What is the drawback of using Finite Fields of form GF(p) with a prime p in a cryptographic algorithm?

Question

What is the drawback of using Finite Fields of form GF(p) with a prime  p  in a cryptographic algorithm?

Accepted Answer

We will waste space on a computer that operates on multiples of 2 (e.g., 2 16  or 2 32 ).

Answer

The algorithm cannot be made secure enough, even for large values of  p .

Answer

Not all elements have a multiplicative inverse, hence we cannot do decryption.

Answer

It is not easy to generate a relatively secure prime number.

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