Upload to Canvas a PDF scan of your written work to problems 1–4. If you would prefer to type, that’s fine, just export to PDF and upload a PDF. The notation “[T]” refers to our textbook: Introduction to Cryptography with Coding Theory by Trappe and Washington.
Use your affineCipher function to encode the
plaintext tragic and the plaintext places,
using the key \(\alpha=13\) and \(\beta=7\). What do you notice? What
number-theoretic properties of \(\alpha\) and/or \(\beta\) make them a bad choice for a
key?
Suppose that an affine cipher \(x
\stackrel{s}{\longmapsto} \alpha x + \beta\) encrypts the
plaintext ab to the ciphertext rw. Find the
key \(\alpha\) and \(\beta\). Use the “chosen plaintext” attack
on [T] page 16, and show your work.
Suppose that an affine cipher encrypts the plaintext
mississippi to the ciphertext ldxxdxxdeed.
Find the key using the method described in the “known plaintext” attack
on pp. 15-16 of [T]. Show your work.
Suppose that \(s_1(x) = \alpha_1 x + \beta_1\) and \(s_2(x) = \alpha_2 x + \beta_2\) represent two affine ciphers. Use algebra to compute a simplified formula for \(s_2(s_1(x))\). Is repeated encryption by an affine cipher more secure than encryption by a single affine cipher? Explain.