Edwards-curve Digital Signature Algorithm (EdDSA)
draft-irtf-cfrg-eddsa-08

Document Type Active Internet-Draft (cfrg RG)
Last updated 2017-01-18 (latest revision 2016-08-19)
Replaces draft-josefsson-eddsa-ed25519
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Network Working Group                                       S. Josefsson
Internet-Draft                                                    SJD AB
Intended status: Informational                              I. Liusvaara
Expires: February 20, 2017                                   Independent
                                                         August 19, 2016

           Edwards-curve Digital Signature Algorithm (EdDSA)
                        draft-irtf-cfrg-eddsa-08

Abstract

   The elliptic curve signature scheme Edwards-curve Digital Signature
   Algorithm (EdDSA) is described.  The algorithm is instantiated with
   recommended parameters for the edwards25519 and edwards448 curves.
   An example implementation and test vectors are provided.

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   Copyright (c) 2016 IETF Trust and the persons identified as the
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Josefsson & Liusvaara   Expires February 20, 2017               [Page 1]
Internet-Draft          EdDSA: Ed25519 and Ed448             August 2016

Table of Contents

   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   3
   2.  Notation and Conventions  . . . . . . . . . . . . . . . . . .   4
   3.  EdDSA Algorithm . . . . . . . . . . . . . . . . . . . . . . .   5
     3.1.  Encoding  . . . . . . . . . . . . . . . . . . . . . . . .   7
     3.2.  Keys  . . . . . . . . . . . . . . . . . . . . . . . . . .   7
     3.3.  Sign  . . . . . . . . . . . . . . . . . . . . . . . . . .   7
     3.4.  Verify  . . . . . . . . . . . . . . . . . . . . . . . . .   8
   4.  PureEdDSA, HashEdDSA, and Naming  . . . . . . . . . . . . . .   8
   5.  EdDSA Instances . . . . . . . . . . . . . . . . . . . . . . .   8
     5.1.  Ed25519ph, Ed25519ctx and Ed25519 . . . . . . . . . . . .   9
       5.1.1.  Modular arithmetic  . . . . . . . . . . . . . . . . .  10
       5.1.2.  Encoding  . . . . . . . . . . . . . . . . . . . . . .  10
       5.1.3.  Decoding  . . . . . . . . . . . . . . . . . . . . . .  11
       5.1.4.  Point addition  . . . . . . . . . . . . . . . . . . .  11
       5.1.5.  Key Generation  . . . . . . . . . . . . . . . . . . .  12
       5.1.6.  Sign  . . . . . . . . . . . . . . . . . . . . . . . .  13
       5.1.7.  Verify  . . . . . . . . . . . . . . . . . . . . . . .  14
     5.2.  Ed448ph and Ed448 . . . . . . . . . . . . . . . . . . . .  14
       5.2.1.  Modular arithmetic  . . . . . . . . . . . . . . . . .  16
       5.2.2.  Encoding  . . . . . . . . . . . . . . . . . . . . . .  16
       5.2.3.  Decoding  . . . . . . . . . . . . . . . . . . . . . .  16
       5.2.4.  Point addition  . . . . . . . . . . . . . . . . . . .  17
       5.2.5.  Key Generation  . . . . . . . . . . . . . . . . . . .  18
       5.2.6.  Sign  . . . . . . . . . . . . . . . . . . . . . . . .  18
       5.2.7.  Verify  . . . . . . . . . . . . . . . . . . . . . . .  19
   6.  Ed25519 Python illustration . . . . . . . . . . . . . . . . .  19
   7.  Test Vectors  . . . . . . . . . . . . . . . . . . . . . . . .  24
     7.1.  Test Vectors for Ed25519  . . . . . . . . . . . . . . . .  24
     7.2.  Test Vectors for Ed25519ctx . . . . . . . . . . . . . . .  28
     7.3.  Test Vectors for Ed25519ph  . . . . . . . . . . . . . . .  30
     7.4.  Test Vectors for Ed448  . . . . . . . . . . . . . . . . .  30
     7.5.  Test Vectors for Ed448ph  . . . . . . . . . . . . . . . .  38
   8.  Acknowledgements  . . . . . . . . . . . . . . . . . . . . . .  39
   9.  IANA Considerations . . . . . . . . . . . . . . . . . . . . .  39
   10. Security Considerations . . . . . . . . . . . . . . . . . . .  39
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