Suppose that there are 10000 = 10^4 banks and 10 payment card organisations (PCOs).
- How many secret keys will be needed if each PCO shares a unique secret key with each bank?
- How many extra secret keys will be needed if every two banks share a unique secret key?
For question 1, I figured that if there are 10,000 banks and 10 PCOs:
10,000 * 10 = 100,000.
For question 2, I need to calculate the number of keys if every 2 banks share a key (so I guess for 10,000 banks there would be 5,000 keys?)
5,000 * 10 = 50,000, right?
I recall that the solution could be calculated differently, something along the lines of 5,000(5,000-1)*10/2 but I don't understand the logic of this.
Could someone please explain?
(I would appreciate explanation of logic or a direction for research to understand because I feel like this should be quite straightforward and I am unsure).
Thank your for taking the time to read this!