Question

In an RSA cryptosystem, a participant A uses two prime numbers p = 13 and q = 17 to generate her public and private keys. If the public key of A is 35, then the private key of A is ______.

Answer 1

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

Given p =13, q= 17, d = 35

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

Ø(n) = (13 – 1) × (17 – 1) = 12 × 16 = 192

Now,

(e × d) mod Ø(n) = 1

(e × 35) mod 192 = 1

e = 11

So, private key of A = 11