Threshold Modes in Elliptic Curves
draft-hallambaker-threshold-03

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Network Working Group                                 P. M. Hallam-Baker
Internet-Draft                                      ThresholdSecrets.com
Intended status: Informational                         September 4, 2020
Expires: March 8, 2021

                   Threshold Modes in Elliptic Curves
                     draft-hallambaker-threshold-03

Abstract

   Threshold cryptography operation modes 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.  A
   Threshold signature scheme is described in a separate document.

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Copyright Notice

   Copyright (c) 2020 IETF Trust and the persons identified as the
   document authors.  All rights reserved.

Hallam-Baker              Expires March 8, 2021                 [Page 1]
Internet-Draft     Threshold Modes in Elliptic Curves     September 2020

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Table of Contents

   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   3
     1.1.  Applications  . . . . . . . . . . . . . . . . . . . . . .   4
       1.1.1.  Cloud control of decryption . . . . . . . . . . . . .   4
       1.1.2.  Device Onboarding . . . . . . . . . . . . . . . . . .   5
       1.1.3.  Cryptographic co-processor  . . . . . . . . . . . . .   5
       1.1.4.  Side Channel Resistance . . . . . . . . . . . . . . .   6
   2.  Definitions . . . . . . . . . . . . . . . . . . . . . . . . .   6
     2.1.  Requirements Language . . . . . . . . . . . . . . . . . .   6
     2.2.  Defined Terms . . . . . . . . . . . . . . . . . . . . . .   6
     2.3.  Related Specifications  . . . . . . . . . . . . . . . . .   7
     2.4.  Implementation Status . . . . . . . . . . . . . . . . . .   7
   3.  Threshold Cryptography in Diffie-Hellman  . . . . . . . . . .   8
     3.1.  Application to Diffie Hellman (not normative) . . . . . .   8
     3.2.  Threshold decryption  . . . . . . . . . . . . . . . . . .   9
       3.2.1.  Direct Key Splitting  . . . . . . . . . . . . . . . .   9
       3.2.2.  Direct Decryption . . . . . . . . . . . . . . . . . .  10
     3.3.  Direct threshold key generation . . . . . . . . . . . . .  10
       3.3.1.  Device Provisioning . . . . . . . . . . . . . . . . .  11
       3.3.2.  Key Rollover  . . . . . . . . . . . . . . . . . . . .  12
       3.3.3.  Host Activation . . . . . . . . . . . . . . . . . . .  13
       3.3.4.  Separation of Duties  . . . . . . . . . . . . . . . .  13
     3.4.  Side Channel Resistance . . . . . . . . . . . . . . . . .  13
   4.  Shamir Secret Sharing . . . . . . . . . . . . . . . . . . . .  14
     4.1.  Shamir secret share generation  . . . . . . . . . . . . .  14
     4.2.  Lagrange basis recovery . . . . . . . . . . . . . . . . .  15
     4.3.  Verifiable Secret Sharing . . . . . . . . . . . . . . . .  15
     4.4.  Distributed Key Generation  . . . . . . . . . . . . . . .  16
   5.  Application to Elliptic Curves  . . . . . . . . . . . . . . .  16
     5.1.  Implementation for Ed25519 and Ed448  . . . . . . . . . .  16
       5.1.1.  Ed25519 . . . . . . . . . . . . . . . . . . . . . . .  17
       5.1.2.  Ed448 . . . . . . . . . . . . . . . . . . . . . . . .  17
     5.2.  Implementation for X25519 and X448  . . . . . . . . . . .  18
       5.2.1.  Point Encoding  . . . . . . . . . . . . . . . . . . .  18
       5.2.2.  X25519 Point Encoding . . . . . . . . . . . . . . . .  19