Threshold Signatures in Elliptic Curves
draft-hallambaker-threshold-sigs-05

Document Type Active Internet-Draft (individual)
Author Phillip Hallam-Baker 
Last updated 2020-11-02
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Network Working Group                                 P. M. Hallam-Baker
Internet-Draft                                      ThresholdSecrets.com
Intended status: Informational                           2 November 2020
Expires: 6 May 2021

                Threshold Signatures in Elliptic Curves
                  draft-hallambaker-threshold-sigs-05

Abstract

   A Threshold signature scheme is described.  The signatures created
   are computationally indistinguishable from those produced using the
   Ed25519 and Ed448 curves as specified in RFC8032 except in that they
   are non-deterministic.  Threshold signatures are a form of digital
   signature whose creation requires two or more parties to interact but
   does not disclose the number or identities of the parties involved.

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Copyright Notice

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

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Internet-Draft   Threshold Signatures in Elliptic Curves   November 2020

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Table of Contents

   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   3
     1.1.  Applications  . . . . . . . . . . . . . . . . . . . . . .   4
       1.1.1.  HSM Binding . . . . . . . . . . . . . . . . . . . . .   4
       1.1.2.  Code Signing  . . . . . . . . . . . . . . . . . . . .   4
       1.1.3.  Signing by Redundant Services . . . . . . . . . . . .   5
   2.  Definitions . . . . . . . . . . . . . . . . . . . . . . . . .   5
     2.1.  Requirements Language . . . . . . . . . . . . . . . . . .   5
     2.2.  Defined Terms . . . . . . . . . . . . . . . . . . . . . .   5
     2.3.  Related Specifications  . . . . . . . . . . . . . . . . .   5
     2.4.  Implementation Status . . . . . . . . . . . . . . . . . .   6
   3.  Principles  . . . . . . . . . . . . . . . . . . . . . . . . .   6
     3.1.  Direct shared threshold signature . . . . . . . . . . . .   7
     3.2.  Shamir shared threshold signature . . . . . . . . . . . .   9
     3.3.  Stateless computation of final share  . . . . . . . . . .  10
       3.3.1.  Side channel resistance . . . . . . . . . . . . . . .  11
     3.4.  Security Analysis . . . . . . . . . . . . . . . . . . . .  12
       3.4.1.  Calculation of r values . . . . . . . . . . . . . . .  12
       3.4.2.  Replay Attack . . . . . . . . . . . . . . . . . . . .  13
       3.4.3.  Malicious Contribution Attack . . . . . . . . . . . .  13
       3.4.4.  Rogue Key Attack  . . . . . . . . . . . . . . . . . .  13
   4.  Ed2519 Signature  . . . . . . . . . . . . . . . . . . . . . .  14
   5.  Ed448 Signature . . . . . . . . . . . . . . . . . . . . . . .  15
   6.  Test Vectors  . . . . . . . . . . . . . . . . . . . . . . . .  16
     6.1.  Direct Threshold Signature Ed25519  . . . . . . . . . . .  16
     6.2.  Direct Threshold Signature Ed448  . . . . . . . . . . . .  19
     6.3.  Shamir Threshold Signature Ed25519  . . . . . . . . . . .  22
     6.4.  Shamir Threshold Signature Ed448  . . . . . . . . . . . .  25
   7.  Security Considerations . . . . . . . . . . . . . . . . . . .  28
     7.1.  Rogue Key attack  . . . . . . . . . . . . . . . . . . . .  28
     7.2.  Disclosure or reuse of the value r  . . . . . . . . . . .  28
     7.3.  Resource exhaustion attack  . . . . . . . . . . . . . . .  28
     7.4.  Signature Uniqueness  . . . . . . . . . . . . . . . . . .  28
   8.  IANA Considerations . . . . . . . . . . . . . . . . . . . . .  29
   9.  Acknowledgements  . . . . . . . . . . . . . . . . . . . . . .  29
   10. Normative References  . . . . . . . . . . . . . . . . . . . .  29
   11. Informative References  . . . . . . . . . . . . . . . . . . .  29

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