerations . . . . . . . . . . . . . . . .   9
   7.  Implementation Status . . . . . . . . . . . . . . . . . . . .  10
   8.  Security Considerations . . . . . . . . . . . . . . . . . . .  11
   9.  Privacy Considerations  . . . . . . . . . . . . . . . . . . .  12
   10. IANA Considerations . . . . . . . . . . . . . . . . . . . . .  12
     10.1.  COSE Elliptic Curves Registration  . . . . . . . . . . .  12
     10.2.  COSE Algorithms Registration (1/2) . . . . . . . . . . .  12
     10.3.  COSE Algorithms Registration (2/2) . . . . . . . . . . .  13
     10.4.  JOSE Elliptic Curves Registration  . . . . . . . . . . .  13
     10.5.  JOSE Algorithms Registration (1/2) . . . . . . . . . . .  13
     10.6.  JOSE Algorithms Registration (2/2) . . . . . . . . . . .  14
   11. Acknowledgements  . . . . . . . . . . . . . . . . . . . . . .  14
   12. References  . . . . . . . . . . . . . . . . . . . . . . . . .  14
     12.1.  Normative References . . . . . . . . . . . . . . . . . .  14
     12.2.  Informative References . . . . . . . . . . . . . . . . .  16
   Appendix A.  Some (non-Binary) Elliptic Curves  . . . . . . . . .  17
     A.1.  Curves in short-Weierstrass Form  . . . . . . . . . . . .  17
     A.2.  Montgomery Curves . . . . . . . . . . . . . . . . . . . .  18
     A.3.  Twisted Edwards Curves  . . . . . . . . . . . . . . . . .  18
   Appendix B.  Elliptic Curve Nomenclature and Finite Fields  . . .  18
     B.1.  Elliptic Curve Nomenclature . . . . . . . . . . . . . . .  18
     B.2.  Finite Fields . . . . . . . . . . . . . . . . . . . . . .  20
   Appendix C.  Elliptic Curve Group Operations  . . . . . . . . . .  21
     C.1.  Group Law for Weierstrass Curves  . . . . . . . . . . . .  21
     C.2.  Group Law for Montgomery Curves . . . . . . . . . . . . .  22