Question

In a 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

Answer:11

Step-by-step explanation:

Euler Totient function(n)=(p-1)(q-1)

=12×16=192

(35×d) mod 192=1

Try to guess the values for d.

One way to approach is considering the following:

(192x+1)/35=0

This will give us the d as follows.

Take x as 1:

(192×1)+1=193

193/35!=0

Take x as 2:

(192×2)+1=385

385/35=0

Therefore, x=2.

384 mod 192=1

(35×11) mod 192=1

Hence d=11