This email got bounced because "5.7.9 Message not accepted for policy reasons. See http://postmaster.yahoo.com/errors/postmaster-28.html";. It might just be me because I relay email to a yahoo address.
In case anyone missed David Gil's email: > On November 13, 2014 at 10:15 AM David Gil <[email protected]> wrote: > > > On Thursday, November 13, 2014 1:56 AM, Steven Galbraith > <[email protected]> wrote: > > > Let E : y^2 = x^3 + a*x + b be an elliptic curve and E' : Y^2 = X^3 + > > d^2*a*x + d^3*b be its quadratic twist. The primality of E( F_q ) and E'( > > F_q ) are not independent events!! Indeed, far from it. > > This is exactly what I was looking for! I had an initial argument that > p(is_prime(|E(F_q)|) && is_prime(|E'(F_q))) > is closer to > p(is_prime(|E(F_q)|)) > than it is to > p(is_prime(|E(F_q)|))*p(is_prime(|E'(F_q)|) > from a sort of symmetry argument; but that was pure hand-waving. > > > Some sort of vague explanation is given in the paper: > > S. D. Galbraith, J. F. McKee, The probability that the number of > points on an elliptic curve over a finite field is prime, Journal of > the London Mathematical Society, 62, no. 3, p. 671-684 (2000) > > This is terrific! Thank you for the reference. (Based on a quick scan through > it, my hand-waving was entirely wrong...) > > I'll run a numerical experiment or two this weekend: E.g., draw from the > distribution of Tf and look for the probability of a prime "pair" for some of > the primes currently being considered. > > (And perhaps cross-check via point-counting that this also makes sense for > Edwards curves with small cofactor drawn via the djb or NUMS methods.) > > > -dlg > _______________________________________________ > Curves mailing list > [email protected] > https://moderncrypto.org/mailman/listinfo/curves _______________________________________________ Curves mailing list [email protected] https://moderncrypto.org/mailman/listinfo/curves
