Pairing-Friendly Curves
draft-irtf-cfrg-pairing-friendly-curves-09
CFRG Y. Sakemi, Ed.
Internet-Draft Lepidum
Intended status: Informational T. Kobayashi
Expires: 20 May 2021 T. Saito
NTT
R. Wahby
Stanford University
16 November 2020
Pairing-Friendly Curves
draft-irtf-cfrg-pairing-friendly-curves-09
Abstract
Pairing-based cryptography, a subfield of elliptic curve
cryptography, has received attention due to its flexible and
practical functionality. Pairings are special maps 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
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Sakemi, et al. Expires 20 May 2021 [Page 1]
Internet-Draft Pairing-Friendly Curves November 2020
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This Internet-Draft will expire on 20 May 2021.
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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 . . . . . . . . . . . . . . . . 6
2. Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . 6
2.1. Elliptic Curves . . . . . . . . . . . . . . . . . . . . . 6
2.2. Pairings . . . . . . . . . . . . . . . . . . . . . . . . 6
2.3. Barreto-Naehrig Curves . . . . . . . . . . . . . . . . . 8
2.4. Barreto-Lynn-Scott Curves . . . . . . . . . . . . . . . . 8
2.5. Representation Convention for an Extension Field . . . . 9
3. Security of Pairing-Friendly Curves . . . . . . . . . . . . . 10
3.1. Evaluating the Security of Pairing-Friendly Curves . . . 10
3.2. Impact of Recent Attacks . . . . . . . . . . . . . . . . 11
4. Selection of Pairing-Friendly Curves . . . . . . . . . . . . 11
4.1. Adoption Status of Pairing-friendly Curves . . . . . . . 12
4.1.1. International Standards . . . . . . . . . . . . . . . 15
4.1.2. Cryptographic Libraries . . . . . . . . . . . . . . . 15
4.1.3. Applications . . . . . . . . . . . . . . . . . . . . 16
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