------------------------------------------------------------------------------
Mohamed G. Gouda						CS 386S
Spring 2008							Midterm 2
------------------------------------------------------------------------------
Open Book and Notes						75 Minutes
------------------------------------------------------------------------------

1. (6 points): 
The Single Password Protocol is designed to defend against several types of
attacks, such as the malicious server attack, the password file compromise,
and the message log compromise. Simplify this protocol in the case where there
is no need to defend against the message log compromise.

-----------------------------------------------------------------------------

2. (7 points):
The antireplay window protocol in IPsec performs its function, of determining
whether each packet that is received along a given security association is 
fresh or not, even when sent packets along the association may be reordered
(subject to the w-reordered condition) or corrupted or lost before they are 
received.

a. Describe in English how can this protocol be simplified if the sent packets 
are somehow guaranteed not to be reordered, but they may be corrupted or lost,
before they are received.

b. Describe in English how can this protocol be simplified if the sent packets
are somehow guaranteed not to be corrupted, but they may be reordered (subject
to the w-reorder condition) or lost, before they are received.

c. Describe in English how can this protocol be simplified if the sent packets
are somehow guaranteed not to be lost, but they may be reordered (subject to
the w-reorder condition) or corrupted, before they are received.

-----------------------------------------------------------------------------

3. (7 points):
Consider a firewall (r.1, .. , r.m) that consists of m rules where each rule
r.i is of the form:
 
	x in R.i --> d.i    

and R.i is an interval of integers. Assume that this firewall is transformed
to an equivalent firewall (s.1, .. , s.n) with the smallest number n of rules
where each rule s.j is of the form:

	x in S.j --> e.j  

and S.j is an interval of integers and for any other interval S.k, in the 
transformed firewall, S.j and S.k are disjoint. What is the largest possible 
value of n (as a function of m)?

------------------------------------------------------------------------------ 


(Solution)

1. 
   C knows P
   S knows (C,H^2(P,S))

   C --> S : H(P,S)

2. 

   a. Keep SK and r no need for array wdw, and each msg is of the form msg(s,t,h)
      where h = H(SK,s,t).
   b. Keep r and wdw, no need for SK, and each msg is of the form msg(s,t).
   c. Keep the protocol unchanged.

3.
   Rule s.1 is the same as rule r.1.
   Rules s.2 and s.3 are of the form
   	 x in S2 --> d.2
	 x in S3 --> d.2

   where 
		R1
   	  S1 |-------|S2
   	 |---------------|
		R2
 

   Rules S.4, S.5 are of the form
   	 x in S4 --> d.3
	 x in S5 --> d.3

   where 
		R2
   	  S4 |-------|S5
   	 |---------------|
		R3

   and so on
       .
       .
       .

   Thus, the largest possible value for n is 1 + 2 (m-1) = 2m -1