Answer:
540, 380,260,440, 0, 40, 500, 380, 20, 440, 60, 460, 20 and 80.
Explanation:
So, we are given the following parameters or data or information which is going to assist us in solving the question above, they are;
(1). "prime p = 29, e1= 3, d = 5 and the random r = 7"
(2). C1C2 reply; "(12, 27), (12, 19), (12, 13), (12, 22), (12, 0), (12, 2), (12, 25), (12, 19), (12, 1), (12, 22), (12, 3), (12, 23), (12, 1), (12, 4)".
So, let us delve into the solution to the question;
Step one: determine the primitive modulo 29.
These are; 2, 3, 8, 10, 11, 14, 15, 18, 19, 21, 26, 27.
Step two: Compute V = k ^c mod p.
Say k = 2.
Then;
V = 2^7 mod 29 = 128 mod 29.
V = 12.
Step three: determine the Public key.
Thus, (p,g,y) = (29,2,12)
Private key = c = 7.
Step four: decipher.
Thus for each code pair we will decided it by using the formula below;
(1). (12,27).
W = j × b^(p - 1 - c) mod p.
W= 27 × 12^(29 -1 -7) mod 29. = 540
(2). (12, 19).
19 × 12^(29 - 1 - 7) mod 29.
( 12^(29 - 1 - 7) mod 29 = 20).
= 19 × 20 = 380.
(3).(12, 13) = 13× 20 = 260.
(4). (12, 22) = 22 × 20 = 440
(5). (12, 0) = 0 × 20 = 0.
(6). (12, 2) = 2× 20= 40.
(7). (12, 25) = 25 × 20 = 500.
(8). (12, 19) = 19 × 20 = 380.
(9).(12, 1) = 1 × 20 = 20.
(10). (12, 22) = 22 × 20 = 440.
(11). (12, 3) = 3× 20 = 60.
(13). (12, 23) = 23 × 20 = 460.
(14). (12, 1) =1 × 20 = 20.
(15). (12, 4) = 4 × 20 = 80.
