Name____________________________________

 

ICOM 5018 EXAM I - Spring 2006

February 16, 2006

 

Open books and notes. Only the text, slide printouts and your own notes may be used.

In the interests of originality and creativity please turn off all electronic communication devices including celulares, laptops, pocket computing devices and telepathic capability if you have it.

1.       The following relate to symmetric (private-key) cryptography.

a.       Is differential cryptanalysis specialized to Feistel block ciphers?  Explain.

Yes and no.  The second-order difference equation is derived using the Feistel block equations.  However, a first-order difference equation can be derived and probed for simple bit propagation patterns.

b.       When trying to find the decryption key in the RSA algorithm (given that you have chosen the encrypting key) you find the generalized Euclidean algorithm fails when calculating the inverse (you don’t arrive at a one in the last line).  What does this mean and how do you resolve the problem?

It means that e is not relatively prime to φ(n), which you have just discovered with Euclid’s algorithm.  You can only try a different e, which in all probability will not be relatively prime.

2.       The following apply to public-key cryptography.  Please answer the following, briefly, but avoiding the dreaded RADQ.

a.       Text problem 9.14 a,b,c (do not work part d)

Just you wait – I gave away all my program copies and will have to provide this later.

b.       What is the purpose of using the relatively small S-boxes in DES, and what other feature of the cipher mitigates the effect of the small scope (6 bits input) of the small S-boxes?

Reduced storage requirements.  In 1976 this was very important, the implementation then was hardware at less than 40K devices per chip.  The permutation that follows the S-boxes provides the additional mixing between various parts of the 32-bit S-box aggregate output.

c.       The statement is often made (p. 191, 4th edition) that with a block cipher you can reuse keys, but with a stream cipher, cryptanalysis is often successful.  Explain how you would perform such a cryptanalysis, given that you have two encrypted streams that you know were encrypted with the same key.

You XOR the two streams; this gives the XOR of the two original plaintexts.  Any monotonous or suspected data in either stream can be XOR’ed to reveal the other.


3.     

a.       Text problem 7.12

George XOR’s the string sent with the one returned.  The result is Bob’s version of the key, making George  (who was never good at math) quite happy.

b.      What are the advantages of OFB over counter mode?

OFB uses an IV (initial vector) – which reduces predictability a bit.