Does anyone know an example of an Elliptic Curve of caracteristic $p$ ($E_p$) that has a point generator $G$ that generates a subgroup of order $q$, with $p$, $q$ being prime numbers and $p = 2q + 1$?
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$\begingroup$ Possible duplicate elliptic curves of prime order $\endgroup$– kelalakaCommented Feb 7, 2020 at 16:57
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1$\begingroup$ I suspect that any such curve would be supersingular, and so (unless you're doing isogenies) wouldn't be a good idea for crypto $\endgroup$– ponchoCommented Feb 7, 2020 at 17:09
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2$\begingroup$ @fgrieu: I believe he's talking about the characteristic $\endgroup$– ponchoCommented Feb 7, 2020 at 17:10
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$\begingroup$ @fgrieu: With $p$ I mean the modulus of the field of the Elliptic Curve. Is that the characteristic? $\endgroup$– FionoCommented Feb 7, 2020 at 17:13
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2$\begingroup$ A finite elliptic curve is based on some finite field $GF(p^k)$. The characteristic of the curve is actually defined to be $p$; however since you have $k=1$, that's the same. fgrieu was confused because 'order' is more typically used to mean 'the size of the (sub)group' (which is how you used it the second time) $\endgroup$– ponchoCommented Feb 7, 2020 at 17:17
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