GATE | GATE-CS-2017 (Set 1) | Question 44

In a RSA cryptosystem a particular A uses two prime numbers p = 13 and q =17 to generate her public and private keys. If the public key of Ais 35. Then the private key of A is ____________.

Note: This questions appeared as Numerical Answer Type.
(A) 11
(B) 13
(C) 16
(D) 17


Answer: (A)

Explanation: In an RSA cryptosystem, for public key:
GCD( ϕ(n) , e) = 1

And, for private key:

(e * d) mod ϕ(n) = 1

Where,

ϕ(n) = (p -1)*(q – 1) = (13 – 1)(17 – 1) =12*16 = 192
Such that 1 < e, d < ϕ(n)

Therefore, the private key is:
(35 * d) mod ϕ(n) = 1
d = 11

This explanation is contributed by Mithlesh Upadhyay.

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