I read that the private key pk has to be any number between 1 and n, where n is almost 10^77. Since pk' s function is practically to be used as a scalar for multiplying the generator point G, why does it have to be strictly less than n?
I've thought that is because the math behind secp256k: inside a order-n group, if I multiply times x a number A (with x > n), it's equivalent to multiply the same number A times y, with y = x % n. So y will be extremely less than x, making A easier to be discovered. Is this argument correct?