Homomorphic Multiplication for X25519 and X448
draft-barnes-cfrg-mult-for-7748-00

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Network Working Group                                          R. Barnes
Internet-Draft                                                     Cisco
Updates: 7748 (if approved)                                     J. Alwen
Intended status: Informational                                     Wickr
Expires: May 7, 2020                                         S. Corretti
                                                                    IOHK
                                                       November 04, 2019

             Homomorphic Multiplication for X25519 and X448
                   draft-barnes-cfrg-mult-for-7748-00

Abstract

   In some contexts it is useful for holders of the private and public
   parts of an elliptic curve key pair to be able to independently apply
   an updates to those values, such that the resulting updated public
   key corresponds to the updated private key.  Such updates are
   straightforward for older elliptic curves, but for X25519 and X448,
   the "clamping" prescribed for scalars requires some additional
   processing.  This document defines a multiplication procedure that
   can be used to update X25519 and X448 key pairs.  This algorithm can
   fail to produce a result, but only with negligible probability.
   Failures can be detected by the holder of the private key.

Note to Readers

   Source for this draft and an issue tracker can be found at
   https://github.com/bifurcation/draft-barnes-cfrg-mult-for-7748 [1].

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Table of Contents

   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   2
   2.  Updating X25519 / X448 key pairs  . . . . . . . . . . . . . .   3
   3.  Failure Cases . . . . . . . . . . . . . . . . . . . . . . . .   4
     3.1.  X25519  . . . . . . . . . . . . . . . . . . . . . . . . .   5
     3.2.  X448  . . . . . . . . . . . . . . . . . . . . . . . . . .   5
   4.  Protocol Considerations . . . . . . . . . . . . . . . . . . .   6
   5.  Security Considerations . . . . . . . . . . . . . . . . . . .   6
   6.  IANA Considerations . . . . . . . . . . . . . . . . . . . . .   7
   7.  References  . . . . . . . . . . . . . . . . . . . . . . . . .   7
     7.1.  Normative References  . . . . . . . . . . . . . . . . . .   7
     7.2.  Informative References  . . . . . . . . . . . . . . . . .   7
     7.3.  URIs  . . . . . . . . . . . . . . . . . . . . . . . . . .   7
   Appendix A.  Test Vectors . . . . . . . . . . . . . . . . . . . .   7
     A.1.  X25519  . . . . . . . . . . . . . . . . . . . . . . . . .   8
     A.2.  X448  . . . . . . . . . . . . . . . . . . . . . . . . . .   8
   Appendix B.  Acknowledgements . . . . . . . . . . . . . . . . . .  10
   Authors' Addresses  . . . . . . . . . . . . . . . . . . . . . . .  10

1.  Introduction

   In some contexts it is useful for holders of the private and public
   parts of an elliptic curve key pair to be able to independently apply
   an updates to those values, such that the resulting updated public
   key corresponds to the updated private key.  [[ TODO: Cite examples
   (e.g.  HKD like BIP32, Tor Hidden Service Identity Blinding, MLS),
   security properties]]

   Such updates are straightforward with traditional elliptic curve
   groups, such as the NIST and Brainpool curve groups
   [NISTCurves][RFC5639], or with the proposed Ristretto groups
   [I-D.hdevalence-cfrg-ristretto].  In these groups, multiplication of

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