Re: [Cfrg] Fwd: I-D Action: draft-yonezawa-pairing-friendly-curves-02.txt

Michael Scott <mike.scott@miracl.com> Fri, 19 July 2019 14:23 UTC

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From: Michael Scott <mike.scott@miracl.com>
Date: Fri, 19 Jul 2019 15:21:03 +0100
Message-ID: <CAEseHRr3wUttdCK2dZ3riRue8rUeW3tqS0T15qjfoTLR4LqnGA@mail.gmail.com>
To: Shoko YONEZAWA <yonezawa@lepidum.co.jp>
Cc: CFRG <cfrg@irtf.org>
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Subject: Re: [Cfrg] Fwd: I-D Action: draft-yonezawa-pairing-friendly-curves-02.txt
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 Hello Shoko,

I welcome your updated draft. A few observations..

1. The BLS48-581 curve uses a rather unfortunate form of towering. Whereas
BLS12-381 and BN462 use irreducible polynomials of the form u^2-u-1,
BLS48-581 uses irreducible polynomials with the opposite sign, e.g.
u^2+u+1. This makes code re-use between curves awkward. It will be
interesting to see what form is used for the proposed 192-bit curves

2. The BLS co-factor is still unnecessarily large, of the form (z-1)^2 when
z-1 is sufficient, and of lower Hamming weight. This point has also
recently been made here https://eprint.iacr.org/2019/830 and here
https://eprint.iacr.org/2019/403

3. All of these curves are now implemented in the most recent version (as
yet unreleased) of our AMCL library. Some indicative timings are given
below (Rust language version, no assembly, projective coordinates in G2).
These should not be considered best-case absolute numbers, but may be
useful for observing how the complexity of common pairing-based operations
scale with increasing security.


Testing/Timing bls12_381 Pairings

G1 mul - 38639 iterations 0.26 ms per iteration

G2 mul - 19596 iterations 0.51 ms per iteration

GT pow - 14476 iterations 0.69 ms per iteration

PAIRing ATE - 12211 iterations 0.82 ms per iteration

PAIRing FEXP - 8430 iterations 1.19 ms per iteration

All tests pass


Testing/Timing bn462 Pairings

G1 mul - 17290 iterations 0.58 ms per iteration

G2 mul - 8666 iterations 1.15 ms per iteration

GT pow - 6142 iterations 1.63 ms per iteration

PAIRing ATE - 4991 iterations 2.00 ms per iteration

PAIRing FEXP - 6591 iterations 1.52 ms per iteration

All tests pass


Testing/Timing bls48_581 Pairings

G1 mul - 11667 iterations 0.86 ms per iteration

G2 mul - 584 iterations 17.12 ms per iteration

GT pow - 377 iterations 26.55 ms per iteration

PAIRing ATE - 1078 iterations 9.28 ms per iteration

PAIRing FEXP - 230 iterations 43.49 ms per iteration

All tests pass


At the 192-bit security level we have implemented our own bls24 curve


Testing/Timing bls24 Pairings

Modulus size 479 bits

64 bit build

G1 mul - 17304 iterations 0.58 ms per iteration

G2 mul - 3295 iterations 3.04 ms per iteration

GT pow - 2202 iterations 4.54 ms per iteration

PAIRing ATE - 3168 iterations 3.16 ms per iteration

PAIRing FEXP - 1397 iterations 7.16 ms per iteration

All tests pass


Mike



On Fri, Jul 19, 2019 at 4:27 AM Shoko YONEZAWA <yonezawa@lepidum.co.jp>;
wrote:

> Hi CFRG folks,
>
> Here is 02 version of our draft "Pairing-Friendly Curves."
> We revised the draft with respect to your comments and feedback from the
> mailing list.
>
> I am going to give a presentation about this draft at CFRG meeting in
> Montreal.
> Your further comments are greatly appreciated.
>
> See you in Montreal.
>
> Thanks,
> Shoko
>
> -------- Forwarded Message --------
> Subject: I-D Action: draft-yonezawa-pairing-friendly-curves-02.txt
> Date: Mon, 08 Jul 2019 04:36:28 -0700
> From: internet-drafts@ietf.org
> Reply-To: internet-drafts@ietf.org
> To: i-d-announce@ietf.org
>
>
> A New Internet-Draft is available from the on-line Internet-Drafts
> directories.
>
>
>          Title           : Pairing-Friendly Curves
>          Authors         : Shoko Yonezawa
>                            Tetsutaro Kobayashi
>                            Tsunekazu Saito
>         Filename        : draft-yonezawa-pairing-friendly-curves-02.txt
>         Pages           : 36
>         Date            : 2019-07-08
>
> 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.
>
>
> The IETF datatracker status page for this draft is:
> https://datatracker.ietf.org/doc/draft-yonezawa-pairing-friendly-curves/
>
> There are also htmlized versions available at:
> https://tools.ietf.org/html/draft-yonezawa-pairing-friendly-curves-02
>
> https://datatracker.ietf.org/doc/html/draft-yonezawa-pairing-friendly-curves-02
>
> A diff from the previous version is available at:
> https://www.ietf.org/rfcdiff?url2=draft-yonezawa-pairing-friendly-curves-02
>
>
> Please note that it may take a couple of minutes from the time of
> submission
> until the htmlized version and diff are available at tools.ietf.org.
>
> Internet-Drafts are also available by anonymous FTP at:
> ftp://ftp.ietf.org/internet-drafts/
>
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