The Diffie$-$Hellman example above is easy to attack since the prime number $19$ is ridiculously small, and we can easily calculate discrete logarithms, i$.$e$.,$ given p$,$ g$,$ and y it is easy to find x that solves g$^$x $=$ y mod p$.$ Alice and Bob are aware of this fact and choose a very large prime $-$ one with $3072$ binary digits $($over $900$ decimal digits!$).$ With such a large modulus, discrete logarithms become a very hard problem.

Alice and Bob agree to share a common secret using $3072-$bit Diffie$-$Hellman, and derive a secret key from this information. They will use this shared secret key for a symmetric cipher.

Bob knows that there is never zero risk, but he thinks that it is almost impossible that anyone can compromise Diffie$-$Hellman key exchange as long as they

choose a large prime number $-3072$ bit or higher and

implement all algorithms in a secure way.

Is Bob's claim justified? $($True means Bob is correct in his claim, False means he is wrong