Hashing to Elliptic Curves
draft-irtf-cfrg-hash-to-curve-01

Document Type Active Internet-Draft (cfrg RG)
Last updated 2018-07-02
Replaces draft-sullivan-cfrg-hash-to-curve
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Network Working Group                                           S. Scott
Internet-Draft                                              Cornell Tech
Intended status: Informational                               N. Sullivan
Expires: January 3, 2019                                      Cloudflare
                                                                 C. Wood
                                                              Apple Inc.
                                                           July 02, 2018

                       Hashing to Elliptic Curves
                  draft-irtf-cfrg-hash-to-curve-01

Abstract

   This document specifies a number of algorithms that may be used to
   hash arbitrary strings to Elliptic Curves.

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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   This Internet-Draft will expire on January 3, 2019.

Copyright Notice

   Copyright (c) 2018 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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   described in the Simplified BSD License.

Scott, et al.            Expires January 3, 2019                [Page 1]
Internet-Draft                hash-to-curve                    July 2018

Table of Contents

   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   2
     1.1.  Requirements  . . . . . . . . . . . . . . . . . . . . . .   3
   2.  Background  . . . . . . . . . . . . . . . . . . . . . . . . .   3
     2.1.  Terminology . . . . . . . . . . . . . . . . . . . . . . .   4
       2.1.1.  Encoding  . . . . . . . . . . . . . . . . . . . . . .   5
       2.1.2.  Serialization . . . . . . . . . . . . . . . . . . . .   5
       2.1.3.  Random Oracle . . . . . . . . . . . . . . . . . . . .   5
   3.  Algorithm Recommendations . . . . . . . . . . . . . . . . . .   6
   4.  Utility Functions . . . . . . . . . . . . . . . . . . . . . .   7
   5.  Deterministic Encodings . . . . . . . . . . . . . . . . . . .   7
     5.1.  Interface . . . . . . . . . . . . . . . . . . . . . . . .   7
     5.2.  Encoding Variants . . . . . . . . . . . . . . . . . . . .   7
       5.2.1.  Icart Method  . . . . . . . . . . . . . . . . . . . .   7
       5.2.2.  Shallue-Woestijne-Ulas Method . . . . . . . . . . . .   9
       5.2.3.  Simplified SWU Method . . . . . . . . . . . . . . . .  10
       5.2.4.  Elligator2 Method . . . . . . . . . . . . . . . . . .  12
     5.3.  Cost Comparison . . . . . . . . . . . . . . . . . . . . .  13
   6.  Random Oracles  . . . . . . . . . . . . . . . . . . . . . . .  14
     6.1.  Interface . . . . . . . . . . . . . . . . . . . . . . . .  14
     6.2.  General Construction (FFSTV13)  . . . . . . . . . . . . .  14
   7.  Curve Transformations . . . . . . . . . . . . . . . . . . . .  14
   8.  IANA Considerations . . . . . . . . . . . . . . . . . . . . .  15
   9.  Security Considerations . . . . . . . . . . . . . . . . . . .  15
   10. Acknowledgements  . . . . . . . . . . . . . . . . . . . . . .  15
   11. Contributors  . . . . . . . . . . . . . . . . . . . . . . . .  15
   12. Normative References  . . . . . . . . . . . . . . . . . . . .  15
   Appendix A.  Related Work . . . . . . . . . . . . . . . . . . . .  17
     A.1.  Probabilistic Encoding  . . . . . . . . . . . . . . . . .  17
     A.2.  Naive Encoding  . . . . . . . . . . . . . . . . . . . . .  17
     A.3.  Deterministic Encoding  . . . . . . . . . . . . . . . . .  18
     A.4.  Supersingular Curves  . . . . . . . . . . . . . . . . . .  18
     A.5.  Twisted Variants  . . . . . . . . . . . . . . . . . . . .  18
   Appendix B.  Try-and-Increment Method . . . . . . . . . . . . . .  19
   Appendix C.  Sample Code  . . . . . . . . . . . . . . . . . . . .  19
     C.1.  Icart Method  . . . . . . . . . . . . . . . . . . . . . .  19
     C.2.  Shallue-Woestijne-Ulas Method . . . . . . . . . . . . . .  21
     C.3.  Simplified SWU Method . . . . . . . . . . . . . . . . . .  23
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