Type gpg genkey and follow the instructionsof this command

c) whether 561 is prime using Fermat’s theorem (perform modular exponentiation

using the fast modular exponentiation algorithm)

f) the values φ(14) and φ(101) (no need to show your work here; just show your

answers)

b) What is the secret exponent d in the private key {d = ?, n = 35}?

3. [Marks: 10%] In a Diffie-Hellman scheme with a common prime q = 11 and a

4. [Marks: 25%] Submit snapshots of Steps 5, 8, and 9:

Step 1. Prepare the environment and get acquainted. Make sure you have a

Step 3. Prepare for key exchange. Prepare your public key to be exchanged with

Bob. Type “$gpg ‐‐export ‐a > myPublicKey.txt”

Step 5. Import key. Incorporate Bob’s public key into your “key ring” by typing:

“$gpg ‐‐import BobsPublicKey.txt”

dummyFile” This will create an encrypted binary file named dummyFile.gpg.

Step 8. Verify a signature. Get a signed text file from Bob named BobSigned.gpg

5. [Marks: 25%] Write a program in a general purpose programming/scripting language

(e.g., Java, C++, Perl) to compute a table with 100 SHA-1 hash values each using a

b) Estimate how long it would take your program to generate a full table with all

possible 2160 hash values.