- Encrypt your name using an affine method (\(ax+b\)) with key \((5,6,29)\) (don't worry about letters), and decrypt BXHBI.
- Create your own \(ax+b\) mod (\(n\)) system of encryption and bring an encrypted message to class.
- Use the Diffie-Hellman method of encryption to encrypt a short (three to five character) message with a \(26<p<50\) "by hand" (i.e. without Sage but with a calculator). Be prepared to explain your choice of \(e\) and \(p\), and calculate that \(ef\equiv 1\) mod (\(p-1\)) by hand.
- Do this two-parter:
- Suppose you discovered that the message 4363094, where \(p=7387543\), actually represented the (numerical) message 2718. What steps might you take to try to discover \(e\)?
- Suppose that you discovered in the previous part by hard work that \(e=35\). Now quickly decrypt the message 6618138.
- Pick two primes between 1000 and 2000 and create a public key \((n,e)\) for them. What is the decryption key \(f\)? Show your work.
- Suppose that \(n=9211\) and \(e=539\).
- Encrypt a (short) message.
- Find the decryption key \(f\) for this situation, and decrypt your message.
- Use \(f\) to sign your name!
- Come up with your own RSA public-key system by choosing \(p\) and \(q\) and \(e\) as appropriate, but with \(n>10000\); then encrypt a short numerical message and hand in only the public key \((n,e)\) and the encrypted message. (My job will be to crack it!)
