Question

Assume p = 13, q = 7, e = 11 and message m = 46.

1) Can given e be suitable for public key? Give reason why.

2) Find d = e-1 if e is suitable.

3) Perform encryption on the message m using RSA algorithm.

4)Perform decryption on the ciphertext c = 56 using the RSA algorithm.

5) is c = 56, the ciphertext for the message m = 46?

Answer 1

N = p*q = 13*7 = 91

r = (p-1)*(q-1) = 12*6 = 72

find two numbers e and d whose product is a number equal to 1 mod r

Choose an integer e such that 1 < e < r and gcd(e, r) = 1; that is, e and r are coprime

1) Can given e be suitable for public key? Give a reason why.

Yes, As it satisfies above conditions

2) Find d = e-1 if e is suitable.

d=59

& e=11

3) Perform encryption on the message m using RSA algorithm.

2

4)Perform decryption on the ciphertext c = 56 using the RSA algorithm.

49

5) is c = 56, the ciphertext for the message m = 46?

No, c=2 for m=46

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