Let me explain you all guy how one can reduce bit size from 2^130 to near to 2^103.
First of all you just focus on how much bits are reduced? around 26 bits right (The first one can always be subtracted from pub key). So how big is 2^26? 2**26 = 67108864
So these are the pub keys in which one of the key is under 2^103.
The moment to try to go one single bit further, things are gonna get a little bulky.
The trick is simple, you have 1 public key, add generator to it and now you have two public keys whose private keys are 89 & 90 or 534354234384847 & 534354234384848.
We we do this, because we want to divide our public key to reduce its size and we don't know whether it is odd or even so add one to it and and now you have both.
Now you divide both and you have one correct result and one incorrect.
In second step you repeat the process of adding 1 to both of them and dividing 4 of them..
So this is like 1, 2, 4, 8, 16, 32, .... yep,, you got it!!