is2150_hw5_stm57 - StevenMadara IS2150Fall09 Due Prof.Joshi...

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Steven Madara IS2150 – Fall 09 Due: 10/30/09 Prof. Joshi HW5 – Section 8.7 #3, 10, 11, 12, 17 3. If one‐time pads are provably secure, why are they so rarely used in practice? The key string is chosen at random, and is at least as long as the message. The implementation issues surrounding random key generation and distribution/storage of that key create problems that prevent one‐time pads from being practiced. Since the key needs to be at least as long as the message – issues arise when long messages need to be sent. Also, since the key needs to be securely sent (needs protected just like the message), the message could simply be sent via a secure channel – removing the need to perform a one‐time pad that creates a key. 10. Prove the following: (a) If p is a prime, φ(p) = p – 1. The totient of p is the number of numbers (less than p) that don’t have any factors in common with p. P is a prime number (as stated above), which means its positive divisors are 1 and p. Therefore, the set of possible numbers is {1, 2, 3, … , p – 1}. This shows that φ(p) is equal to (p – 1).
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