Alternative Elliptic Curve Representations
draft-ietf-lwig-curve-representations-12
lwig R. Struik
Internet-Draft Struik Security Consultancy
Intended status: Informational August 24, 2020
Expires: February 25, 2021
Alternative Elliptic Curve Representations
draft-ietf-lwig-curve-representations-12
Abstract
This document specifies how to represent Montgomery curves and
(twisted) Edwards curves as curves in short-Weierstrass form and
illustrates how this can be used to carry out elliptic curve
computations using existing implementations of, e.g., ECDSA and ECDH
using NIST prime curves. We also provide extensive background
material that may be useful for implementers of elliptic curve
cryptography.
Requirements Language
The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
"SHOULD", "SHOULD NOT", "RECOMMENDED", "NOT RECOMMENDED", "MAY", and
"OPTIONAL" in this document are to be interpreted as described in BCP
14 [RFC2119] [RFC8174] when, and only when, they appear in all
capitals, as shown here.
Status of This Memo
This Internet-Draft is submitted in full conformance with the
provisions of BCP 78 and BCP 79.
Internet-Drafts are working documents of the Internet Engineering
Task Force (IETF). Note that other groups may also distribute
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material or to cite them other than as "work in progress."
This Internet-Draft will expire on February 25, 2021.
Struik Expires February 25, 2021 [Page 1]
Internet-Draft lwig-curve-representations August 2020
Copyright Notice
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Table of Contents
1. Fostering Code Reuse with New Elliptic Curves . . . . . . . . 5
2. Specification of Wei25519 . . . . . . . . . . . . . . . . . . 6
3. Use of Representation Switches . . . . . . . . . . . . . . . 6
4. Examples . . . . . . . . . . . . . . . . . . . . . . . . . . 7
4.1. Implementation of X25519 . . . . . . . . . . . . . . . . 7
4.2. Implementation of Ed25519 . . . . . . . . . . . . . . . . 8
4.3. Specification of ECDSA25519 . . . . . . . . . . . . . . . 8
4.4. Other Uses (Wei448, ECDH448, ECDSA448, and Others) . . . 9
5. Caveats . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
5.1. Wire Format . . . . . . . . . . . . . . . . . . . . . . . 10
5.2. Representation Conventions . . . . . . . . . . . . . . . 10
5.3. Domain Parameters . . . . . . . . . . . . . . . . . . . . 10
6. Implementation Considerations . . . . . . . . . . . . . . . . 11
7. Implementation Status . . . . . . . . . . . . . . . . . . . . 12
8. Security Considerations . . . . . . . . . . . . . . . . . . . 13
9. Privacy Considerations . . . . . . . . . . . . . . . . . . . 14
10. Using Wei25519 and Wei448 with COSE and JOSE . . . . . . . . 14
10.1. Using Wei25519 and Wei448 Keys with COSE and JOSE . . . 14
10.1.1. Encoding of Short-Weierstrass Curves with COSE . . . 15
10.1.2. Encoding of Short-Weierstrass Curves with JOSE . . . 16
10.2. Using ECDSA25519 and ECDSA448 with COSE and JOSE . . . . 16
10.2.1. Encoding of ECDSA Instantiations with COSE . . . . . 17
10.2.2. Encoding of ECDSA Instantiations with JOSE . . . . . 18
10.3. Using ECDH25519 and ECDH448 with COSE and JOSE . . . . . 19
10.3.1. Encoding of co-factor ECDH with COSE . . . . . . . . 20
10.3.2. Encoding of co-factor ECDH with JOSE . . . . . . . . 20
11. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 20
11.1. IANA Considerations for Wei25519 . . . . . . . . . . . . 21
11.1.1. COSE Elliptic Curves Registration . . . . . . . . . 21
11.1.2. COSE Algorithms Registration (1/2) . . . . . . . . . 21
11.1.3. COSE Algorithms Registration (2/2) . . . . . . . . . 21
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