Paper No: 1
Q1(2.5 point). Marie Curie encoded the PIN number to open the door at her
house using public-key cryptography. She use (5,221) as her Public Key
(E=5,n=221). She recorded the value of the ciphertext as 76 (76 = X^5 mod
221). Unfortunately, she forgot the private key to decrypt 76 (the cipher text) to
get the PIN code. She only remembers when generating the key, she chose p =
17. Please help her to find the PIN code.
Q2(1 point). You agreed to use a Caesar cipher with a key of k-5 with a friend.
While sitting in a group, you want to hand over a message that says
"GOHOMENOW". Let's encrypt your message?
Q3(1 point). Suppose you actually forgot the key. How many decryption
computations of the cipher text "MRNMSKTUC" do you need to perform to
reach to the plaintext?
Q4(1.5 point). Decrypt this message "12 34 18 48 16 10 18 2" using the
following paragraph as reference code book: "Once upon a time there was a
piece of yellow wood. It was not an expensive piece of wood. Far from it. Just a
common block of firewood, one of those thick, solid logs that are put on the fire
in winter to make cold rooms cozy, vivid and warm"?
Q5(0.5 point). Euler totient function of n (we use the Greek symbol phi to
denote Euler totient function) is the number of positive integers that are between
1 and n-1, inclusive, and are relatively prime to n. What is the Euler totient
function of 605?
