Hashing to Elliptic Curves
draft-irtf-cfrg-hash-to-curve-05

Document Type Active Internet-Draft (cfrg RG)
Last updated 2019-11-02
Replaces draft-sullivan-cfrg-hash-to-curve
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Network Working Group                                   A. Faz-Hernandez
Internet-Draft                                                Cloudflare
Intended status: Informational                                  S. Scott
Expires: May 5, 2020                                        Cornell Tech
                                                             N. Sullivan
                                                              Cloudflare
                                                                R. Wahby
                                                     Stanford University
                                                                 C. Wood
                                                              Apple Inc.
                                                       November 02, 2019

                       Hashing to Elliptic Curves
                    draft-irtf-cfrg-hash-to-curve-05

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.

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   This Internet-Draft will expire on May 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

Faz-Hernandez, et al.      Expires May 5, 2020                  [Page 1]
Internet-Draft                hash-to-curve                November 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  . . . . . . . . . . . . . . . . . . . . . . . .   4
     1.1.  How to use this document  . . . . . . . . . . . . . . . .   4
     1.2.  Requirements  . . . . . . . . . . . . . . . . . . . . . .   5
   2.  Background  . . . . . . . . . . . . . . . . . . . . . . . . .   5
     2.1.  Elliptic curves . . . . . . . . . . . . . . . . . . . . .   5
     2.2.  Terminology . . . . . . . . . . . . . . . . . . . . . . .   6
       2.2.1.  Mappings  . . . . . . . . . . . . . . . . . . . . . .   6
       2.2.2.  Encodings . . . . . . . . . . . . . . . . . . . . . .   7
       2.2.3.  Random oracle encodings . . . . . . . . . . . . . . .   7
       2.2.4.  Serialization . . . . . . . . . . . . . . . . . . . .   8
       2.2.5.  Domain separation . . . . . . . . . . . . . . . . . .   8
   3.  Roadmap . . . . . . . . . . . . . . . . . . . . . . . . . . .   9
     3.1.  Domain separation requirements  . . . . . . . . . . . . .  10
   4.  Utility Functions . . . . . . . . . . . . . . . . . . . . . .  11
     4.1.  sgn0 variants . . . . . . . . . . . . . . . . . . . . . .  12
       4.1.1.  Big endian variant  . . . . . . . . . . . . . . . . .  13
       4.1.2.  Little endian variant . . . . . . . . . . . . . . . .  14
   5.  Hashing to a Finite Field . . . . . . . . . . . . . . . . . .  14
     5.1.  Security considerations . . . . . . . . . . . . . . . . .  15
     5.2.  Performance considerations  . . . . . . . . . . . . . . .  16
     5.3.  Implementation  . . . . . . . . . . . . . . . . . . . . .  16
     5.4.  Alternative hash_to_base functions  . . . . . . . . . . .  17
   6.  Deterministic Mappings  . . . . . . . . . . . . . . . . . . .  18
     6.1.  Choosing a mapping function . . . . . . . . . . . . . . .  18
     6.2.  Interface . . . . . . . . . . . . . . . . . . . . . . . .  19
     6.3.  Notation  . . . . . . . . . . . . . . . . . . . . . . . .  19
     6.4.  Sign of the resulting point . . . . . . . . . . . . . . .  20
     6.5.  Exceptional cases . . . . . . . . . . . . . . . . . . . .  20
     6.6.  Mappings for Weierstrass curves . . . . . . . . . . . . .  20
       6.6.1.  Shallue-van de Woestijne Method . . . . . . . . . . .  20
       6.6.2.  Simplified Shallue-van de Woestijne-Ulas Method . . .  24
       6.6.3.  Simplified SWU for AB == 0  . . . . . . . . . . . . .  25
     6.7.  Mappings for Montgomery curves  . . . . . . . . . . . . .  27
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