(a) (1 point) Let Alice and Bob share a block cipher key Kab while Alice and Charlie share a block cipher key Kac. Define a method of encryption that allows Alice to encrypt an m-block message in such a way that it can only be decrypted cooperatively by both Bob and Charlie (and neither of them should have an advantage over the other). The resulting ciphertext should be a constant number of blocks longer than the plaintext, i.e. [c] = m+1 for some l > 1. (b) (2 points) Now in addition to Kab and Kac, let Alice shares a key Kad with David. Define a way for Alice to encrypt an m-block message such that it can only be decrypted by any two cooperating people (ex. Bob and David). The resulting ciphertext should be a constant number of blocks longer than the plaintext, i.e. [c] = m +1 for some l > 1. (c) (1 point) How does the size of your solution for (b) scale with the number of recipients? For example, suppose there are n recipients such that any k out of n can decrypt but k-1 cannot, what would be the size of the ciphertext as a function of n and k