Cryptology ePrint Archive: Report 2014/027

Twisting Edwards curves with isogenies

Mike Hamburg

Abstract: Edwards’ elliptic curve form is popular in modern cryptographic implementations thanks to their fast, strongly unified addition formulas. Twisted Edwards curves with a = −1 are slightly faster, but their addition formulas are not complete over Fp where p ≡ 3 (mod 4). In this short note, we propose that designers specify Edwards curves, but implement scalar multiplications and the like using an isogenous twisted Edwards curve.

Category / Keywords: implementation / twisted Edwards curves, isogeny

Date: received 9 Jan 2014

Contact author: mike at shiftleft org

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Version: 20140110:092345 (All versions of this report)

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