Question

5. Now suppose you receive an encrypted message, C = 287. Given that p = 13 and q = 29 and that e = 5, show all necessary steps to decrypt the message, and then give the final plaintext decryption of the message. (15 points)

Answer 1

Given Data:

C= 287

p=13

q=29

e=5

Final plaintext decryption of the Massage

M= C^{​​​​​​d} mod n Equation (1)

so find ''d"

Now apply formula

(e×d) mod (n)=1 Equation (2)

(n) = (p-1) ×(q-1)

= (13-1)×(29-1)

(n) =336

From equation (2)

(5×d) mod 336 = 1

d = 269

From equation (1)

M= (287)²⁶⁹ mod 377

(287)²⁶⁹ =((287)¹⁰ )²⁶ × (287)⁹

(287)¹⁰ mod 377 = 92

(287)⁹ mod 377 = 66

M= (92)²⁶ ×66 mod 377

(92)²⁶ =((92)¹⁰)² × (92)⁶mod 377

(92)⁶ mod 377= 313

(92)¹⁰ ​​​​​​mod 377 = 339

M= (339)²×313 ×66 mod 377

= 2374038018 mod 377

M=27

Massage (M) = 27

Please give up vote

Thanks for given this opportunity

Have a nice day