Hashing to Elliptic Curves
draft-irtf-cfrg-hash-to-curve-04

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Network Working Group                                   A. Faz-Hernandez
Internet-Draft                                                Cloudflare
Intended status: Informational                                  S. Scott
Expires: January 9, 2020                                    Cornell Tech
                                                             N. Sullivan
                                                              Cloudflare
                                                                R. Wahby
                                                     Stanford University
                                                                 C. Wood
                                                              Apple Inc.
                                                           July 08, 2019

                       Hashing to Elliptic Curves
                    draft-irtf-cfrg-hash-to-curve-04

Abstract

   This document specifies a number of algorithms that may be used to
   encode or hash an arbitrary string to a point on an elliptic curve.

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
   Task Force (IETF).  Note that other groups may also distribute
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   Drafts is at https://datatracker.ietf.org/drafts/current/.

   Internet-Drafts are draft documents valid for a maximum of six months
   and may be updated, replaced, or obsoleted by other documents at any
   time.  It is inappropriate to use Internet-Drafts as reference
   material or to cite them other than as "work in progress."

   This Internet-Draft will expire on January 9, 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

Faz-Hernandez, et al.    Expires January 9, 2020                [Page 1]
Internet-Draft                hash-to-curve                    July 2019

   to this document.  Code Components extracted from this document must
   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.

Table of Contents

   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   3
     1.1.  Requirements  . . . . . . . . . . . . . . . . . . . . . .   4
   2.  Background  . . . . . . . . . . . . . . . . . . . . . . . . .   4
     2.1.  Elliptic curves . . . . . . . . . . . . . . . . . . . . .   4
     2.2.  Terminology . . . . . . . . . . . . . . . . . . . . . . .   5
       2.2.1.  Mappings  . . . . . . . . . . . . . . . . . . . . . .   5
       2.2.2.  Encodings . . . . . . . . . . . . . . . . . . . . . .   6
       2.2.3.  Random oracle encodings . . . . . . . . . . . . . . .   6
       2.2.4.  Serialization . . . . . . . . . . . . . . . . . . . .   7
       2.2.5.  Domain separation . . . . . . . . . . . . . . . . . .   7
   3.  Roadmap . . . . . . . . . . . . . . . . . . . . . . . . . . .   8
     3.1.  Domain separation requirements  . . . . . . . . . . . . .   9
   4.  Utility Functions . . . . . . . . . . . . . . . . . . . . . .  10
   5.  Hashing to a Finite Field . . . . . . . . . . . . . . . . . .  13
     5.1.  Security considerations . . . . . . . . . . . . . . . . .  13
     5.2.  Performance considerations  . . . . . . . . . . . . . . .  14
     5.3.  Implementation  . . . . . . . . . . . . . . . . . . . . .  15
   6.  Deterministic Mappings  . . . . . . . . . . . . . . . . . . .  16
     6.1.  Interface . . . . . . . . . . . . . . . . . . . . . . . .  16
     6.2.  Notation  . . . . . . . . . . . . . . . . . . . . . . . .  16
     6.3.  Sign of the resulting point . . . . . . . . . . . . . . .  16
     6.4.  Exceptional cases . . . . . . . . . . . . . . . . . . . .  17
     6.5.  Mappings for Weierstrass curves . . . . . . . . . . . . .  17
       6.5.1.  Icart Method  . . . . . . . . . . . . . . . . . . . .  17
       6.5.2.  Simplified Shallue-van de Woestijne-Ulas Method . . .  18
     6.6.  Mappings for Montgomery curves  . . . . . . . . . . . . .  20
       6.6.1.  Elligator 2 Method  . . . . . . . . . . . . . . . . .  21
     6.7.  Mappings for Twisted Edwards curves . . . . . . . . . . .  23
       6.7.1.  Rational maps from Montgomery to twisted Edwards
               curves  . . . . . . . . . . . . . . . . . . . . . . .  23
       6.7.2.  Elligator 2 Method  . . . . . . . . . . . . . . . . .  25
     6.8.  Mappings for Supersingular curves . . . . . . . . . . . .  25
       6.8.1.  Boneh-Franklin Method . . . . . . . . . . . . . . . .  25