1. Briefly compare and contrast how asymmetric cryptography is used to provide encryption as opposed to how it can be used to provide a digital signature.
2. What is the purpose of the Diffie-Hellman algorithm? What are its major strength(s) and weakness(es)?
3. Using RSA, let p = 17, q = 13 and e = 5. What is the complete private key?
4. Encrypt-It-Rite, a vendor of encryption software, sells a symmetric cipher that uses a 56-bit key. The company decides to conduct a "challenge" to crack an encrypted message using a brute-force approach. The average time to crack the message is found to be 2 hrs. As a result, Encrypt-It-Rite decides to increase the key length by 8 bits, from 56 to 64 bits. They then conduct another challenge. What average cracking time would be expected for the new, improved cipher? If Encrypt-It-Rite would like to increase the average cracking time to at least 100 years, what will be the minimal length of the key?
5. A foreign navy has implemented a secure communications system in which submarine commanders transmit a single 5-letter message every day. The messages may only use capital (English) letters, and all messages are equally probable. A crypto device encrypts each message into 20 bits of ciphertext.
a. What is the entropy of the plaintext message?
b. What is the entropy of the ciphertext message?
c. Is this a good cryptosystem? Why or why not?
6. Bob is concerned about the possibility of having his 100k byte file modified without his knowledge, so he calculates a 100 byte hash. Alice, unbeknownst to Bob, changes a single character in Bob's file. Assuming that Bob used a strong hash function, what would the hash value of the modified file look like, as compared with the original hash value?
7. Suppose that Alice and Bob need to communicate, and have decided to use asymmetric (public key) encryption.
a. Using only asymmetric encryption algorithms, describe a process that would allow Alice to send a message that can only be read by Bob. You should also include any steps taken by Bob that allow him to read the message.
b. Using only asymmetric encryption algorithms, describe a process that would allow Alice to send a message that Bob could be confident was sent by Alice. You should also include any steps taken by Bob to determine whether or not Alice actually sent the message.
c. Using only asymmetric encryption algorithms, describe a process that would allow Alice to send a message that can only be read by Bob, and that Bob could be confident was sent by Alice. You should include any steps taken by Bob to read the message, or to determine whether Alice actually sent the message.
8. Suppose that Eve runs a key server. Alice downloads a key from the key server which Eve claims is Bob's public key. Bob downloads a key from the key server which Eve claims is Alice's public key.
a. Given that Alice and Bob both assume that they have the correct public keys for the other party, and assuming that Eve can intercept any messages passed between Alice and Bob, is there any way that Eve can read the encrypted communications between the two parties? If so, how could she do it, and would Bob or Alice know that Eve was reading their messages?
b. What steps could Alice take to ensure that the public key which Eve claims belongs to Bob is actually correct?