Hashing to Elliptic Curves
draft-irtf-cfrg-hash-to-curve-03
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.
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This Internet-Draft will expire on September 12, 2019.
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Copyright (c) 2019 IETF Trust and the persons identified as the
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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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