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
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.