Hashing to Elliptic Curves
draft-irtf-cfrg-hash-to-curve-04
Network Working Group A. Faz-Hernandez
Internet-Draft Cloudflare
Intended status: Informational S. Scott
Expires: January 9, 2020 Cornell Tech
N. Sullivan
Cloudflare
R. Wahby
Stanford University
C. Wood
Apple Inc.
July 08, 2019
Hashing to Elliptic Curves
draft-irtf-cfrg-hash-to-curve-04
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
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Copyright (c) 2019 IETF Trust and the persons identified as the
document authors. All rights reserved.
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Internet-Draft hash-to-curve July 2019
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Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1. Requirements . . . . . . . . . . . . . . . . . . . . . . 4
2. Background . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.1. Elliptic curves . . . . . . . . . . . . . . . . . . . . . 4
2.2. Terminology . . . . . . . . . . . . . . . . . . . . . . . 5
2.2.1. Mappings . . . . . . . . . . . . . . . . . . . . . . 5
2.2.2. Encodings . . . . . . . . . . . . . . . . . . . . . . 6
2.2.3. Random oracle encodings . . . . . . . . . . . . . . . 6
2.2.4. Serialization . . . . . . . . . . . . . . . . . . . . 7
2.2.5. Domain separation . . . . . . . . . . . . . . . . . . 7
3. Roadmap . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3.1. Domain separation requirements . . . . . . . . . . . . . 9
4. Utility Functions . . . . . . . . . . . . . . . . . . . . . . 10
5. Hashing to a Finite Field . . . . . . . . . . . . . . . . . . 13
5.1. Security considerations . . . . . . . . . . . . . . . . . 13
5.2. Performance considerations . . . . . . . . . . . . . . . 14
5.3. Implementation . . . . . . . . . . . . . . . . . . . . . 15
6. Deterministic Mappings . . . . . . . . . . . . . . . . . . . 16
6.1. Interface . . . . . . . . . . . . . . . . . . . . . . . . 16
6.2. Notation . . . . . . . . . . . . . . . . . . . . . . . . 16
6.3. Sign of the resulting point . . . . . . . . . . . . . . . 16
6.4. Exceptional cases . . . . . . . . . . . . . . . . . . . . 17
6.5. Mappings for Weierstrass curves . . . . . . . . . . . . . 17
6.5.1. Icart Method . . . . . . . . . . . . . . . . . . . . 17
6.5.2. Simplified Shallue-van de Woestijne-Ulas Method . . . 18
6.6. Mappings for Montgomery curves . . . . . . . . . . . . . 20
6.6.1. Elligator 2 Method . . . . . . . . . . . . . . . . . 21
6.7. Mappings for Twisted Edwards curves . . . . . . . . . . . 23
6.7.1. Rational maps from Montgomery to twisted Edwards
curves . . . . . . . . . . . . . . . . . . . . . . . 23
6.7.2. Elligator 2 Method . . . . . . . . . . . . . . . . . 25
6.8. Mappings for Supersingular curves . . . . . . . . . . . . 25
6.8.1. Boneh-Franklin Method . . . . . . . . . . . . . . . . 25
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