Hashing to Elliptic Curves
draft-irtf-cfrg-hash-to-curve-02

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Network Working Group                                           S. Scott
Internet-Draft                                              Cornell Tech
Intended status: Informational                               N. Sullivan
Expires: April 25, 2019                                       Cloudflare
                                                                 C. Wood
                                                              Apple Inc.
                                                        October 22, 2018

                       Hashing to Elliptic Curves
                  draft-irtf-cfrg-hash-to-curve-02

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 April 25, 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 April 25, 2019                 [Page 1]
Internet-Draft                hash-to-curve                 October 2018

Table of Contents

   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   3
     1.1.  Requirements  . . . . . . . . . . . . . . . . . . . . . .   3
   2.  Background  . . . . . . . . . . . . . . . . . . . . . . . . .   3
     2.1.  Terminology . . . . . . . . . . . . . . . . . . . . . . .   4
       2.1.1.  Encoding  . . . . . . . . . . . . . . . . . . . . . .   4
       2.1.2.  Serialization . . . . . . . . . . . . . . . . . . . .   5
       2.1.3.  Random Oracle . . . . . . . . . . . . . . . . . . . .   5
   3.  Algorithm Recommendations . . . . . . . . . . . . . . . . . .   6
   4.  Utility Functions . . . . . . . . . . . . . . . . . . . . . .   6
   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 . . . . . . . . . . . . . . . .  11
       5.2.4.  Elligator2 Method . . . . . . . . . . . . . . . . . .  12
     5.3.  Cost Comparison . . . . . . . . . . . . . . . . . . . . .  14
   6.  Random Oracles  . . . . . . . . . . . . . . . . . . . . . . .  14
     6.1.  Interface . . . . . . . . . . . . . . . . . . . . . . . .  14
     6.2.  General Construction (FFSTV13)  . . . . . . . . . . . . .  14
   7.  Curve Transformations . . . . . . . . . . . . . . . . . . . .  15
   8.  Ciphersuites  . . . . . . . . . . . . . . . . . . . . . . . .  15
   9.  IANA Considerations . . . . . . . . . . . . . . . . . . . . .  17
   10. Security Considerations . . . . . . . . . . . . . . . . . . .  17
   11. Acknowledgements  . . . . . . . . . . . . . . . . . . . . . .  17
   12. Contributors  . . . . . . . . . . . . . . . . . . . . . . . .  17
   13. Normative References  . . . . . . . . . . . . . . . . . . . .  17
   Appendix A.  Related Work . . . . . . . . . . . . . . . . . . . .  19
     A.1.  Probabilistic Encoding  . . . . . . . . . . . . . . . . .  20
     A.2.  Naive Encoding  . . . . . . . . . . . . . . . . . . . . .  20
     A.3.  Deterministic Encoding  . . . . . . . . . . . . . . . . .  21
     A.4.  Supersingular Curves  . . . . . . . . . . . . . . . . . .  21
     A.5.  Twisted Variants  . . . . . . . . . . . . . . . . . . . .  21
   Appendix B.  Try-and-Increment Method . . . . . . . . . . . . . .  22
   Appendix C.  Sample Code  . . . . . . . . . . . . . . . . . . . .  22
     C.1.  Icart Method  . . . . . . . . . . . . . . . . . . . . . .  22
     C.2.  Shallue-Woestijne-Ulas Method . . . . . . . . . . . . . .  23