Re: [Cfrg] Curve25519 meets NUMS rigidity definition

Tanja Lange <tanja@hyperelliptic.org> Sat, 03 January 2015 20:58 UTC

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Date: Sat, 3 Jan 2015 21:58:28 +0100
From: Tanja Lange <tanja@hyperelliptic.org>
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Subject: Re: [Cfrg] Curve25519 meets NUMS rigidity definition
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> So I'll take p=2^255-19, y^2=x^3+ux^2+x, and search for the minimal
> positive u that makes the order of the curve 8 times prime, order of
> the twist 4 times other prime, and minimal x coordinate on the curve
> with prime order for the generator, with u congruent to 2 mod 4. I can
> even throw in restrictions on endomorphism ring and supersingularity,
> and it won't change the result.
> 
Thanks for spelling this out in full detail. 

See also http://safecurves.cr.yp.to/rigid.html 
	
	Tanja