Threshold Key Generation and Decryption in Ed25519 and Ed448
draft-hallambaker-threshold-00

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Network Working Group                                 P. M. Hallam-Baker
Internet-Draft                                     Venture Cryptography.
Intended status: Informational                            5 January 2020
Expires: 8 July 2020

      Threshold Key Generation and Decryption in Ed25519 and Ed448
                     draft-hallambaker-threshold-00

Abstract

   Threshold cryptography schemes are described with application to the
   Ed25519, Ed448, X25519 and X448 Elliptic Curves.  Threshold key
   generation allows generation of keypairs to be divided between two or
   more parties with verifiable security guaranties.  Threshold
   decryption allows elliptic curve key agreement to be divided between
   two or more parties such that all the parties must co-operate to
   complete a private key agreement operation.  The same primitives may
   be applied to improve resistance to side channel attacks.

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Hallam-Baker               Expires 8 July 2020                  [Page 1]
Internet-Draft   Threshold Key Generation and Decryption    January 2020

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Table of Contents

   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   3
   2.  Definitions . . . . . . . . . . . . . . . . . . . . . . . . .   3
     2.1.  Requirements Language . . . . . . . . . . . . . . . . . .   3
     2.2.  Defined Terms . . . . . . . . . . . . . . . . . . . . . .   3
     2.3.  Related Specifications  . . . . . . . . . . . . . . . . .   5
     2.4.  Implementation Status . . . . . . . . . . . . . . . . . .   5
   3.  Principles  . . . . . . . . . . . . . . . . . . . . . . . . .   5
     3.1.  Application to Diffie Hellman (not normative) . . . . . .   5
     3.2.  Threshold Decryption  . . . . . . . . . . . . . . . . . .   7
       3.2.1.  Key Splitting . . . . . . . . . . . . . . . . . . . .   7
       3.2.2.  Decryption  . . . . . . . . . . . . . . . . . . . . .   7
     3.3.  Threshold Key Generation  . . . . . . . . . . . . . . . .   8
       3.3.1.  Device Provisioning . . . . . . . . . . . . . . . . .   8
       3.3.2.  Key Rollover  . . . . . . . . . . . . . . . . . . . .   9
       3.3.3.  Host Activation . . . . . . . . . . . . . . . . . . .  10
       3.3.4.  Separation of Duties  . . . . . . . . . . . . . . . .  10
     3.4.  Side Channel Resistance . . . . . . . . . . . . . . . . .  10
   4.  Application to Elliptic Curves  . . . . . . . . . . . . . . .  11
     4.1.  Implementation for Ed25519 and Ed448  . . . . . . . . . .  11
       4.1.1.  Ed25519 . . . . . . . . . . . . . . . . . . . . . . .  12
       4.1.2.  Ed448 . . . . . . . . . . . . . . . . . . . . . . . .  12
     4.2.  Implementation for X25519 and X448  . . . . . . . . . . .  13
       4.2.1.  Point Encoding  . . . . . . . . . . . . . . . . . . .  14
       4.2.2.  X25519 Point Encoding . . . . . . . . . . . . . . . .  14
       4.2.3.  X448 Point Encoding . . . . . . . . . . . . . . . . .  14
       4.2.4.  Point Addition  . . . . . . . . . . . . . . . . . . .  14
       4.2.5.  Montgomery Ladder with Coordinate Recovery  . . . . .  15
   5.  Test Vectors  . . . . . . . . . . . . . . . . . . . . . . . .  17
     5.1.  Threshold Key Generation  . . . . . . . . . . . . . . . .  17
       5.1.1.  X25519  . . . . . . . . . . . . . . . . . . . . . . .  17
       5.1.2.  X448  . . . . . . . . . . . . . . . . . . . . . . . .  19
       5.1.3.  Ed25519 . . . . . . . . . . . . . . . . . . . . . . .  21
       5.1.4.  Ed448 . . . . . . . . . . . . . . . . . . . . . . . .  22
     5.2.  Threshold Decryption  . . . . . . . . . . . . . . . . . .  24
       5.2.1.  Key Splitting X25519  . . . . . . . . . . . . . . . .  24