Part II (6 points each, Total 30)
Q1a Complete the following Truth Table: F denotes false and T denotes true
A B C=A or B D= A xor B E= A and B
F F
F T
T T
T F

Q1b In the following Θ denotes one of the following operators: ’or’, ‘xor’ or ‘and’.
Input1 Θ input2 = Result
where, input1 and, Input2 are ‘A’ and ‘B’ and Results are C, D, or E from the above table.
Which operation will yield? (what is Θ?)
input1 Θ result = input 2
input2 Θ result = input 1
Please show proof for one, or disprove other two
Hint:
Check
Input1 OR result = Input2?
Input2 OR result = Input1? For results C, D and E, and inputs A and B
Repeat replacing OR with AND, and XOR
As soon as the given operator is not valid for an operation go to the next operator.
Please show proof. Without proof you will get partial credit only

Q2 Using the English alphabet (i.e., mod 26 arithmetic) let plaintext = {p1, p2, pn,} and corresponding cipher text = {c1, c2, cn}.
{start A as 1, B as 2 and so on}
Suppose the encryption function is ci = pi + 8 (mod 26).
You receive the cipher text message CUCKQAVWECUOK
What type of cipher is this?
What is the decryption function, and the decrypted/recovered plaintext, (insert spaces to make readable)?
Show all your steps.

Q3 You are Alice. You have agreed with your friend Bob that you will use the Diffie-Hellman public-key algorithm to exchange secret keys. You and Bob have agreed to use the public base g = 7 and public modulus p = 941.
You have secretly picked the value SA = 17 You begin the session by sending Bob your calculated value of TA. Bob responds by sending you the value TB = 268.

What is the value of TA
What is the value of your shared secret key?
Can you guess Bob’s secret value SB and what it would be?
Show each and every step of your calculations, if you use Excel for mod calculation include the spreadsheet, for any other method include the screenshot of that method
[without the spreadsheet or screenshot, you will not get the full credit]
for mod calculation, the following identity may be useful
mod(XY,p) = mod[mod(X,p)mod(Y,p),p]
mod ( X^n, p) = mod [mod(X^k, p)*mod(X^m, p), p]; where k+m=n
e.g. mod (X^17, 941) = mod [mod (X^8, 941) *mod (X^9, 941), 941]; where 8+9=17

Q4 Bob believes that he has come up with a nifty hash function. He assigns a numeric value VChar to each letter in the alphabet equal to the letter’s position in the alphabet, i.e., VA = 1, VB = 2, …, VZ = 26. For a message, he calculates the hash value H = (VChar 1 x VChar 2 x VChar 3 …x VChar N) mod (26).
Bob uses this function to send a one-word message, “FATHER” to his supervisor Bill, along with his calculated hash value for the message. Alice is able to intercept the message and generates an alternative message that has a hash value that collides with Bob’s original hash value.

Give definition and properties of the hash function.

Show a message that Alice may have used to spoof Bob’s message and demonstrate that its hash value collides with Bob’s original hash.

Q5 Consider the following plaintext message: IT IS EXCITING TO KNOW THAT WE MAY HAVE FOUND A PLANET SIMILAR TO EARTH MATTER IN THE UNIVERSE.
a. (3 pts) If this message is sent unencrypted and successfully received, what is its entropy? And why?
b. (3 pts) If this message is encrypted with DES using a random 56-bit key, what is the encrypted message’s entropy? And why

Sample Solution

Share on Facebook

Tweet

Follow us