# what is the public information in Elliptic curve cryptosystems [closed]

Currently my knowledge about Elliptic curve is quite limited to the textbook and I don't know how a practical Elliptic curve cryptosystem works.

I read an example about key exchange using Elliptic curves. And I am wondering what is the public information (key) of a practical Elliptic curve cryptosystem.

First, the equation of the Elliptic curve should be public. How about other parameters? Such as the order of the curve ( number of points on the curve), the generator point of the curve and so on.

Can you give me a good reference about how a practical Elliptic curve cryptosystem works?

Those domain parameters will be public. For example for curves over finite fields those parameters are: ${p,a,b,G,n,h}$. The lower level operations will be made in $\mathbb{F}_p$ and the operations will be made using points on a curve. Then $a$ and $b$ (or the equivalents is uses different notation) is also public and also the equation used. About the generator point $\langle G\rangle$, you can think like public it is in DLP over finite fields.
About the order of the cyclic subgroup of points where the ECDLP is defined is public ($ord(G)=n$), together with the cofactor $h$ (that shall be very small number and both primes, with relation $h \lll n$), and the product of them is the number of points of the curve.
The only thing secret is the secret key, often labelled as $d$, where the public key is $P=d[G]$.