Verifiable Oblivious Pseudorandom Functions (VOPRFs) in Prime-Order Groups
draft-sullivan-cfrg-voprf-02

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Network Working Group                                        A. Davidson
Internet-Draft                 ISG, Royal Holloway, University of London
Intended status: Informational                               N. Sullivan
Expires: April 25, 2019                                       Cloudflare
                                                                 C. Wood
                                                              Apple Inc.
                                                        October 22, 2018

  Verifiable Oblivious Pseudorandom Functions (VOPRFs) in Prime-Order
                                 Groups
                      draft-sullivan-cfrg-voprf-02

Abstract

   A Verifiable Oblivious Pseudorandom Function (VOPRF) is a two-party
   protocol for computing the output of a PRF that is symmetrically
   verifiable.  In summary, the PRF key holder learns nothing of the
   input while simultaneously providing proof that its private key was
   used during execution.  VOPRFs are useful for computing one-time
   unlinkable tokens that are verifiable by secret key holders.  This
   document specifies a VOPRF construction instantiated within prime-
   order subgroups, including elliptic curves.

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Davidson, et al.         Expires April 25, 2019                 [Page 1]
Internet-Draft                   VOPRFs                     October 2018

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Table of Contents

   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   2
     1.1.  Terminology . . . . . . . . . . . . . . . . . . . . . . .   3
     1.2.  Requirements  . . . . . . . . . . . . . . . . . . . . . .   4
   2.  Background  . . . . . . . . . . . . . . . . . . . . . . . . .   4
   3.  Security Properties . . . . . . . . . . . . . . . . . . . . .   4
   4.  VOPRF Protocol  . . . . . . . . . . . . . . . . . . . . . . .   5
     4.1.  Instantiations of GG  . . . . . . . . . . . . . . . . . .   6
     4.2.  Algorithmic Details . . . . . . . . . . . . . . . . . . .   7
       4.2.1.  VOPRF_Blind . . . . . . . . . . . . . . . . . . . . .   7
       4.2.2.  VOPRF_Sign  . . . . . . . . . . . . . . . . . . . . .   8
       4.2.3.  VOPRF_Unblind . . . . . . . . . . . . . . . . . . . .   8
       4.2.4.  VOPRF_Finalize  . . . . . . . . . . . . . . . . . . .   8
   5.  NIZK Discrete Logarithm Equality Proof  . . . . . . . . . . .   9
     5.1.  DLEQ_Generate . . . . . . . . . . . . . . . . . . . . . .   9
     5.2.  DLEQ_Verify . . . . . . . . . . . . . . . . . . . . . . .  10
     5.3.  Elliptic Curve Group and Hash Function Instantiations . .  10
   6.  Security Considerations . . . . . . . . . . . . . . . . . . .  12
     6.1.  Timing Leaks  . . . . . . . . . . . . . . . . . . . . . .  13
     6.2.  Hashing to curves . . . . . . . . . . . . . . . . . . . .  13
   7.  Privacy Considerations  . . . . . . . . . . . . . . . . . . .  13
     7.1.  Key Consistency . . . . . . . . . . . . . . . . . . . . .  13
   8.  Acknowledgements  . . . . . . . . . . . . . . . . . . . . . .  13
   9.  Normative References  . . . . . . . . . . . . . . . . . . . .  13
   Appendix A.  Test Vectors . . . . . . . . . . . . . . . . . . . .  15
   Appendix B.  Applications . . . . . . . . . . . . . . . . . . . .  17
     B.1.  Privacy Pass  . . . . . . . . . . . . . . . . . . . . . .  17
     B.2.  Private Password Checker  . . . . . . . . . . . . . . . .  18
       B.2.1.  Parameter Commitments . . . . . . . . . . . . . . . .  18
   Authors' Addresses  . . . . . . . . . . . . . . . . . . . . . . .  18

1.  Introduction

   A pseudorandom function (PRF) F(k, x) is an efficiently computable
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