1. Alice is sending a signed message to Bob using El-Gamal signature scheme. The message, M = "I have sent you $1000 yesterday" and the corresponding hash value of the message is given in the table below based on the algorithm. The hash algorithm is determined based on your ID and selected as, Algorithm No. = Your IDmod 10.

Hash Algorithm, H ()	H (I have sent you $1000 yesterday)
Algorithm -0	13
Algorithm -1	15
Algorithm -2	17
Algorithm -3	16
Algorithm -4	20
Algorithm -5	12
Algorithm -6	19
Algorithm -7	22
Algorithm -8	18
Algorithm -9	25

Bob is verifying the signature using the same signature scheme with the following parameters and available cryptographic hash table: (6 Marks)

Alice picked up a prime number P= 251 and a generator for this prime number g = 11is chosen.

Alice chooses his/her secret key x =[(2022 + 12 + 18+ 30128555) * 2] mod 249

If x = 0/1, then update x = 81

Alice is signing the above message using the followingrandom k parameter and calculated as:

k =[int ((2022 + 12 + 18+ 30128555) / 3] mod 249

If k = 0/1, then update k = 93

If GCD (k, P-1) 1, then chose a nearest prime from the following table for k and check GCD (k, P-1) == 1,

The list of Prime Numbers from 1 to 251:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251

1. Calculate the public key of Alice
2. Calculate the signature generated by Alice
3. Show the verification of the signature (by Bob)