EdDSA and Ed25519
draft-josefsson-eddsa-ed25519-00

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Network Working Group                                       S. Josefsson
Internet-Draft                                                    SJD AB
Intended status: Informational                          February 7, 2015
Expires: August 11, 2015

                           EdDSA and Ed25519
                    draft-josefsson-eddsa-ed25519-00

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
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Table of Contents

   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   2
   2.  Notation  . . . . . . . . . . . . . . . . . . . . . . . . . .   3
   3.  EdDSA . . . . . . . . . . . . . . . . . . . . . . . . . . . .   3
     3.1.  Encoding  . . . . . . . . . . . . . . . . . . . . . . . .   3
     3.2.  Keys  . . . . . . . . . . . . . . . . . . . . . . . . . .   3
     3.3.  Sign  . . . . . . . . . . . . . . . . . . . . . . . . . .   4
     3.4.  Verify  . . . . . . . . . . . . . . . . . . . . . . . . .   4
   4.  Ed25519 . . . . . . . . . . . . . . . . . . . . . . . . . . .   4
   5.  Test Vectors for Ed25519  . . . . . . . . . . . . . . . . . .   9
   6.  Acknowledgements  . . . . . . . . . . . . . . . . . . . . . .  10
   7.  IANA Considerations . . . . . . . . . . . . . . . . . . . . .  10
   8.  Security Considerations . . . . . . . . . . . . . . . . . . .  10
   9.  References  . . . . . . . . . . . . . . . . . . . . . . . . .  10
     9.1.  Normative References  . . . . . . . . . . . . . . . . . .  10
     9.2.  Informative References  . . . . . . . . . . . . . . . . .  10
   Appendix A.  Ed25519 Python Library . . . . . . . . . . . . . . .  11
   Appendix B.  Library driver . . . . . . . . . . . . . . . . . . .  14
   Author's Address  . . . . . . . . . . . . . . . . . . . . . . . .  15

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 Ed25519 is described
   in this document.  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.

   3.  Collision resilience, meaning that hash-function collisions do
       not break this system.

   4.  More resilient to side-channel attacks.

   5.  Small public keys (32 bytes) and signatures (64 bytes).

   For further background, see the original EdDSA paper [EDDSA].

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2.  Notation

   The following notation is used throughout the document:

   GF(p) finite field with p elements

   x^y x multiplied by itself y times

   h_i the i'th byte of h

   a || b (bit-)string a concatenated with (bit-)string b

3.  EdDSA

   EdDSA has seven parameters:

   1.  an integer b >= 10.

   2.  a cryptographic hash function H producing 2b-bit outputs.

   3.  a prime power q congruent to 1 modulo 4.

   4.  a (b-1)-bit encoding of elements of the finite field GF(q).

   5.  a non-square element d of GF(q)
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