Hashing to Elliptic Curves
draft-irtf-cfrg-hash-to-curve-07
CFRG A. Faz-Hernandez
Internet-Draft Cloudflare
Intended status: Informational S. Scott
Expires: 29 October 2020 Cornell Tech
N. Sullivan
Cloudflare
R.S. Wahby
Stanford University
C.A. Wood
Cloudflare
27 April 2020
Hashing to Elliptic Curves
draft-irtf-cfrg-hash-to-curve-07
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 29 October 2020.
Copyright Notice
Copyright (c) 2020 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/
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Please review these documents carefully, as they describe your rights
and restrictions with respect to this document. Code Components
Faz-Hernandez, et al. Expires 29 October 2020 [Page 1]
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Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 5
1.1. Requirements . . . . . . . . . . . . . . . . . . . . . . 5
2. Background . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1. Elliptic curves . . . . . . . . . . . . . . . . . . . . . 6
2.2. Terminology . . . . . . . . . . . . . . . . . . . . . . . 7
2.2.1. Mappings . . . . . . . . . . . . . . . . . . . . . . 7
2.2.2. Encodings . . . . . . . . . . . . . . . . . . . . . . 8
2.2.3. Random oracle encodings . . . . . . . . . . . . . . . 8
2.2.4. Serialization . . . . . . . . . . . . . . . . . . . . 9
2.2.5. Domain separation . . . . . . . . . . . . . . . . . . 9
3. Encoding byte strings to elliptic curves . . . . . . . . . . 10
3.1. Domain separation requirements . . . . . . . . . . . . . 11
4. Utility Functions . . . . . . . . . . . . . . . . . . . . . . 12
4.1. The sgn0 function . . . . . . . . . . . . . . . . . . . . 14
5. Hashing to a Finite Field . . . . . . . . . . . . . . . . . . 15
5.1. Security considerations . . . . . . . . . . . . . . . . . 16
5.2. hash_to_field implementation . . . . . . . . . . . . . . 16
5.3. expand_message . . . . . . . . . . . . . . . . . . . . . 17
5.3.1. expand_message_xmd . . . . . . . . . . . . . . . . . 18
5.3.2. expand_message_xof . . . . . . . . . . . . . . . . . 20
5.3.3. Using DSTs longer than 255 bytes . . . . . . . . . . 20
5.3.4. Defining other expand_message variants . . . . . . . 21
6. Deterministic Mappings . . . . . . . . . . . . . . . . . . . 22
6.1. Choosing a mapping function . . . . . . . . . . . . . . . 22
6.2. Interface . . . . . . . . . . . . . . . . . . . . . . . . 22
6.3. Notation . . . . . . . . . . . . . . . . . . . . . . . . 23
6.4. Sign of the resulting point . . . . . . . . . . . . . . . 23
6.5. Exceptional cases . . . . . . . . . . . . . . . . . . . . 23
6.6. Mappings for Weierstrass curves . . . . . . . . . . . . . 24
6.6.1. Shallue-van de Woestijne Method . . . . . . . . . . . 24
6.6.2. Simplified Shallue-van de Woestijne-Ulas Method . . . 26
6.6.3. Simplified SWU for AB == 0 . . . . . . . . . . . . . 28
6.7. Mappings for Montgomery curves . . . . . . . . . . . . . 29
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