Hashing to Elliptic Curves
draft-irtf-cfrg-hash-to-curve-07

Document Type Active Internet-Draft (cfrg RG)
Last updated 2020-04-27
Replaces draft-sullivan-cfrg-hash-to-curve
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CFRG                                                    A. Faz-Hernandez
Internet-Draft                                                Cloudflare
Intended status: Informational                                  S. Scott
Expires: 29 October 2020                                    Cornell Tech
                                                             N. Sullivan
                                                              Cloudflare
                                                              R.S. Wahby
                                                     Stanford University
                                                               C.A. Wood
                                                              Cloudflare
                                                           27 April 2020

                       Hashing to Elliptic Curves
                    draft-irtf-cfrg-hash-to-curve-07

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

   This Internet-Draft will expire on 29 October 2020.

Copyright Notice

   Copyright (c) 2020 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 to this document.  Code Components

Faz-Hernandez, et al.    Expires 29 October 2020                [Page 1]
Internet-Draft                hash-to-curve                   April 2020

   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  . . . . . . . . . . . . . . . . . . . . . . . .   5
     1.1.  Requirements  . . . . . . . . . . . . . . . . . . . . . .   5
   2.  Background  . . . . . . . . . . . . . . . . . . . . . . . . .   5
     2.1.  Elliptic curves . . . . . . . . . . . . . . . . . . . . .   6
     2.2.  Terminology . . . . . . . . . . . . . . . . . . . . . . .   7
       2.2.1.  Mappings  . . . . . . . . . . . . . . . . . . . . . .   7
       2.2.2.  Encodings . . . . . . . . . . . . . . . . . . . . . .   8
       2.2.3.  Random oracle encodings . . . . . . . . . . . . . . .   8
       2.2.4.  Serialization . . . . . . . . . . . . . . . . . . . .   9
       2.2.5.  Domain separation . . . . . . . . . . . . . . . . . .   9
   3.  Encoding byte strings to elliptic curves  . . . . . . . . . .  10
     3.1.  Domain separation requirements  . . . . . . . . . . . . .  11
   4.  Utility Functions . . . . . . . . . . . . . . . . . . . . . .  12
     4.1.  The sgn0 function . . . . . . . . . . . . . . . . . . . .  14
   5.  Hashing to a Finite Field . . . . . . . . . . . . . . . . . .  15
     5.1.  Security considerations . . . . . . . . . . . . . . . . .  16
     5.2.  hash_to_field implementation  . . . . . . . . . . . . . .  16
     5.3.  expand_message  . . . . . . . . . . . . . . . . . . . . .  17
       5.3.1.  expand_message_xmd  . . . . . . . . . . . . . . . . .  18
       5.3.2.  expand_message_xof  . . . . . . . . . . . . . . . . .  20
       5.3.3.  Using DSTs longer than 255 bytes  . . . . . . . . . .  20
       5.3.4.  Defining other expand_message variants  . . . . . . .  21
   6.  Deterministic Mappings  . . . . . . . . . . . . . . . . . . .  22
     6.1.  Choosing a mapping function . . . . . . . . . . . . . . .  22
     6.2.  Interface . . . . . . . . . . . . . . . . . . . . . . . .  22
     6.3.  Notation  . . . . . . . . . . . . . . . . . . . . . . . .  23
     6.4.  Sign of the resulting point . . . . . . . . . . . . . . .  23
     6.5.  Exceptional cases . . . . . . . . . . . . . . . . . . . .  23
     6.6.  Mappings for Weierstrass curves . . . . . . . . . . . . .  24
       6.6.1.  Shallue-van de Woestijne Method . . . . . . . . . . .  24
       6.6.2.  Simplified Shallue-van de Woestijne-Ulas Method . . .  26
       6.6.3.  Simplified SWU for AB == 0  . . . . . . . . . . . . .  28
     6.7.  Mappings for Montgomery curves  . . . . . . . . . . . . .  29
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