Elgamal Digital Signature

    Solve the following
    
    Exercise 1
    Demonstrate how Elgamal Digital Signature Algorithm can be used for verifying the source and integrity of a message. Consider the following values in your demonstration 
    •	Prime number p=17
    •	Primitive root g=11
    •	Random integer d=4 (private key)
    •	m=H(M)=14 (hash value of the input message is given as m)
    •	random integer k = 7
    
    Exercise 2
    Demonstrate how Elgamal Digital Signature Algorithm can be used for verifying the source and integrity of a message. Consider the following values in your demonstration 
    •	Prime number p=13
    •	Primitive root g=6
    •	Random integer d=6 (private key)
    •	m=H(M)=14 (hash value of the input message is given as m)
    •	random integer k = 5
    
    Exercise 3
    Generate the Digital Signature using Elgamal Digital Signature Algorithm for  the following parameters [10 Marks]
    •	prime number p = 37
    •	generator g = 13
    •	Consider H(M) = 9
    •	Select the value for the private key d as the sum the last two digits of your registration number. If you registration number is 12BCE0021 then the private key d is 2+1 that is 3. If the sum of the last two digits of your registration number is less than 2 then add 5 to the result. For instance if your registration number is 12BCE0001 then the result of the last two digits is 0+1 = 1 then add 5 to the result so that the private key value is 1+5 = 6. 
    •	Random integer K = 19