Computer Science CS 4/57221 Introduction to Cryptology
				  Fall 2009
				First Midterm
		      Due by email October 28 at 11:00 PM

Please be brief: Irrelevant or incorrect material will cost you points.

1) What techniques have been covered for finding multiplicative inverses
mod m? Describe them.

2) Given a space X where a multiplication and addition has been defined,
we can define an affine cipher on this space X; the set of ciphertexts will
also be X. Define this affine cipher and give conditions for the cipher to
work.

3) Single DES has been cracked. Why isn't double DES a solution?

                                                           3
4) Compute A(x) . B(x) mod P(x) in the extension field GF(2  ) 
              3    2
where P(x) = x  + x  + 1
      A(x) = x + 1
              2
      B(x) = x  + 1

5) What is a cryptographic random number? How would you generate one?

6) What is the reason for the peculiar distribution of the input bytes into
the input work array in Rijndael?

7) From the list of primes in
http://primes.utm.edu/lists/small/1000.txt
choose 2 distinct four-digit primes from somewhere down the middle of the list.
Use these primes to set up an RSA cryptosystem.