Introduction to Cryptography with Coding Theory, 3rd Edition

12.8 Exercises

1. In a family of four, what is the probability that no two people have birthdays in the same month? (Assume that all months have equal probabilities.)

2. Each person in the world flips 100 coins and obtains a sequence of length 100 consisting of Heads and Tails. (There are $2^{100}\approx {10}^{30}$ possible sequences.) Assume that there are approximately ${10}^{10}$ people in the world. What is the probability that two people obtain the same sequence of Heads and Tails? Your answer should be accurate to at least two decimal places.

3. 1. Let $E_K$ be an encryption function with $N$ possible keys $K$, $N$ possible plaintexts, and $N$ possible ciphertexts. Assume that if you know the encryption key $K$, then it is easy to find the decryption function $D_K$ (therefore, this ...