Suppose Alice and Bob follow stage 1 and phase 1 of stage 2 of the BB84 protocol, but that they skip phase 2 of stage 2. Also suppose that Eve opaquely eavesdrops on every qubit, in the way of slide 10. Eve also eavesdrops on the stage 2, phase 1 communication between Alice and Bob. Suppose the raw keys consist of k bits each.
1. What is the expected number of bits on which Alice's and Bob's raw keys agree? Explain your answer.
2. What is the expected number of bits of Alice's raw key that Eve will know? Explain your answer.