EdDSA and Ed25519
draft-josefsson-eddsa-ed25519-02

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Network Working Group                                       S. Josefsson
Internet-Draft                                                    SJD AB
Intended status: Informational                                N. Moeller
Expires: August 26, 2015
                                                       February 22, 2015

                           EdDSA and Ed25519
                    draft-josefsson-eddsa-ed25519-02

Abstract

   The elliptic curve signature scheme EdDSA and one instance of it
   called Ed25519 is described.  An example implementation and test
   vectors are provided.

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   Copyright (c) 2015 IETF Trust and the persons identified as the
   document authors.  All rights reserved.

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Table of Contents

   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   2
   2.  Notation  . . . . . . . . . . . . . . . . . . . . . . . . . .   3
   3.  Background  . . . . . . . . . . . . . . . . . . . . . . . . .   3
   4.  EdDSA . . . . . . . . . . . . . . . . . . . . . . . . . . . .   4
     4.1.  Encoding  . . . . . . . . . . . . . . . . . . . . . . . .   4
     4.2.  Keys  . . . . . . . . . . . . . . . . . . . . . . . . . .   5
     4.3.  Sign  . . . . . . . . . . . . . . . . . . . . . . . . . .   5
     4.4.  Verify  . . . . . . . . . . . . . . . . . . . . . . . . .   5
   5.  Ed25519 . . . . . . . . . . . . . . . . . . . . . . . . . . .   5
     5.1.  Modular arithmetic  . . . . . . . . . . . . . . . . . . .   6
     5.2.  Encoding  . . . . . . . . . . . . . . . . . . . . . . . .   6
     5.3.  Decoding  . . . . . . . . . . . . . . . . . . . . . . . .   6
     5.4.  Point addition  . . . . . . . . . . . . . . . . . . . . .   7
     5.5.  Key Generation  . . . . . . . . . . . . . . . . . . . . .   8
     5.6.  Sign  . . . . . . . . . . . . . . . . . . . . . . . . . .   8
     5.7.  Verify  . . . . . . . . . . . . . . . . . . . . . . . . .   9
     5.8.  Python illustration . . . . . . . . . . . . . . . . . . .   9
   6.  Test Vectors for Ed25519  . . . . . . . . . . . . . . . . . .  14
   7.  Acknowledgements  . . . . . . . . . . . . . . . . . . . . . .  17
   8.  IANA Considerations . . . . . . . . . . . . . . . . . . . . .  18
   9.  Security Considerations . . . . . . . . . . . . . . . . . . .  18
     9.1.  Side-channel leaks  . . . . . . . . . . . . . . . . . . .  18
   10. References  . . . . . . . . . . . . . . . . . . . . . . . . .  18
     10.1.  Normative References . . . . . . . . . . . . . . . . . .  18
     10.2.  Informative References . . . . . . . . . . . . . . . . .  18
   Appendix A.  Ed25519 Python Library . . . . . . . . . . . . . . .  19
   Appendix B.  Library driver . . . . . . . . . . . . . . . . . . .  23
   Authors' Addresses  . . . . . . . . . . . . . . . . . . . . . . .  24

1.  Introduction

   The Edwards-curve Digital Signature Algorithm (EdDSA) is a variant of
   Schnorr's signature system with Twisted Edwards curves.  EdDSA needs
   to be instantiated with certain parameters and this document describe
   Ed25519 - an instantiation of EdDSA in a curve over GF(2^255-19).  To
   facilitate adoption in the Internet community of Ed25519, this
   document describe the signature scheme in an implementation-oriented
   way, and we provide sample code and test vectors.

   The advantages with EdDSA and Ed25519 include:

   1.  High-performance on a variety of platforms.

   2.  Does not require the use of a unique random number for each
       signature.

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