CIS 3360 Homework 3
Due Date: September 27
Worth: 4%
1)
A value g is known as a primitive root of a prime p if and only if the smallest positive
integer n for which g
n
≡ 1 (mod p) is n = p1. Write a short C program that prompts the
user for the value of p and prompts the user for the value of g and prints out whether or
not g is a primitive root of p. Simply implement a brute force algorithm that successively
computes g
1
(mod p), g
2
(mod p), etc. You may also write a function that checks to see
whether or not the value entered by the user is prime. Simply turn in a printout of your
source code.
2)
The idea of hierarchical key control was briefly introduced in class.
In this sort of
system, if A wants to communicate with B, it may be the case that a
different
KDC has
access to communication with B than with A. Sketch out the set of steps that would be
necessary for A to obtain a secret key with which to communicate with B through a
system of hierarchical key control. Keep the following sample situation in mind where A,
B, …, J are end users and there are three KDCs arranged in a hierarchical structure as
shown below, while putting together your protocol:
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 Fall '06
 Guha
 Cryptography, Publickey cryptography, Alice Bob Alice, hierarchical key control

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