Problem 3. Consider the following variant of a shift cipher: instead of shifting each letter by the same amount, we shift each letter by a different amount. The key consists of two integers n and m, and to encrypt, we shift the ith letter by n + im places in the alphabet. In other words, if pi is the ith plaintext letter, and c is the ith ciphertext letter, then the encryption rule is: P im (mod 26) Let's count letters from 0, so that po is the first plaintext letter, p is the second plaintext letter, and so forth. (a) Encrypt "mathematics" using n = 2, m = 3. (b) Decrypt "hvvahivknzhfgh1', using n = 5, m = 2. (c) Discuss the relative strength of this cipher under the four different attack models: ciphertext only, known plaintext, chosen plaintext, chosen ciphertext. (d) Can you launch a successful "ciphertext only" attack on the following message? tqgnafkdsvlpbllcarblnaxaewxjpwnlfpskpyzt ypzcvkoghzegtkhjagyzchkfrmfpsbsijlwothtu jtvfvzlwvmtvlnjrakcdhuonhrdjjfvonxuotkpu fwqnczwpdbxxoyklzoahyegtkewdfjzko