# Base Point on elliptic curve

How can i define the base point of the elliptic curve group element used as the elliptic curve domain parameter over Fp (prime)

• What exactly is your question? How to find a point on a given curve? How to verify the order of said point? How to encode a base point in ASN.1? – SEJPM Oct 14 '17 at 17:27
• my question is, how to find the right point for generator (base point) on elliptic curve? is there any special provision to find that point? – Adan Kalamsyah Oct 15 '17 at 3:54
• I'm doing research on the application of digital signature using elliptic curve cryptography in block chaining, now I've stage the combination of both.. – Adan Kalamsyah Oct 16 '17 at 4:35

It can easily be shown that any base point is as good as any other with regards to resistance to discrete logarithm: if you can solve DL efficiently in base $G$, then you can solve it efficiently in any other base $G'$ by first solving $G'$ with regards to $G$: first, use your efficient DL solving algorithm to compute $k$ such that $G'$ = $kG$; then, given $xG'$, solve it in base $G$ to get $xG' = rG$, then the solution will be $x = r/k \pmod n$ (where $n$ is the group order).
In practice, the "base point" is considered to be part of the curve definition, along with the other curve parameters. For instance, FIPS 186-4 defines the "NIST curves" (in annex D); for each of them, it lists the field modulus ($p$), the curve order ($n$), the curve equation parameters (NIST curves in a prime field use $y^2 = x^3 -3x + b$, so the only equation parameter is $b$), and the two coordinates $G_x$ and $G_y$ of the conventional base point.