Our goal is to show that a one-time pad is a perfect cipher,
and now that we have the definition of a perfect cipher,
we should be able to argue that formally.
This was our definition.
Since our definition uses the conditional probability,
we should also remember the definition of conditional probability,
which is the probability of some event A conditioned on event B happening
is equal to the probability of A intersect B divided by the probability of B.
To show that the one-time pad is a perfect cipher,
we just need to calculate this where A will be this event and B will be this event.
We need to know the probability of B,
which is the probability that some message with some key encrypts to C.
Let's compute that first. Then we'll need to compute the probability of A intersect B.
We'll have a little quiz.
Given any message and any cipher text C, and we're using a one-time pad,
how many different keys are there that encrypt that message to that cipher text?
