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 nim places in the alphabet. In other words, if pi is the ith plaintext letter, and ci is the ith ciphertext letter, then the encryption rule is: ci Pi + n + im (mod 26) Let's count letters from 0, so that po is the first plaintext letter, pi is the second plaintext letter, and so forth (a) Encrypt "mathematics', using n = 2, m = 3 (b) Decrypt "hvvahivknzhfqhl" 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? dtahxkbmlvgbdzfrnsodptogruzhoeuqfskirbpe pgntnjlrvecjzfhnbyfjkrhusmtweoawtxyoajja isvuwacovlpzbfykkgrvxcbggzpplqxyenrpwmsa rulwevfsjnosymlvtlrdkwcaxcsz 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 nim places in the alphabet. In other words, if pi is the ith plaintext letter, and ci is the ith ciphertext letter, then the encryption rule is: ci Pi + n + im (mod 26) Let's count letters from 0, so that po is the first plaintext letter, pi is the second plaintext letter, and so forth (a) Encrypt "mathematics', using n = 2, m = 3 (b) Decrypt "hvvahivknzhfqhl" 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? dtahxkbmlvgbdzfrnsodptogruzhoeuqfskirbpe pgntnjlrvecjzfhnbyfjkrhusmtweoawtxyoajja isvuwacovlpzbfykkgrvxcbggzpplqxyenrpwmsa rulwevfsjnosymlvtlrdkwcaxcsz