Hashing to Elliptic Curves
draft-irtf-cfrg-hash-to-curve-03
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Network Working Group S. Scott
Internet-Draft Cornell Tech
Intended status: Informational N. Sullivan
Expires: September 12, 2019 Cloudflare
C. Wood
Apple Inc.
March 11, 2019
Hashing to Elliptic Curves
draft-irtf-cfrg-hash-to-curve-03
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
working documents as Internet-Drafts. The list of current Internet-
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 September 12, 2019.
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
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.
Scott, et al. Expires September 12, 2019 [Page 1]
Internet-Draft hash-to-curve March 2019
Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1. Requirements . . . . . . . . . . . . . . . . . . . . . . 3
2. Background . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.1. Terminology . . . . . . . . . . . . . . . . . . . . . . . 5
2.1.1. Encoding . . . . . . . . . . . . . . . . . . . . . . 5
2.1.2. Serialization . . . . . . . . . . . . . . . . . . . . 5
2.1.3. Random Oracle . . . . . . . . . . . . . . . . . . . . 6
3. Algorithm Recommendations . . . . . . . . . . . . . . . . . . 6
4. Utility Functions . . . . . . . . . . . . . . . . . . . . . . 7
5. Deterministic Encodings . . . . . . . . . . . . . . . . . . . 8
5.1. Interface . . . . . . . . . . . . . . . . . . . . . . . . 8
5.2. Notation . . . . . . . . . . . . . . . . . . . . . . . . 8
5.3. Encodings for Weierstrass curves . . . . . . . . . . . . 9
5.3.1. Icart Method . . . . . . . . . . . . . . . . . . . . 9
5.3.2. Shallue-Woestijne-Ulas Method . . . . . . . . . . . . 10
5.3.3. Simplified SWU Method . . . . . . . . . . . . . . . . 13
5.3.4. Boneh-Franklin Method . . . . . . . . . . . . . . . . 14
5.3.5. Fouque-Tibouchi Method . . . . . . . . . . . . . . . 16
5.4. Encodings for Montgomery curves . . . . . . . . . . . . . 19
5.4.1. Elligator2 Method . . . . . . . . . . . . . . . . . . 19
6. Random Oracles . . . . . . . . . . . . . . . . . . . . . . . 22
6.1. Interface . . . . . . . . . . . . . . . . . . . . . . . . 22
7. Curve Transformations . . . . . . . . . . . . . . . . . . . . 22
8. Ciphersuites . . . . . . . . . . . . . . . . . . . . . . . . 22
9. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 24
10. Security Considerations . . . . . . . . . . . . . . . . . . . 25
11. Acknowledgements . . . . . . . . . . . . . . . . . . . . . . 25
12. Contributors . . . . . . . . . . . . . . . . . . . . . . . . 25
13. Normative References . . . . . . . . . . . . . . . . . . . . 25
Appendix A. Related Work . . . . . . . . . . . . . . . . . . . . 28
A.1. Probabilistic Encoding . . . . . . . . . . . . . . . . . 28
A.2. Naive Encoding . . . . . . . . . . . . . . . . . . . . . 29
A.3. Deterministic Encoding . . . . . . . . . . . . . . . . . 29
A.4. Supersingular Curves . . . . . . . . . . . . . . . . . . 30
A.5. Twisted Variants . . . . . . . . . . . . . . . . . . . . 30
Appendix B. Try-and-Increment Method . . . . . . . . . . . . . . 30
Appendix C. Sample Code . . . . . . . . . . . . . . . . . . . . 31
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