Question

Let P = 17 and Q = 11 is taken in RSA algorithm, what are possible values of E( (public key), N and D (Private key) respectively?
1. 5, 187, 37
2. 7, 160, 23
3. 7, 187, 23
4. 9, 160, 37

Answer 1

Correct Answer - Option 3 : 7, 187, 23

Compute the value of N and Φ

It is given as,

N = P × Q and  Φ = (P-1) × (Q-1)

Here in the example,

N = 17 × 11 = 187

Φ = (17-1) × (11-1) = 16 × 10 = 160

Find the value of E (public key)

Choose E, such that e should be co-prime. Co-prime means it should not multiply by factors of Φ and also not divide by Φ

Gcd(E, Φ (N) ) =1

Gcd(E, 160 ) =1

Gcd(7,160) =1 // taken from option

Compute the value of D (private key)

The condition is given as,

E × D ≡ 1 mod Φ 

(7 × 23) ≡ 1 mod 160  //taking from Options

Because 161mod160 ≡ 1