Did you even look at the picture you posted? OP is talking about the public key.

The associative law and the distributive law hold for EC and can be used.  Kp = Ks * G, hence
   (1013+Ks) * G = 1013*G + Ks*G = 1013*G + Kp
and
   (1013*Ks) * G = 1013 * (Ks * G) = 1013 * Kp

Note that + and * have two different meanings above.  Operator + is point addition or number addition modulo group order.  Operator * is point multiplication or number multiplication modulo group order.

So 1013+Ks is the private key for 1013*G + Kp  and 1013*Ks is the private key for 1013 * Kp.

I think it doesn't really matter which method you use.  See also BIP32, which uses a variant of the first method for non-hardened derivation  (hardened derivation is not what you want, because then you cannot compute the public key without the private key).  A problem is that if one private key is leaked the others can easily be computed, but there is no general way to avoid it.

So lets do the math.  vanitygen can generate about 1 MKey/s with a few tweaks (e.g. try positive/negative, compressed and uncompressed keys at the same time) on today's computer.    Lets assume that using ASIC technology (which you have to build from scratch, since SHA-256 is not enough to generate private/public key pairs) you can get a speedup of a trillion (the current Bitcoin network has significantly less than a trillion times more computing power than Satoshi's computer).  Lets assume there are about 100 million addresses that currently have a non-zero balance (I think it's less).  There are only 2^160 addresses (since we hash to 160 bits).  So you need on average

This are around 465 trillion years to find a single key for a non-empty address, if I'm not mistaken.

Okay, if Moore's law will still hold for 75 years, then this method might become feasible -- if you want to invest as much money as all miners together and let the computer work for half a year to find a fraction of a Bitcoin in some random address.

BTW, there are faster ways than brute-forcing all addresses. You could take an address with lot of funds where the public key is known (e.g. Bitstamp's cold wallet) and use the big-step, baby-step algorithm that "only" has complexity 2^128.  That may be 100 times faster.

And since you asked for quantum computers:  The current quantum computers can probably not be used, but if you have a real 65000-qbit quantum computer that can do complex computations without decoherence for a few seconds, then you can probably crack a public key in a few seconds.