Homework 6

1. Suppose a top-secret organization has 5,000 employees, all of whom need to communicate with every other employee in the organization.

(a) How many keys are needed if the organization used a symmetric key cryptosystem where two users use a single shared secret key to communicate with each other?

(b) How many keys are needed if the organization used an asymmetric, or public, key cryptosystem where each user has a public key and a private key?

2. Calculate the timing of password-guessing attacks:

(a) If passwords are three uppercase alphabetic characters long, how much time would it take to determine a particular password, assuming that testing an individual password requires 5 seconds? How much time if testing requires 0.001 seconds?

(b) Argue for a particular amount of time as the starting point for secure. That is, suppose an attacker plans to use a brute-force attack to determine a password. For what value of x(the total amount of time to try as many passwords as necessary) would the attacker find this attack prohibitively long?

(c) If the cutoff between insecure and secure were xamount of time, how long would a secure password have to be? State and justify your assumptions regarding the character set from which the password is selected and the amount of time required to test a single password.

What are the risks of having the US government select a cryptosystem for widespread commercial use (both inside and outside the United States)? How could users from outside the United States overcome some or all of these risks?

An affine cipher is a generalization of the Caesar cipher and has the following form: , where xis the plaintext letter and is the ciphertext letter. Now, assume that a ciphertext has been generated using an affine cipher where the first and second most frequent letter in the ciphertext are B and U, respectively. Use the given information and what weve covered in class to break this code! Hint: You are being asked to solve for a and b using a system of linear equations.

5. In DES, find the output (in hex) of the initial permutation box when the input is given in hexadecimal as: 0xFF00 0000 0000 0000

Decipher SFCXZY NSJFUW SMKEYYthat was enciphered using the Vigenre method with the keyword SURE.

Decrypt the following message that was encrypted using a rail-fence cipher:

TDRLTILTIEAEIYHVSIPWOAMWEIROTOILAIIDENORSSRTNULSTLMPIHDAAHHD

Note that you are not given the number of columns, so you will have to use some trial-and-error to decrypt this message.