Hashing to Elliptic Curves
draft-irtf-cfrg-hash-to-curve-05
Network Working Group A. Faz-Hernandez
Internet-Draft Cloudflare
Intended status: Informational S. Scott
Expires: May 5, 2020 Cornell Tech
N. Sullivan
Cloudflare
R. Wahby
Stanford University
C. Wood
Apple Inc.
November 02, 2019
Hashing to Elliptic Curves
draft-irtf-cfrg-hash-to-curve-05
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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This Internet-Draft will expire on May 5, 2020.
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
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Internet-Draft hash-to-curve November 2019
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Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 4
1.1. How to use this document . . . . . . . . . . . . . . . . 4
1.2. Requirements . . . . . . . . . . . . . . . . . . . . . . 5
2. Background . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1. Elliptic curves . . . . . . . . . . . . . . . . . . . . . 5
2.2. Terminology . . . . . . . . . . . . . . . . . . . . . . . 6
2.2.1. Mappings . . . . . . . . . . . . . . . . . . . . . . 6
2.2.2. Encodings . . . . . . . . . . . . . . . . . . . . . . 7
2.2.3. Random oracle encodings . . . . . . . . . . . . . . . 7
2.2.4. Serialization . . . . . . . . . . . . . . . . . . . . 8
2.2.5. Domain separation . . . . . . . . . . . . . . . . . . 8
3. Roadmap . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3.1. Domain separation requirements . . . . . . . . . . . . . 10
4. Utility Functions . . . . . . . . . . . . . . . . . . . . . . 11
4.1. sgn0 variants . . . . . . . . . . . . . . . . . . . . . . 12
4.1.1. Big endian variant . . . . . . . . . . . . . . . . . 13
4.1.2. Little endian variant . . . . . . . . . . . . . . . . 14
5. Hashing to a Finite Field . . . . . . . . . . . . . . . . . . 14
5.1. Security considerations . . . . . . . . . . . . . . . . . 15
5.2. Performance considerations . . . . . . . . . . . . . . . 16
5.3. Implementation . . . . . . . . . . . . . . . . . . . . . 16
5.4. Alternative hash_to_base functions . . . . . . . . . . . 17
6. Deterministic Mappings . . . . . . . . . . . . . . . . . . . 18
6.1. Choosing a mapping function . . . . . . . . . . . . . . . 18
6.2. Interface . . . . . . . . . . . . . . . . . . . . . . . . 19
6.3. Notation . . . . . . . . . . . . . . . . . . . . . . . . 19
6.4. Sign of the resulting point . . . . . . . . . . . . . . . 20
6.5. Exceptional cases . . . . . . . . . . . . . . . . . . . . 20
6.6. Mappings for Weierstrass curves . . . . . . . . . . . . . 20
6.6.1. Shallue-van de Woestijne Method . . . . . . . . . . . 20
6.6.2. Simplified Shallue-van de Woestijne-Ulas Method . . . 24
6.6.3. Simplified SWU for AB == 0 . . . . . . . . . . . . . 25
6.7. Mappings for Montgomery curves . . . . . . . . . . . . . 27
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