Entropy

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.