If an EC private key k is very small, say "1", is it feasible to calculate the private key k from its public key K, since there would only be one step back to generator point G and therefore the discrete logarithm would only need to be found once to land on G?
Even if this is not feasible without brute force, is there anything preventing a database of private/public keys being built over time, starting at 1,2,3... etc, such that all very low-numbered private keys could easily be revealed.
For instance, for the first billions of possible values of k, their K is saved in a database. Any public K could then be checked against these values for a match and if there is a match the private k is instantly known. I know the probability is still infinitesimally small but also billions of times higher than randomly checking values of k (and would continue increasing over time)