In RSA algorithm if p = 7, q = 11 and e = 13 then what will be the value of d?

In RSA algorithm if p = 7, q = 11 and e = 13 then what will be the value of d? Correct Answer 37

Step:

RSA Algorithm:

1) Calculate value of n = p × q, where p and q are prime no.’s

2) calculate Ø(n) = (p-1) × (q-1)

3) consider d as public key such that Ø(n) and d has no common factors.

4) consider e as private key such that (e × d) mod Ø(n) = 1

5) Cipher text c = message i.e. m^d mod n

6) message = cipher text i.e. c^e mod n

Calculation

p =7, q= 11, e = 13

Use step 2 and 4 of RSA algorithm to calculate private key.

Ø(n) = (7– 1) × (11 – 1) = 6 × 10 = 60

Now,

(e × d) mod Ø(n) = 1

(13 × d) mod 60 = 1

d = 37

So, key of A = 37