Hello,
I need a math clarification please.
Since the points on the Elliptic Curve (secp256k1) form a group, we can apply the laws of addition, substruction and multiplication.
This require a zero.
I checked that -1*G+1*G=N*G (with N=0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141).
Therefore, could we consider N*G as the zero ?
If yes, then why -2*G+2*G = M such as there seems to be no link between M and N.
Generaly speaking, is there any link between (-1*G+1*G) and (-k*G+k*G) ?
Prove that if ϕ : G → H is a group homomorphism and G is cyclic, then the subgroup ϕ(G) is cyclic. Proof Suppose G is cyclic, so G = 〈a〉 = {ak : k ∈ Z} for some a ∈ G. ... Then, as a generates G, we have c = ak for some integer k. Thus b = ϕ(c) = ϕ(ak) = ϕ(a)k ∈ 〈ϕ(a)〉.