If an RSA public key encryption system were based on the primes p = 3 and q = 7,which of the following pairs of values would be suitable for the encryption and decryption keys e and d?
A) 2 and 6
B) 5 and 29
C) 4 and 9
D) 7 and 23

Question

Quizplus · Accepted Answer

To find suitable values for e and d, we need to follow the RSA process. 
First, we need to calculate n = p*q , so in this case 
n = 3*7 = 21 
Then, we need to calculate the totient of n, which is 
phi(n) = (p-1)*(q-1) = 2*6 = 12

Next, we need to choose a value for e that is relatively prime to phi(n) (i.e., they share no common factors other than 1). 
The only suitable value in the given choices is e = 5, since gcd(5, 12) = 1.

Then, we need to find a value for d such that (d*e) mod phi(n) = 1. 
We can use the Extended Euclidean Algorithm to find d: 
12 = 2*5 + 2 
5 = 2*2 + 1 
1 = 5 - 2*2

So, we get d = 2.

Therefore, the suitable values for e and d are 5 and 2, respectively.

If an RSA Public Key Encryption System Were Based on the Primes