Re: [Cfrg] Compression of tori in draft-irtf-cfrg-pairing-friendly-curves-02
Yumi Sakemi <yumi.sakemi@lepidum.co.jp> Sat, 21 March 2020 07:29 UTC
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From: Yumi Sakemi <yumi.sakemi@lepidum.co.jp>
Date: Sat, 21 Mar 2020 16:29:36 +0900
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To: Watson Ladd <watson=40cloudflare.com@dmarc.ietf.org>
Cc: cfrg@irtf.org, Tetsutaro Kobayashi <tetsutaro.kobayashi.dr@hco.ntt.co.jp>, SAITO Tsunekazu <tsunekazu.saito.hg@hco.ntt.co.jp>
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Subject: Re: [Cfrg] Compression of tori in draft-irtf-cfrg-pairing-friendly-curves-02
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Dear Dr. Watson, Thank you for your comments. I'm glad you to read our draft!! The compress techniques are very interesting for us. According to your comments, I will discuss with co-authors and update our draft. Best regards, Yumi --- Yumi Sakemi, Ph. D. Lepidum Co. Ltd. E-Mail: yumi.sakemi@lepidum.co.jp 2020年3月20日(金) 6:09 Watson Ladd <watson=40cloudflare.com@dmarc.ietf.org>: > Dear all, > > In the latest draft I see that F_{p^k} is represented directly as > polynomials modulo an irreducible of degree k, and GT is encoded > accordingly. This is space inefficient. > > In most cases k is even. Let q=p^(k/2) Consider F_q[x]/(x^2+d), the > quadratic extension of F_{q }, and now consider the result of a > pairing in it. As in https://eprint.iacr.org/2004/032.pdf, it is clear > that the result satisfies a quadratic equation: a^2-db^2=1, where the > element is a+bx. > > Therefore we can send only a, which is much smaller, and ecode b as a > single bit. > > This technique is very useful in any protocol where an element of GT > must be sent. > > Sincerely, > Watson Ladd > > _______________________________________________ > Cfrg mailing list > Cfrg@irtf.org > https://www.irtf.org/mailman/listinfo/cfrg >
- [Cfrg] Compression of tori in draft-irtf-cfrg-pai… Watson Ladd
- Re: [Cfrg] Compression of tori in draft-irtf-cfrg… Yumi Sakemi
- Re: [Cfrg] Compression of tori in draft-irtf-cfrg… Yumi Sakemi