Read Singh, pp. 250-267 before class on Thursday (11/01).
The problems below are due Thursday, November 1.

Privacy

Consider the difference between some traditional (pre-Internet) uses of cryptography and some modern-day uses. For example, perhaps if you were living almost a century ago, you might not concern yourself about the privacy of everyday messages (e.g., US Mail, telegraph, telephone, and radio). Every so often, you would have important news to send to someone that might warrant the use of a cipher. Contrast that with carrying on a daily e-mail dialogue with a close friend. You realize that everyone can eavesdrop on your dialogue so you opt to use a cryptosystem.

1. It certainly seems to be the case that more people are using or relying on cryptography on a daily basis than previously in history. Perhaps people have more important things to say or have a stronger need for privacy. Or, perhaps there are other reasons. In a clear and concise paragraph, comment on these issues.

2. How does this increased frequency of the "need" for private communication effect the choice of a cryptosystem?

   Feistel Ciphers

   For the following problems think of the Feistel cryptosystem in which the "mangler" function is just the the exclusive-or of the bits in the right half of the input (R) with the key that corresponds to that round (as on the previous homework and as we have done in class). It will also be useful to consult this ASCII table for conversion between characters, binary numbers, and decimal numbers. For example, the table indicates that ASCII character 70 is F and that the number 70 is written as 01000110 using 8-bit binary notation. The table allows us to convert easily between all three representations. For example we might write:

   
     Hello
   
   

   or

   
     72  101  108  108  111
   
   

   or

   
      01001000
      01100101
      01101100
      01101100
      01101111
   
   

3. Using a Feistel cipher consisting of 4 rounds, a block size of 8 bits, and the key

     0001001111101011
   

   encrypt the plaintext

     Obvious
   

   using the decimal notation. That is, first translate the plaintext to a sequence of binary numbers (using the ASCII codes corresponding to each symbol), then use the Feistel cipher to generate a new sequence of binary numbers, and then translate that sequence into a list of decimal numbers.

4. Using a Feistel cipher consisting of 4 rounds, a block size of 8 bits, and the key

     1101101110010110
   

   decrypt the ciphertext

      3   185   3   207   48
   

   That is, first translate the decimal numbers into a sequence of binary numbers, then use the Feistel cipher (with the keys in reverse!) to generate another sequence of binary numbers, and then translate that sequence into a list of symbols to form an English phrase.

5. This problem concerns the cryptanalysis of a Feistel cipher when part of the key is already known. Suppose you know that the plaintext symbol "e" is encrypted as the ciphertext symbol "L" (i.e., as the ASCII code for "L") using a Feistel cipher consisting of 4 rounds, a block size of 8 bits, and that the first four bits of the key are 0101 and the last four bits of the key are 0110. Find the missing bits of the key. (Hint: if a, b, and c are all binary numbers then the a XOR b XOR c XOR a = b XOR c. In other words, using the same number twice in a sequence of exclusive-or operations cancels out.)

6. Comment on the effectiveness of using exclusive-or as the mangler function in DES and other Feistel ciphers.