Collective Edwards-Curve Digital Signature Algorithm
draft-ford-cfrg-cosi-00

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CFRG                                                             B. Ford
Internet-Draft                                                 N. Gailly
Intended status: Informational                                 L. Gasser
Expires: January 1, 2018                                    P. Jovanovic
                                                                    EPFL
                                                           June 30, 2017

          Collective Edwards-Curve Digital Signature Algorithm
                        draft-ford-cfrg-cosi-00

Abstract

   Collective signatures are compact cryptographic proofs showing that
   several distinct secret key holders, called cosigners, have
   cooperated to sign a given message.  This document describes a
   collective signature extension to the EdDSA signing schemes for the
   Ed25519 and Ed448 elliptic curves.  A collective EdDSA signature
   consists of a point R, a scalar s, and a bitmask Z indicating the
   specific subset of a known group of cosigners that produced this
   signature.  A collective signature produced by n cosigners is of size
   64+ceil(n/8) bytes for Ed25519 and 114+ceil(n/8) bytes for Ed448,
   respectively, instead of 64n and 114n bytes for n individual
   signatures.  Further, collective signature verification requires only
   one double scalar multiplication rather than n.  The verifier learns
   exactly which subset of the cosigners participated, enabling the
   verifier to implement flexible acceptance-threshold policies, and
   preserving transparency and accountability in the event a bad message
   is collectively signed.

Status of This Memo

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   This Internet-Draft will expire on January 1, 2018.

Ford, et al.             Expires January 1, 2018                [Page 1]
Internet-Draft         Collective EdDSA Signatures             June 2017

Copyright Notice

   Copyright (c) 2017 IETF Trust and the persons identified as the
   document authors.  All rights reserved.

   This document is subject to BCP 78 and the IETF Trust's Legal
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Table of Contents

   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   3
   2.  Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . .   4
   3.  Notations and Conventions . . . . . . . . . . . . . . . . . .   4
   4.  Collective Signing  . . . . . . . . . . . . . . . . . . . . .   5
     4.1.  Collective Public Key Setup . . . . . . . . . . . . . . .   5
     4.2.  Signature Generation  . . . . . . . . . . . . . . . . . .   5
     4.3.  Signature Verification  . . . . . . . . . . . . . . . . .   6
   5.  Collective Signing Protocol . . . . . . . . . . . . . . . . .   7
     5.1.  Collective Signature  . . . . . . . . . . . . . . . . . .   7
       5.1.1.  Announcement  . . . . . . . . . . . . . . . . . . . .   7
       5.1.2.  Commitment  . . . . . . . . . . . . . . . . . . . . .   7
       5.1.3.  Challenge . . . . . . . . . . . . . . . . . . . . . .   8
       5.1.4.  Response  . . . . . . . . . . . . . . . . . . . . . .   8
       5.1.5.  Signature Generation  . . . . . . . . . . . . . . . .   8
     5.2.  Collective Verification . . . . . . . . . . . . . . . . .   8
   6.  Tree-based CoSi Protocol  . . . . . . . . . . . . . . . . . .   8
     6.1.  CoSi Tree . . . . . . . . . . . . . . . . . . . . . . . .   9
     6.2.  Collective Signature  . . . . . . . . . . . . . . . . . .   9
       6.2.1.  Announcement  . . . . . . . . . . . . . . . . . . . .   9
       6.2.2.  Commitment  . . . . . . . . . . . . . . . . . . . . .   9
       6.2.3.  Challenge . . . . . . . . . . . . . . . . . . . . . .  10
       6.2.4.  Response  . . . . . . . . . . . . . . . . . . . . . .  10
       6.2.5.  Signature Generation  . . . . . . . . . . . . . . . .  11
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