# Elliptic curve of order $p = 2q + 1$

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 $$p = 2q + 1$$?

• Possible duplicate elliptic curves of prime order Feb 7, 2020 at 16:57
• I suspect that any such curve would be supersingular, and so (unless you're doing isogenies) wouldn't be a good idea for crypto Feb 7, 2020 at 17:09
• @fgrieu: I believe he's talking about the characteristic Feb 7, 2020 at 17:10
• @fgrieu: With $p$ I mean the modulus of the field of the Elliptic Curve. Is that the characteristic? Feb 7, 2020 at 17:13
• 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) Feb 7, 2020 at 17:17