GATE CS 2017 Set 1 Q44 — Concept of Layering: OSI and TCP/IP Protocol Stacks

In the RSA cryptosystem, the public key $e$ and private key $d$ are related by the congruence relation:

Given the prime numbers:

• $p = 13$
• $q = 17$

We calculate Euler's totient function $\phi(n)$ as:

Given the public key $e = 35$, we need to find the private key $d$ such that:

Using the Extended Euclidean Algorithm or testing small multiples of $192$:

For $k = 2$:

Thus, the private key of $A$ is 11.