Blom's key distribution

Having a difficult time wrapping my head around the Blom's key distribution. I found an online resource to understand this but still couldn't get it. I am attaching the screenshot from the book where the author first mentions the algorithm and then he solves an example . A better explanation to the example how values are taken and derived would be better .

How are the different $g$ values and $K_{AB}$ and $K_{BA}$ derived ? Any help to break this algorithm would be highly appreciated .

It’s pretty straightforward; let’s take user $A$ as an example. We first calculate $a_A$ and $b_A$ according to step 3. $$a_A=a+br_A=8+3\times11\mod{23}=18,$$ $$b_A=b+cr_A=3+1\times11\mod{23}=14.$$ These values allow us to write down $g_A$ per step 4: $$g_A(x)=a_A+b_Ax=18+14x.$$ This allows user $A$ to compute $K_{AB}$ by evaluating this polynomial at $r_B$ modulo $p$ (it was remiss of the authors not to say that the calculations in step 5 are performed modulo $p$): $$K_{AB}=g_A(r_b)=18+14\times3\mod{23}=14$$

A similar process gives $$K_{BA}=17+6\times11\mod{23}=14$$

Both $K_{AB}$ and $K_{BA}$ are different ways of computing $$a+b(r_A+r_B)+cr_Ar_B\mod p.$$ This makes it critical to keep $a$, $b$ and $c$ secret, because anybody who knows these values can compute the shared secrets of all pairs of users.