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 Feb 28 awarded Teacher Feb 27 awarded Commentator Feb 27 comment Is sharing the modulus for multiple RSA key pairs secure? @Ricky: Not sure what you mean? In my comment, $\phi$ is the size of the multiplicative group modulo $n$, i.e. $\phi = (p-1)(q-1)$ for the standard RSA setup with two primes. In almost all cases in practice, $e$ is fixed at $65537$ and $d$ is taken to be the multiplicative inverse of $e$ modulo $\phi$, that is $ed = 1 \, (\textrm{mod} \, \phi)$ (if it exists - otherwise new primes are generated). Feb 27 answered Is sharing the modulus for multiple RSA key pairs secure? Feb 26 asked Sextic twist of BN pairing parameters vs security Feb 25 comment Sextic twist optimization of BN pairing - cubic root extraction required? Great thanks... didn't think of f(x) = 0 (mod f(x)), so now it all makes sense :) Feb 25 accepted Sextic twist optimization of BN pairing - cubic root extraction required? Feb 24 revised Sextic twist optimization of BN pairing - cubic root extraction required? Prettified the math Feb 24 asked Sextic twist optimization of BN pairing - cubic root extraction required? Feb 5 comment Generating bilinear pairing parameters - running time of finding member of p-torsion group Thanks just the answer I was looking for :-) I already know the number of points on the curve over the base field so it is easy to calculate the number of points over the extended field. Feb 5 comment Generating bilinear pairing parameters - running time of finding member of p-torsion group gmoktop: Thanks! Feb 5 accepted Generating bilinear pairing parameters - running time of finding member of p-torsion group Feb 4 awarded Scholar Feb 4 awarded Supporter Feb 4 comment Generating bilinear pairing parameters - running time of finding member of p-torsion group Thanks, but does this algorithm perform (much) better than the original? Because it seems improbable to get a success in step 1-3 (probability ~2^512 / 2^3072)? And steps 4-5 are the original. Feb 4 comment Generating bilinear pairing parameters - running time of finding member of p-torsion group Yes, replacing p by p^2 immediately solved the problem (it found a point on the first iteration). Yes I read I can use twist curves but wanted to keep it as simple as possible in the beginning. By the way can you recommend a way to calculate the number of points on the curve (over the q^12 field)? Right now I use Sage and it's very fast but I need to implement my own point counting. I was wondering if this type of curve, due to its construction, has characteristics that makes it easier than in the general case? Feb 4 comment Generating bilinear pairing parameters - running time of finding member of p-torsion group gmoktop: Actually what I'm looking for is a point in the p-torsion group, i.e. a point that satisfies p*P = O so it must have either order p, or the order must be a divisor in p. But since p is prime, this should mean the point must have order p. I'm not sure I understand what you mean that the algorithm gives points of order is divided by p^s? What is this algorithm (the one in my post!) called and is there a reference where I could read more about it? I only saw it mentioned for use for this specific problem but I don't know how it works! Feb 3 awarded Editor Feb 3 revised Generating bilinear pairing parameters - running time of finding member of p-torsion group Rephrased question due to better understanding of the problem. Jan 27 asked Generating bilinear pairing parameters - running time of finding member of p-torsion group