if my private key is 123456789123456789, doesn't that mean I have to dot G point that many times to generate my pubkey? there must be a shortcut to generate pubkey, otherwise the time complicity of generating the pubkey is the same compare to brutal force from trying from 1 to k? Am I missing anything here?
it looks like generating pubkey from a random generated private key(which could be a 32 bytes BigInteger) requires to dot many times = integer value of the private key. which is impossible considering the key size for the private key is 2^256(32 bytes key space).