[Cfrg] Prime order + twisty DH benefit (theoretical)

Dan Brown <dbrown@certicom.com> Mon, 21 July 2014 21:09 UTC

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From: Dan Brown <dbrown@certicom.com>
To: "cfrg@irtf.org" <cfrg@irtf.org>
Thread-Topic: Prime order + twisty DH benefit (theoretical)
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Date: Mon, 21 Jul 2014 21:09:50 +0000
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Subject: [Cfrg] Prime order + twisty DH benefit (theoretical)
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‎Sorry, if the following has been discussed previously. Curve25519 has cofactor 8 because it uses a different shape curve.

If cofactor multiplication DH is used, this gives the shared secrets about 3 bits of information theoretical bias. Of course, the kdf etc should hide that bias just fine, but it would be theoretically simpler to have a shared secret with potentially no bias, eg prime order for both curve and twist.

Best regards, 

-- Dan