On 1/29/14, Mike Hamburg <[email protected]> wrote: > > On Jan 29, 2014, at 6:52 AM, Robert Ransom <[email protected]> wrote:
>> The first pattern is that Ed(1, d) is isogenous to Ed(-1, d-1) for >> every d that I have tested. > > I noticed this too, and I wrote up pretty much exactly what you're thinking. > See http://eprint.iacr.org/2014/027.pdf :-) If d is a non-square, there's also an isomorphism to an a=-1 curve, obtained by composing the twist maps Ed(1, d) -> Ed(1, 1/d) -> Ed(-1, -1/d). That has the advantages that the result always also has d/a non-square (whereas Ed(-1, 3617-1) doesn't), and the map is simpler to describe; and the disadvantage that one set of implementations has to handle a non-small-integer d. The isogeny is probably better overall, unless d is chosen to be random. Robert Ransom _______________________________________________ Curves mailing list [email protected] https://moderncrypto.org/mailman/listinfo/curves
