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Mohamed G. Gouda						Homework 1
CS 395T: Network Protocol Security				Fall 2006
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1. (4 Points):

The one-grid protocol for assigning symmetric keys to processes in a (fully-
connected) network can be modified such that its two-dimensional grid is 
replaced by a three-dimensional grid. Describe the modified protocol, and show
that the number of keys assigned to each process by the modified protocol is 
in fact larger than the number of keys assigned to each process by the 
original protocol.

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2. (3 Points):

The three-grid protocol for assigning symmetric keys to processes in a network
has three two-dimensional grids: AB-grid, BC-grid, and AC-grid. Show that if 
the protocol is modified to use only two two-dimensional grids, for instance 
AB-grid and BC-grid, then the modified protocol is incorrect. (Hint: show that
the modified protocol allows three or more processes to share the same set of
symmetric keys.) 

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3. (3 Points):

Consider a communication network that consists of five processes p[0..4]. This
network has the following seven undirected edges: 
	{p[0], p[1]}, 
	{p[0], p[2]},
	{p[0], p[3]}, 
	{p[1], p[3]}, 
	{p[1], p[4]},
	{p[2], p[3]}, 
	{p[2], p[4]}.
Use a "logarithmic keying scheme" to assign symmetric keys to the processes in
this network. Based on this scheme, describe the keys assigned to each process
in the network and define the (equality) relationships beteen the assigned 
keys.

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