Question

In an RSA cryptosystem, a user Alice 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 Alice is?

Answer 1

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.

may be it helps you