Assignment 8

Problem 1

Suppose I want to send you a secret message. We agree to convert the message to a sequence of numbers by the correspondence A<->30, B<->29, C<->28, ..., Y<->6, Z<->5 (ignore spaces and punctuation marks). I am then to send you the sequence of coded numbers. You announce the public key (35, 29), but keep the secret private key (35, 5) to yourself. Using the public key, I code my message and send you the coded sequence

29, 31, 17, 05, 13, 31, 16, 11, 17, 16, 05, 27, 06, 23, 25, 16, 18

What is the message?

Problem 2

Gettysburg Gadgets uses e-mail to communicate with its suppliers. Unfortunately, competitors have been reading the e-mail messages in transit and using the information to sell similar products at a lower cost. A computer security expert is hired to work out a secure means of communication.

Gettysburg Gadgets and its suppliers are assigned private and public keys, and the suppliers are also assigned unique identification numbers. The public keys are stored in a public-key repository on the Internet, and Gettysburg Gadgets is given a list of the suppliers' identification numbers and private keys.

Whenever Gettysburg Gadgets and a supplier communicate, they observe the following procedure:

  1. The supplier encrypts its identification number using Gettysburg Gadgets' public key and sends the message to Gettysburg Gadgets.

    2.  
  2. Gettysburg Gadgets decrypts the message using its private key and then uses the supplier's identification number to look up the supplier's private key.

    3.  
  3. Gettysburg Gadgets selects a random number as a secret symmetric session key, encrypts the session key using the supplier's private key, and sends the message to the supplier.

    4.  
  4. The supplier decrypts the message using its public key and extracts the private symmetric session key. Since only the supplier and Gettysburg Gadgets know the supplier's private key, the supplier can verify that Gettysburg Gadgets actually sent the message.

    5.  
  5. Subsequent messages between Gettysburg Gadgets and the supplier are exchanged using the secret symmetric session key.
Despite this elaborate protocol, the messages are still being intercepted successfully.

What's wrong? Be precise!

Groundrules

  • This is an individual assignment. You may not discuss the problems, the solutions, or the answers with anyone else.

    •  
  • Be sure to write and sign the full Honor Pledge.

    • Submission

    Your answers must be submitted on the tan sheet of paper handed out in class.

    Due Date and Time

    This assignment is due at the beginning of class on Friday, April 20. Late work will not be accepted.