Schnorr NIZK Proof: Non-interactive Zero Knowledge Proof for Discrete Logarithm
draft-hao-schnorr-06

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Internet Engineering Task Force                              F. Hao, Ed.
Internet-Draft                                 Newcastle University (UK)
Intended status: Informational                            April 26, 2017
Expires: October 28, 2017

 Schnorr NIZK Proof: Non-interactive Zero Knowledge Proof for Discrete
                               Logarithm
                          draft-hao-schnorr-06

Abstract

   This document describes Schnorr NIZK proof, a non-interactive variant
   of the three-pass Schnorr identification scheme.  The Schnorr NIZK
   proof allows one to prove the knowledge of a discrete logarithm
   without leaking any information about its value.  It can serve as a
   useful building block for many cryptographic protocols to ensure the
   participants follow the protocol specification honestly.  This
   document specifies the Schnorr NIZK proof in both the finite field
   and the elliptic curve settings.

Status of This Memo

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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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   (http://trustee.ietf.org/license-info) in effect on the date of
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   carefully, as they describe your rights and restrictions with respect

Hao                     Expires October 28, 2017                [Page 1]
Internet-Draft             Schnorr NIZK Proof                 April 2017

   to this document.  Code Components extracted from this document must
   include Simplified BSD License text as described in Section 4.e of
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   described in the Simplified BSD License.

Table of Contents

   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   2
     1.1.  Requirements Language . . . . . . . . . . . . . . . . . .   3
     1.2.  Notations . . . . . . . . . . . . . . . . . . . . . . . .   3
   2.  Schnorr NIZK Proof over Finite Field  . . . . . . . . . . . .   4
     2.1.  Group Parameters  . . . . . . . . . . . . . . . . . . . .   4
     2.2.  Schnorr Identification Scheme . . . . . . . . . . . . . .   4
     2.3.  Non-Interactive Zero-Knowledge Proof  . . . . . . . . . .   5
     2.4.  Computation Cost  . . . . . . . . . . . . . . . . . . . .   6
   3.  Schnorr NIZK Proof over Elliptic Curve  . . . . . . . . . . .   6
     3.1.  Group Parameters  . . . . . . . . . . . . . . . . . . . .   6
     3.2.  Schnorr Identification Scheme . . . . . . . . . . . . . .   7
     3.3.  Non-Interactive Zero-Knowledge Proof  . . . . . . . . . .   8
     3.4.  Computation Cost  . . . . . . . . . . . . . . . . . . . .   8
   4.  Variants of Schnorr NIZK proof  . . . . . . . . . . . . . . .   8
   5.  Applications of Schnorr NIZK proof  . . . . . . . . . . . . .   9
   6.  Security Considerations . . . . . . . . . . . . . . . . . . .   9
   7.  IANA Considerations . . . . . . . . . . . . . . . . . . . . .  10
   8.  Acknowledgements  . . . . . . . . . . . . . . . . . . . . . .  11
   9.  References  . . . . . . . . . . . . . . . . . . . . . . . . .  11
     9.1.  Normative References  . . . . . . . . . . . . . . . . . .  11
     9.2.  Informative References  . . . . . . . . . . . . . . . . .  12
     9.3.  URIs  . . . . . . . . . . . . . . . . . . . . . . . . . .  12
   Author's Address  . . . . . . . . . . . . . . . . . . . . . . . .  12

1.  Introduction

   A well-known principle for designing robust public key protocols
   states as follows: "Do not assume that a message you receive has a
   particular form (such as g^r for known r) unless you can check this"
   [AN95].  This is the sixth of the eight principles defined by Ross
   Anderson and Roger Needham at Crypto'95.  Hence, it is also known as
   the "sixth principle".  In the past thirty years, many public key
   protocols failed to prevent attacks, which can be explained by the
   violation of this principle [Hao10].

   While there may be several ways to satisfy the sixth principle, this
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