Is secp256k1 a prime field?

Now, it turns out that the secp256k1 field is a prime field and therefore isomorphic to a ring of integers modulo a prime, but this is not true for all ECDSA curves -- in fact, the "sectXXXyZ" curves (for which much faster hardware exists than the "secpXXXyZ" curves) cannot be described using rings of integers.

What is elliptic curve secp256k1?

The elliptic curve secp256k1 is defined as y2 = x3 + 7 y 2 = x 3 + 7. The prime for the field is set to: So now, one should be able to calculate the order by using the Schoof's Algorithm.

Why does secp256k1 have an additional automorphism?

secp256k1 have an additional automorphism because it belongs to a special class of elliptic curves, sometimes referred to as Koblitz (although this has lead to some confusion, and some people have mistakenly called it a binary curve), which have an additional automorphism.

How do you check n n of secp256k1?

Note: The order n n of secp256k1 is well-known, and it's easy to verify it: pick any point T T (other than the neutral O O) and check nT =O n T = O, which proves the order of T T divides n n. Now check n n is prime and close to p p (within 30% will do; or Hasses' bound ).