Let the two primes p = 41 and q = 17 be given as set-up parameters for RSA. 1) Which of the parameters e1 = 32, e2 = 49 is a valid RSA exponent (i. e., is a valid public key, e1 or e2)? Justify your choice. 2) Compute the corresponding private key Kpr = (p, q, d). Use the extended Euclidean algorithm for the inversion and point out every calculation step.

Solution :

It is given in the question that :

Two prime numbers : p = 41

                                    q = 17

Therefore, n = p x q

                     = 41 x 17

                    = 697

Now we know that :

       = 40 x 16

      = 640

a). For the public key

Now the implies

But this is false as the

Therefore the public key will prefer , that is 49.

b). We have to find the private key d. So we know that

Therefore the value of d = 209

c). The encryption of the message M, we will use the relation:

;  here "C" is cipher text

Given M = 26 and we know that and

Therefore,

                     = 468

Thus the cipher text for the plain text 26 is 468.

d). For the decryption of message C,

    (here C = cipher text, M = plain text)

    Given . And the value of d is 209 and n is 697

    Therefore,

Therefore, the plain text for cipher text 513 is 326.

a² + b²= c²

24² + 7² = c²

c= 25

true

step-by-step explanation: