Cryptography and Data Protection
Part I
Q1 a Complete the following Truth Table: F denotes false and T denotes true
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A
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B
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C=A or B
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D= A xor B
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E= A and B
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F
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F
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F
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T
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T
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T
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T
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F
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Q1 b In the following Θ denotes one of the following operators: 'or', ‘xor' or ‘and'.
Input1 Θ input2 = Result where, input1 and,Inpuut2 are ‘A' and ‘B' and Result is one of C, D, or E.
Which operation will yield? (what is Θ?)
input1 (2) Θ result = input 2(1)
Q2 Using the English alphabet (i.e., mod 26 arithmetic) let plaintext = {p1, p2, pn} and corresponding cipher text = {c1, c2, cn}.
Suppose the encryption function is ci = pi + 10 (mod 26). You receive the cipher text message EWEM SC K QBOKD CMRYYV
What are the decryption function, and the decrypted/recovered plaintext? What type of cipher is this? Show 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 = 1013.
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 = 839.
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
(for mod calculation, the following identity may be useful
mod( X^n, p) = mod (mod(X,p)*mod(X^n-1, p), p)
mod(X*Y,p) = mod(mod(X,p)*mod(Y,p),p)
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, GLARE, to his banker 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: THE SIXTEENTH PRESIDENT WAS ABRAHAM LINCOLN.
a. If this message is sent unencrypted and successfully received, what is its entropy? And why?
b. If this message is encrypted with DES using a random 56-bit key, what is the encrypted message's entropy? And why
Part II
Essay Question: Length: 800- 900 words. Use APA format for in-line citations and references.
Compare and contrast symmetric and asymmetric encryption algorithms.
- Your response should include a brief overview of the cryptographic basis for each type of algorithm, and a comparison of their relative strengths and vulnerabilities.
- Describe how a hacker might go about cracking a message encrypted with each type of algorithm.
- Suggest a specific application for each type of algorithm (symmetric and asymmetric)where the advantages clearly outweigh the disadvantages.
- Remember to address all points