Hashing to Elliptic Curves
draft-irtf-cfrg-hash-to-curve-02
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.
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This Internet-Draft will expire on April 25, 2019.
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Copyright (c) 2018 IETF Trust and the persons identified as the
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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
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