Pairing-Friendly Curves
draft-irtf-cfrg-pairing-friendly-curves-02

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Replaces draft-yonezawa-pairing-friendly-curves
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CFRG                                                      Y. Sakemi, Ed.
Internet-Draft                                                   Lepidum
Intended status: Experimental                               T. Kobayashi
Expires: 20 September 2020                                      T. Saito
                                                                     NTT
                                                           19 March 2020

                        Pairing-Friendly Curves
               draft-irtf-cfrg-pairing-friendly-curves-02

Abstract

   This memo introduces pairing-friendly curves used for constructing
   pairing-based cryptography.  It describes recommended parameters for
   each security level and recent implementations of pairing-friendly
   curves.

Status of This Memo

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   This Internet-Draft will expire on 20 September 2020.

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

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Sakemi, et al.          Expires 20 September 2020               [Page 1]
Internet-Draft           Pairing-Friendly Curves              March 2020

Table of Contents

   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   2
     1.1.  Pairing-Based Cryptography  . . . . . . . . . . . . . . .   2
     1.2.  Applications of Pairing-Based Cryptography  . . . . . . .   3
     1.3.  Goal  . . . . . . . . . . . . . . . . . . . . . . . . . .   4
     1.4.  Requirements Terminology  . . . . . . . . . . . . . . . .   4
   2.  Preliminaries . . . . . . . . . . . . . . . . . . . . . . . .   4
     2.1.  Elliptic Curve  . . . . . . . . . . . . . . . . . . . . .   4
     2.2.  Pairing . . . . . . . . . . . . . . . . . . . . . . . . .   5
     2.3.  Barreto-Naehrig Curve . . . . . . . . . . . . . . . . . .   6
     2.4.  Barreto-Lynn-Scott Curve  . . . . . . . . . . . . . . . .   6
     2.5.  Representation Convention for an Extension Field  . . . .   7
   3.  Security of Pairing-Friendly Curves . . . . . . . . . . . . .   8
     3.1.  Evaluating the Security of Pairing-Friendly Curves  . . .   8
     3.2.  Impact of the Recent Attack . . . . . . . . . . . . . . .   9
   4.  Selection of Pairing-Friendly Curves  . . . . . . . . . . . .   9
     4.1.  Adoption Status of Pairing-friendly Curves  . . . . . . .   9
       4.1.1.  International Standards . . . . . . . . . . . . . . .  13
       4.1.2.  Cryptographic Libraries . . . . . . . . . . . . . . .  13
       4.1.3.  Applications  . . . . . . . . . . . . . . . . . . . .  14
     4.2.  For 100 Bits of Security  . . . . . . . . . . . . . . . .  15
     4.3.  For 128 Bits of Security  . . . . . . . . . . . . . . . .  15
       4.3.1.  BN Curves . . . . . . . . . . . . . . . . . . . . . .  15
       4.3.2.  BLS Curves  . . . . . . . . . . . . . . . . . . . . .  17
     4.4.  For 192 Bits of Security  . . . . . . . . . . . . . . . .  19
     4.5.  For 256 Bits of Security  . . . . . . . . . . . . . . . .  19
   5.  Security Considerations . . . . . . . . . . . . . . . . . . .  23
   6.  IANA Considerations . . . . . . . . . . . . . . . . . . . . .  24
   7.  Acknowledgements  . . . . . . . . . . . . . . . . . . . . . .  24
   8.  References  . . . . . . . . . . . . . . . . . . . . . . . . .  24
     8.1.  Normative References  . . . . . . . . . . . . . . . . . .  24
     8.2.  Informative References  . . . . . . . . . . . . . . . . .  25
   Appendix A.  Computing Optimal Ate Pairing  . . . . . . . . . . .  31
     A.1.  Optimal Ate Pairings over Barreto-Naehrig Curves  . . . .  31
     A.2.  Optimal Ate Pairings over Barreto-Lynn-Scott Curves . . .  32
   Appendix B.  Test Vectors of Optimal Ate Pairing  . . . . . . . .  32
   Authors' Addresses  . . . . . . . . . . . . . . . . . . . . . . .  43

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