Homework 2 - What is entropy, Calculate the entropy of a fair die toss

 

Homework-2

Question 1 [12 pts]

What is entropy?

Calculate the entropy of a fair die toss.

Calculate the entropy of a biased die, where the probability of landing “6” is 1/2, the probabilities of the others are equal.

Compare the entropies of the fair die and the biased die? What does higher entropy mean?

You can use the Log Base 2 Calculator hosted here:

https://miniwebtool.com/log-base-2-calculator/

 

Use the exponents calculator in this address to verify the number of possible landings of a fair dice, which should be 6.

https://www.rapidtables.com/calc/math/Exponent_Calculator.html

Question 2 [5 pts]

What is the difference between a RNGS and PRNGS?

Question 3 [10 pts]

Which one is used for assessing the security of a cryptographic algorithm: Informational security or computational security? Why?

Which is of the following statements are correct? Choose more than one.

a. One-time pad is informationally secure.

b. AES algorithm is computationally secure.

c. Organizations should prefer using informationally secure algorithms over computationally secure algorithms as much as they can.

d. A new cipher that is using 5096-bit key and takes 10^10000 years to break in even by the help of parallel computing infrastructure composed of all microprocesses in the world is informationally secure.

Question 4 [8 pts]

Think about two encryption keys with lengths 80-bit and 128-bit, respectively. Assume that the ciphers using these keys are NIST-approved ciphers. What can be said about these keys?

Do both keys provide similar level of security in practical real-world applications? Please justify your answer.