Pairing-Friendly Curves
draft-irtf-cfrg-pairing-friendly-curves-05

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Document Type Active Internet-Draft (cfrg RG)
Last updated 2020-06-09 (latest revision 2020-04-28)
Replaces draft-yonezawa-pairing-friendly-curves
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Document shepherd Stanislav Smyshlyaev
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Send notices to Stanislav Smyshlyaev <smyshsv@gmail.com>
CFRG                                                      Y. Sakemi, Ed.
Internet-Draft                                                   Lepidum
Intended status: Experimental                               T. Kobayashi
Expires: 11 December 2020                                       T. Saito
                                                                     NTT
                                                                R. Wahby
                                                     Stanford University
                                                             9 June 2020

                        Pairing-Friendly Curves
               draft-irtf-cfrg-pairing-friendly-curves-05

Abstract

   Pairing-based cryptography, a subfield of elliptic curve
   cryptography, has received attention due to its flexible and
   practical functionality.  Pairing is a special map defined using
   elliptic curves and it can be applied to construct several
   cryptographic protocols such as identity-based encryption, attribute-
   based encryption, and so on.  At CRYPTO 2016, Kim and Barbulescu
   proposed an efficient number field sieve algorithm named exTNFS for
   the discrete logarithm problem in a finite field.  Several types of
   pairing-friendly curves such as Barreto-Naehrig curves are affected
   by the attack.  In particular, a Barreto-Naehrig curve with a 254-bit
   characteristic was adopted by a lot of cryptographic libraries as a
   parameter of 128-bit security, however, it ensures no more than the
   100-bit security level due to the effect of the attack.  In this
   memo, we list the security levels of certain pairing-friendly curves,
   and motivate our choices of curves.  First, we summarize the adoption
   status of pairing-friendly curves in standards, libraries and
   applications, and classify them in the 128-bit, 192-bit, and 256-bit
   security levels.  Then, from the viewpoints of "security" and "widely
   used", we select the recommended pairing-friendly curves considering
   exTNFS.

Status of This Memo

   This Internet-Draft is submitted in full conformance with the
   provisions of BCP 78 and BCP 79.

   Internet-Drafts are working documents of the Internet Engineering
   Task Force (IETF).  Note that other groups may also distribute
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   Drafts is at https://datatracker.ietf.org/drafts/current/.

Sakemi, et al.          Expires 11 December 2020                [Page 1]
Internet-Draft           Pairing-Friendly Curves               June 2020

   Internet-Drafts are draft documents valid for a maximum of six months
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   This Internet-Draft will expire on 11 December 2020.

Copyright Notice

   Copyright (c) 2020 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
     1.1.  Pairing-based Cryptography  . . . . . . . . . . . . . . .   3
     1.2.  Applications of Pairing-based Cryptography  . . . . . . .   3
     1.3.  Motivation and Contribution . . . . . . . . . . . . . . .   5
     1.4.  Requirements Terminology  . . . . . . . . . . . . . . . .   5
   2.  Preliminaries . . . . . . . . . . . . . . . . . . . . . . . .   6
     2.1.  Elliptic Curves . . . . . . . . . . . . . . . . . . . . .   6
     2.2.  Pairings  . . . . . . . . . . . . . . . . . . . . . . . .   7
     2.3.  Barreto-Naehrig Curves  . . . . . . . . . . . . . . . . .   7
     2.4.  Barreto-Lynn-Scott Curves . . . . . . . . . . . . . . . .   8
     2.5.  Representation Convention for an Extension Field  . . . .   9
   3.  Security of Pairing-Friendly Curves . . . . . . . . . . . . .   9
     3.1.  Evaluating the Security of Pairing-Friendly Curves  . . .   9
     3.2.  Impact of Recent Attacks  . . . . . . . . . . . . . . . .  10
   4.  Selection of Pairing-Friendly Curves  . . . . . . . . . . . .  10
     4.1.  Adoption Status of Pairing-friendly Curves  . . . . . . .  11
       4.1.1.  International Standards . . . . . . . . . . . . . . .  15
       4.1.2.  Cryptographic Libraries . . . . . . . . . . . . . . .  15
       4.1.3.  Applications  . . . . . . . . . . . . . . . . . . . .  17
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