CNT4704 (Fall 2010)
Homework 5 Solution
1.
(25 points)
Suppose N people want to communicate with each of N1 other people
using symmetric key encryption. All communication between any two people, i and
j,
is visible to all other people in this group of N, and no other people in this group
should be able to decode their comunication. How many keys are required in this
system as a whole? Now suppose that public key encryption is used. How many keys
are required in this case?
Answer: Any pair of persons needs one symmetric key for encryption. This means the N
nodes form a completely connected graph. Each person (node) has N1 links to others, thus
there are overall N(N1)/2 links in this graph, which means N(N1)/2 keys are needed.
When using public key encryption, each person needs his own public/private key pairs.
Thus overall N pairs of public/private key pairs are needed.
2.
(25 points)
Using the Cesear cipher introduced in lecture, decode the message
"JU'T UJNF OPX.". Also show what is the shifting key used here? Using the same
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 Fall '08
 Guha,R
 Cryptography, Public Key Encryption, public/private key pairs

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